Chapter 11 Refraction

What You Will Learn

In this chapter, you will learn how to…
• explain refraction and the
conditions that are required for
partial reflection, partial refraction,
and total internal reflection
• identify factors that affect the
refraction of light as it passes
from one medium to another
• explain natural effects of refraction,
such as apparent depth, mirages,
and rainbows, using the ray model
of light

Why It Matters
Many modern technologies used in
communications and medicine depend
on how light behaves when travelling
from one substance to another. Also,
many of the mysteries of atmospheric
phenomena, such as sundogs and
rainbows, have been solved by applying
our knowledge of how light behaves.

Skills You Will Use

In this chapter, you will learn how to…
• investigate the refraction of light
and total internal reflection
• calculate the velocity of light in a
variety of media
• analyze how the angles of refraction
and incidence change in materials
with different indices of refraction

On a cold, crisp day, when the Sun is shining brightly, you might
see a halo around the Sun similar to the one shown here. The
bright spots beside the Sun are called sundogs. They are created
when ice crystals in the air refract the sunlight. Sundogs are just
one of the many natural effects of refraction that you will learn
about in this chapter.

446 MHR • Unit 4 Light and Geometric Optics

Activity 11–1
The Re-appearing Coin
For you to see an object, light must reflect from the object and reach your
eyes. Sometimes, after reflecting off the object, light will change direction
before it reaches your eye, and this will trick your brain. In this activity, you
will demonstrate and try to explain this phenomenon.

Safety Precaution
• Be careful not to splash the
water on the floor. Wet floors
are slippery and dangerous.

Materials
• cup or another container with
opaque sides
• coin
• water

Use this diagram for question 1.

Procedure
1. Work with a partner. Place the coin at the bottom of the empty cup,
in the middle. Cover one eye with your hand, and look down at the
coin with the other eye. Lower your head until the edge of the cup
just blocks your view of the coin. Keep your head in this position.

2. Your partner will slowly pour water into the cup. If the coin starts
to move, your partner should hold it in place with the end of a pencil.
Your partner will continue to pour water into the cup until you can
see the coin again.

3. Empty the water in a sink. Be careful not to lose the coin.

4. Change places so that your partner can watch the coin while you
pour water into the cup.

Questions
1. Copy the diagram above. Note that the ray in the diagram shows
that light from the coin cannot reach your eye if the cup is empty.

2. Sketch a ray diagram to illustrate how light reflects off the coin,
travels through the water, and then reaches your eye.

3. How has your brain been tricked by the water?

Chapter 11 Refraction • MHR 447

Study Toolkit
These strategies will help you use this textbook to develop your understanding of science concepts and skills.
To find out more about these and other strategies, refer to the Study Toolkit Overview, which begins on page 560.

Organizing Your Learning Reading Effectively

Summarizing Making Inferences

A summary restates the main ideas of a text concisely, Making inferences means figuring out the implied
using your own words. It can be in sentence form, meaning of a text. It involves connecting your prior
paragraph form, point form, or graphic form. The table knowledge with information from the text and, often,
below shows one way to summarize the “Describing from visuals. The second paragraph on page 457
Refraction Using Rays” section on page 451. says, “The objects outside the area directly above you
are not visible because no light from these objects
Summarizing Text
is penetrating the surface of the water.” Here is an
Main Ideas example of an inference you might make about
Section Main About the Supporting
of Text Topic Topic Details this information:

page 451, how to 1. Use the 1. Incident • prior knowledge: To see an object, light must
third describe same terms ray, normal, reflect from the object and go to my eyes.
paragraph refraction to describe and angle
using rays refraction of incidence • inference: Light is not reflecting from objects
as you use are all used to the side and above the water, so I cannot
to describe to describe see the objects.
reflection. refraction.
2. Use two new 2. Capital R
terms: the is used for Use the Strategy
refracted ray refraction, Read the first paragraph of Section 11.2 on page 457.
and angle of and lower-
refraction. case r is used Think about your prior knowledge, combine it with
for reflection. the text and the visual on the page, and then make
Summary sentence: The terms used to describe refraction
an inference.
include incident ray, normal, angle of incidence, refracted
ray, and angle of refraction (labelled R).

Use the Strategy

Read the first paragraph under “Partial Reflection and
Refraction” on page 458. Summarize the paragraph
using a table like the one above. Compare your work
with that of a partner and revise as necessary.

Word Study

Multiple Meanings
To reinforce your understanding of a word’s multiple a size between
clothing
meanings, draw a word map like the one on the right. It small and large

shows the meaning of medium in two different contexts.

Use the Strategy medium

What does incident mean in the context of a police

report? in the context of a science chapter about light
a substance through
rays? Draw a word map to show the word’s multiple optics
which light can travel
meanings. Use a dictionary if you wish.

448 MHR • Unit 4 Light and Geometric Optics

 Key Terms
refraction
refracted ray
11.1 Refraction of Light angle of refraction
index of refraction
Some aeronautic engineers need to study patterns of moving air so that dispersion
they can design shapes to reduce air friction. How can they see something
that is transparent? The colours in Figure 11.1 show moving air. As air
hits the cone, it gets compressed in different ways. Compressed air has a
higher density than uncompressed air. Even though air is transparent, a refraction the bending
technique called Schlieren photography uses certain properties of light to of light as it travels, at an
create the light and dark regions where changes in density occur. Then, angle, from a material with
a computer converts the light and dark regions into different colours. one refractive index to a
material with a different
All of this is possible because of a property called refraction. Refraction
refractive index
is a property of light in which the speed of light and its direction of
travel change.

Understanding Refraction
To understand refraction, consider a familiar analogy. What happens if
you are riding in a golf cart and you hit some mud or gravel? The front
wheels suddenly slow down, but the back wheels keep going and the golf
cart twists around. Similarly, when light travels from one medium into a
different medium, both its speed and direction may change.

Figure 11.1 Aeronautic engineers

use photographs like this one to study
the flow of air around a cone-shaped
cylinder in a wind tunnel. When they
can visualize the flow of air, they can
design aircraft to reduce air friction as
much as possible.

Chapter 11 Refraction • MHR 449

 Describing Refraction
As mentioned in Chapter 10, light has many properties. For example,
light reflects from smooth surfaces according to the two laws of reflection.
There are additional properties of light that are important in describing
refraction. Light travels in a straight line and at a constant speed as long
as the medium it is travelling in is the same. However, when light travels
from one medium to another, for example, from air to water, the light
rays refract (bend). Recall that this means that both its direction and
speed change. Figure 11.2 shows how a beam of light refracts as it enters a
container of water.
Figure 11.2 Dust particles in the
Since light travels as a wave, it is helpful to use the wave model of light
air scatter the light and allow you
to see the beam. A fluorescent
along with the concept of a ray to visualize the mechanism that causes
substance in the water emits a light to change direction. To see how the wave model of light and the
green light, which allows you to concept of a ray fit together, look at Figure 11.3. Scientists often choose a
see the path of the light beam in specific part of a wave to follow and call it a wave front. As you can see in
the water.
Figure 11.3, the crests, or high points, of the waves are wave fronts. The ray
(red arrow), which shows the direction in which the waves are travelling,
is perpendicular to the wave fronts.
ray To visualize what happens when a wave front reaches the surface
between two media—called the boundary—imagine each wave front as a
row of students in a marching band. Figure 11.4 shows the movement of
the band as it marches from an area of firm ground to an area of mud. The
mud is so sticky that the students cannot march as fast. As each student
reaches the mud, he or she slows down. The slower students “pull” the line
back and cause a bend in the line, representing the wave front. As a result,
wave fronts the direction in which the entire row is marching changes. The larger red
arrow in the diagram shows the direction in which the band, as a whole,
Figure 11.3 All the points on a is moving. This is what happens when a light wave crosses the boundary
wave front move together in the between two media: its speed changes.
direction in which the wave itself
is moving.

firm ground

Suggested Investigation
Inquiry Investigation 11-A,
Investigating Refraction, from mud
Air to Water, on page 476

Figure 11.4 Each row of students represents the crest of a wave. When one end of
the wave front slows down, the direction of the wave changes. This analogy, like all
analogies, has limitations. However, it can help you visualize refraction.

450 MHR • Unit 4 Light and Geometric Optics

 Learning Check
1. What property of light changes from one medium to another?

2. Define the term refraction.

3. Examine Figure 11.2. Explain why light bends when it enters the
water. Include a ray diagram with your explanation.
4. Think of an analogy, other than a marching band, that helps you
understand why light refracts when it goes from one medium to
another. Include a sketch to illustrate your analogy.

Fermat’s Principle
The exact path of light as it travels from one medium to another can be
A
found by applying Fermat’s principle, which says that when light travels
from one point to another, it follows the path that will take the least time.
In a single medium, the path that takes the least time is a straight line. air
When travelling from one medium to another, the path that takes the water
least time is not a straight line.
Compare the dashed line in Figure 11.5 with the solid, bent line going
from point A in air to point B in water. In air, where light travels faster, B
the solid line is longer than the dashed line. In water, where light travels
Figure 11.5 When light travels
slower, the solid line is shorter than the dashed line. Light travels a longer
a greater distance in air (where
distance in air and a shorter distance in water than it would if it followed light travels faster) and a shorter
a straight line. Following the bent path (solid line) takes less time than distance in water (where light
following the straight path (dashed line). travels slower), the time of travel
is minimized.

Describing Refraction Using Rays

Most of the terms used to describe refraction are the same as the terms
refracted ray the ray that is
used to describe reflection. In Figure 11.6, notice that in addition to bent upon entering a second
the incident ray and the reflected ray, there is now a third ray called medium
the refracted ray. As you can see, the incident ray is divided into two angle of refraction the
rays—one that reflects and one that refracts. (The word refract comes angle between the normal
from the Latin word refringere, which means to break up). Because there and a refracted ray
is an additional ray, there is an additional angle to keep track of. The new
angle is the angle of refraction, shown by the upper-case R. The angle of
refraction is the angle between the normal and the refracted ray.

normal

Suggested Investigation
i r Real World Investigation 11-C,
air Saving Time, on page 478
water

R
angle of refracted
refraction ray Figure 11.6 Note the new terms:
angle of refraction and refracted ray.

Chapter 11 Refraction • MHR 451

 The Direction of the Refracted Ray
In Figure 11.6, a light ray travels from a medium in which its speed
is faster (such as air) to a medium in which its speed is slower (such
i
as water). The refracted ray bends toward the normal. However, in
Figure 11.7, a light ray travels from a medium in which its speed is slower
water
air
to a medium in which its speed is faster, and the refracted ray bends away
R from the normal. Note that reflection always occurs. However, when
discussing only refraction, the reflected ray will be omitted from the
diagrams to focus on the angle of refraction and the refracted ray. Later in
the chapter, you will see that the reflected rays are important. For now, as
Figure 11.7 Going from water to in Figures 11.6 and 11.7, only the refracted ray will be drawn.
air, the refracted ray is bent away
from the normal.
Index of Refraction
How much a light ray refracts is determined by the extent of the change
in the speed of light as it travels from one medium to another. When light
passes from one medium to the next and the change in the speed of light
becomes greater, the angle of refraction becomes greater.
The speed of light is 3.00 × 108 m/s in a vacuum, such as space, where
there is no matter. The speed of light is less than 3.00 × 108 m/s in any
other medium. For example, the speed of light in water is 2.26 × 108 m/s.
These numbers are extremely large and inconvenient to use for describing
relative speeds. Therefore, scientists have devised a much easier system for
describing relative speeds.
index of refraction the The index of refraction is the ratio of the speed of light in a vacuum
ratio of the speed of light in a to the speed of light in a given medium. The symbol for the index of
vacuum to the speed of light refraction is n, the symbol for the speed of light in a vacuum is c, and the
in a given medium symbol for the speed of light in any given medium is v. Therefore, you can
express the index of refraction in mathematical form as shown below.

Study Toolkit Index of Refraction

_c
Multiple Meanings The n = v , where
word index has multiple n is the index of refraction
meanings. Drawing a
c is the speed of light in a vacuum
word map like the one on
v is the speed of light in a medium
page 448 can reinforce your
understanding of a word’s
multiple meanings.
For example, the index of refraction of water is in a given medium.
speed of light in a vacuum __ 8
___ = 3.00 × 10 8 m/s = 1.33
speed of light in water 2.26 × 10 m/s

452 MHR • Unit 4 Light and Geometric Optics

Dispersion
In Figure 11.8A, white light, which includes all the wavelengths of visible
dispersion the process
light, is refracting twice: once when it enters the prism and again when of separating colours by
it leaves the prism. When the white light leaves the prism, the light is refraction
separated into a spectrum of colours. This process is called dispersion.
This is also illustrated in Figure 11.8B. Notice that blue light bends more
than red light. So, blue light must travel slower than red light. In fact,
each colour of light travels at a slightly different speed in any medium.
Only in a vacuum do all the wavelengths of light, and all other forms of
electromagnetic waves, travel at the same speed—3.00 × 108 m/s.

normals red R
B orange O
yellow Y
of t
e am ligh green G
b ite
h blue B
w
indigo I
violet V

white
screen

Figure 11.8 A When white light leaves the prism, it is refracted again. Since each
colour of light travels at a different speed, each colour of light refracts a different
amount. B You can remember the order of the colours of light in a spectrum by
remembering the name Roy G. Biv, which stands for red, orange, yellow, green,
blue, indigo, violet.

Chapter 11 Refraction • MHR 453

 Reporting Indices of Refraction
If each colour of light has its own index of refraction, what value do you
Sense of hXVaZ
A single aluminum atom
use as the index of refraction for “light”? Scientists have agreed to use one
specific wavelength of light as a standard for reporting. When scientists
is about the size of a were first studying indices (plural of index) of refraction, one of the easiest
nanometre. A nanometre is pure colours to produce was a yellow with a wavelength of 589 nm (nm
one billionth of a metre. is the symbol for nanometre, which is 10−9 m). This wavelength of light is
emitted from heated sodium vapour. So scientists use yellow as a standard
for reporting the index of refraction for light.
When reporting the index of refraction for a gas, remember that gases
are affected by both temperature and pressure. Liquids and solids are
Suggested Investigation affected much less by pressure, but they can be affected by temperature.
Inquiry Investigation 11-B, So, in tables of indices of refraction, such as Table 11.1, the temperature
Analyzing the Index of (in °C) is reported for liquids and solids, but both the temperature
Refraction, on page 477
and pressure (in kPa) are reported for gases. Notice that the index of
refraction is always greater than 1. This is because the speed of light
is always higher in a vacuum than in a medium. As the speed of light
decreases due to the medium, the index of refraction increases.
The indices of refraction (n) for the solids and liquids at 20°C in
Table 11.1 have been measured. Therefore, you can count on the accuracy
of the values when you work with the substances at room temperature. All
the liquids are clear and colourless. You may recognize the names of some
of the substances, such as the liquid carbon disulfide. Carbon disulfide is
an example of a solvent. The solid called fused quartz is used in making
lenses and mirrors. It is not the same as the mineral with the common name
quartz. The three types of glass (crown, crystal, and flint) have different
values of n because different substances are added in the glass-making
process, and that process varies.
If you know the index of refraction of a substance, you can calculate
the speed of light in that substance. See the Sample Problem on page 455.

Table 11.1 Indices of Refraction of Various Substances

Index of Index of
Substance Refraction (n) Substance Refraction (n)

Vacuum 1.000 00 Solids at 20°C

Gases at 0°C and 101.3 kPa Quartz (fused) 1.46

Hydrogen 1.000 14 Plexiglas™ or Lucite™ 1.51

Oxygen 1.000 27 Glass (crown) 1.52

Air 1.000 29 Sodium chloride 1.54

Carbon dioxide 1.000 45 Glass (crystal) 1.54

Liquids at 20°C Ruby 1.54

Water 1.333 Glass (flint) 1.65

Ethyl alcohol 1.362 Zircon 1.92

Glycerol 1.470 Diamond 2.42

Carbon disulfide 1.632

454 MHR • Unit 4 Light and Geometric Optics

Sample Problem: Calculating the Speed of Light in GRASP
Different Media Go to Science Skills Toolkit 11
to learn about an alternative
problem solving method.
Problem
Calculate the speed of light in fused quartz.

Solution
Look up the index of refraction for fused quartz in Table 11.1.
n = 1.46
Write the equation that relates the index of refraction to the speed
of light in the medium.
n=_ c
v
Speed in the medium (v) is the unknown variable, so arrange the
equation to solve for v.
nv = _c A
vv
nv = _
_ c
n n
v=_ c
n
Insert the values for the index of refraction for fused quartz and the
speed of light in a vacuum, and calculate v.
3.00 × 108 m/s
v = __
1.46
= 2.05 × 108 m/s
The speed of light in fused quartz is 2.05 × 108 m/s. B

Check Your Solution

The value for v is smaller than the speed of light in a vacuum, which
it must be. The units are metres per second, which they should be
for speed.

Practice Problems
1. Calculate the speed of light in flint glass.
C
2. Calculate the speed of light in crown glass.

3. a. The speed of light in a solid is 1.24 × 108 m/s. Calculate the

index of refraction.
b. Use Table 11.1 to identify the substance.

4. The diagrams at the right show the path of light as it passes from
air into the three solids in the first three problems. The angle of
incidence is the same for all three solids. Examine the index of
refraction values in the problems, and identify each solid. Use these diagrams to answer
question 4.

Chapter 11 Refraction • MHR 455

Section 11.1 Review

Section Summary
• Light rays refract when they cross a boundary • The index of refraction of a medium is the ratio
between media in which the speeds of light of the speed of light in a vacuum to the speed
are different. of light in the medium n = _ c
v . A ratio greater
• If a light ray goes from a medium in which its than 1 results.
speed is higher (such as air) into a medium in • Dispersion is the separation of the various colours
which its speed is lower (such as water), the of light when white light crosses the boundary
refracted ray bends toward the normal. between different media at an angle.
• If a light ray goes from a medium in which its • The speed of each wavelength of light is different in
speed is lower (such as water) into a medium any given medium. The speed of all wavelengths of
in which its speed is higher (such as air), the light is 3.00 × 108 m/s in a vacuum.
refracted ray bends away from the normal.

Review Questions
K/U 1. In the diagram on the right, a light ray is crossing the
boundary between air and water. Which medium is air,
and which medium is water? Explain your reasoning.
K/U 2. Define the index of refraction.

T/I 3. Calculate the speed of light in glycerol. medium 1

K/U 4. Why must a table that lists indices of refraction of gases medium 2

include the temperature and pressure of the gases?

K/U 5. When white light exits a prism, the light is dispersed.
a. Explain the dispersion of white light through a prism.
b. Which colour of light travels faster in glass: yellow or Use this diagram to answer question 1.
violet? Explain your reasoning. Review Figure 11.8
if necessary.
C 6. Use the symbols n, v, and c to show why the index of refraction
of any substance is always greater than 1.
A 7. “Light can travel across the boundary between two media that
have different indices of refraction without bending.” What is
the angle of incidence for which this statement is true? Use a
diagram to support your answer.
T/I 8. Suppose that you have two blocks of glass that look very similar.
You are asked to determine which block is crown glass and
which block is flint glass. Describe a method you could use to
do this. What equipment would you need?

456 MHR • Unit 4 Light and Geometric Optics

 Key Terms
partial reflection and
refraction
11.2 Partial Refraction and critical angle

Total Internal Reflection total internal reflection

If you have never been diving, you might be surprised by what a diver
can and cannot see when looking up toward the surface of the water.
The photograph in Figure 11.9 was taken underwater from a diver’s
perspective. As you can see, only the objects in an area directly above
you are clearly visible. The water at the sides is dark, even though the
day appears to be clear and bright.
You can analyze Figure 11.9 based on what you have learned about
the refraction of light. To be able to see an object above the water while
you are underwater, you know that light must travel from the object to
your eyes. The objects outside the area directly above you are not visible
because no light from these objects is penetrating the surface of the water.
Light is energy so it cannot disappear. If it is not penetrating the water,
where is it going? You could find some clues by reviewing Figure 10.12
on page 411. In Figure 10.12, light is reflected from the surface of the
water. When light rays reach a boundary between two media, such as air
and water, some light is always reflected and some is often refracted. In
this section, you will learn about the conditions in which more refraction
than reflection occurs and the conditions in which only reflection occurs.

Figure 11.9 When

underwater and looking up,
you can only see objects in
an area directly above you.

Chapter 11 Refraction • MHR 457

 Partial Reflection and Refraction
Sometimes, when you look out a window, you see what is outside as well
as your own reflection, as shown in Figure 11.10. In the photograph, light
is obviously coming through the window because you can see objects that
are outside. But light is also reflecting off the window because you can
see your own reflection. In addition, someone standing outside could see
you through the window. As mentioned earlier, some light reflects and
some light refracts at a surface between two media that have different
indices of refraction, as shown in Figure 11.11. This phenomenon is called
Figure 11.10 While looking out partial reflection and refraction. The amount of reflection compared
of a window, you can often see with the amount of refraction depends on the angle of incidence as well
the reflection of objects inside
as the relative indices of refraction of the two media.
the room as well as objects that
are outside of the window.
normal

incident ray reflected ray

partial reflection and i r

refraction a phenomenon in air
which some of the light that glass
is travelling from one medium R
into another is reflected
and some is refracted at the refracted ray
boundary between the media

Figure 11.11 Both refraction and reflection occur, but not equally. The amount of each
depends on the angle. In this case, more light is refracted than reflected, as indicated by
the thickness of the rays.

Consider, first, light travelling from air into water. If the angle of incidence
is nearly zero—that is, the light is travelling directly toward the water—most
of the light penetrates the surface and very little is reflected. As the angle
of incidence increases, more light is reflected at the surface and less light
penetrates the surface and is refracted.
You have probably seen evidence of this phenomenon. Figure 11.12A
shows water with the Sun overhead. You see very little reflection of
sunlight because most of the light is penetrating the surface of the water.
In Figure 11.12B, however, the Sun is close to the horizon, shining light on
the water at a large angle of incidence. You can see that much of the light
is reflected from the surface of the water.
Figure 11.12 A The sunlight
is shining on the water, but A B
you do not see any reflection
because the Sun is almost
directly overhead. B When
the Sun reflects off the water
(for example, at sunset), the
reflection of the light can be
almost blinding.

458 MHR • Unit 4 Light and Geometric Optics

Activity 11–2
Investigating Properties of Light
In this activity, you will answer the following questions. Procedure
How does the angle of incidence of a ray striking a glass 1. In your notebook, make a table like the one below to
surface compare with record your observations. Give your table a title.
(a) the angle of reflection at the surface,
(b) the angle of refraction at the surface, and 2. Place the glass block in the centre of the sheet of paper.
(c) the angle of refraction when the ray emerges into Carefully draw an outline of the block.
air again? 3. Place a single slit in the ray box. Shine the light toward
the longest side of the block as shown in the diagram on
normal emergent ray the left.
(second refraction,
glass block b in air) 4. Make small pencil marks on the incident, reflected, and
emergent rays.
normal 5. Remove the block, and use a ruler to connect the dots with
a
transmitted ray a solid line to show the path of the light ray. The light ray
R (first refraction, should change direction at the outline of the block.
in glass)
6. Draw a normal at the point where the incident ray enters
incident ray reflected ray
the block. Draw a second normal where the emergent
i r ray leaves the block. Measure the angles of incidence
(i), reflection (r), and refraction (R), as well as the angles
labelled a and b in the diagram.

Questions
1. Explain how the reflection you observed in this activity
(a) is the same as and (b) is different from the reflection
of light at the surface of a plane mirror.
Materials
2. In previous activities and investigations, you have not
• glass block • pencil considered a refracted light ray that enters and then
• sheet of paper • ruler continues on through and out the other side of the same
• ray box (single slit) • protractor medium. Explain how the refracted ray as it enters the
medium (a) is the same as and (b) is different from the
ray as it leaves.

Transmitted Ray Emergent Ray

Incident Ray Reflected Ray First Refraction, in Glass Second Refraction, in Air

∠i ∠r ∠R ∠a ∠b

Reflection and Refraction in a Rearview Mirror

The rearview mirror in most cars has a lever that allows the driver to choose
how much light from behind the car will reach his or her eyes. During the
day, the driver wants to clearly see the traffic that is behind the car. At night,
however, the driver does not want to be blinded by headlights.

Chapter 11 Refraction • MHR 459

 How a Rearview Mirror Works
As shown in Figure 11.13A, rearview mirrors are wedge-shaped and silvered
on the back. A lever can quickly flip a rearview mirror from daytime to
nighttime positions. Light coming from behind the car hits the mirror at a
very small angle of incidence. As a result, most of the light is refracted and
reaches the silvered back of the mirror, where it is reflected.
Daytime Setting of a Rearview Mirror
In the daytime, the mirror is positioned as shown in Figure 11.13B. The light
that has reflected off the back of the mirror is directed to the driver’s eyes.
Thus, in the daytime, the driver has a clear view of the traffic behind the
car. If the mirror was left in this position at night, however, any headlights
behind the car would shine brightly in the driver’s eyes, making it very
difficult for the driver to see.
Nighttime Setting of a Rearview Mirror
Figure 11.13C shows how a driver can flip a rearview mirror to the night
setting. At this angle, most of the light penetrates the mirror glass and is
refracted as before. However, in this case, only a small amount of reflected
light is directed toward the driver’s eyes. This allows the driver to see the
headlights, but at a low intensity. Most of the light penetrates the mirror,
refracts, hits the silvered back of the mirror, and is reflected away from the
driver’s eyes. Such mirrors are designed so that the angles of incidence,
reflection, and refraction direct the right amount of light toward the
driver’s eyes for both daytime and nighttime.

A silvered mirror B driver C

(back surface driver
transparent of wedge)
glass wedge
light from
light from behind car
behind car
day-night day setting night setting
lever

Figure 11.13 A A rearview mirror reflects light to the driver’s eyes. B With the daytime
setting, most of the light goes to the driver’s eyes. C With the nighttime setting, just
a small amount of the incoming light goes to the driver’s eyes.

Large Angles of Incidence

Now that you understand partial reflection and refraction, you can
explain Figure 11.9 on page 457. Imagine that you are scuba diving and are
underwater looking up, as shown in Figure 11.14. The light coming from
the area directly above you or at a small angle of incidence will penetrate
the surface of the water, refract, and be visible to you. But as the angle of
incidence of the light increases, more of the light will reflect off the water,
and a smaller amount will refract and be visible to you. Nearly all the light
that is coming in your direction from large angles of incidence will reflect
from the surface and never reach you. Therefore, from below the surface
of the water, it looks like light is coming through a hole.

460 MHR • Unit 4 Light and Geometric Optics

 air

water

Figure 11.14 When you are

underwater, you can only see the
light that reaches you from an
area directly above. The bottom
of the water–air boundary and the
sky above look dark because light
that is coming from this direction
is reflected away and you cannot
see it.

Learning Check
1. The term partial refraction implies that only part of the light
that hits a boundary between two media refracts. What happens
to the rest of the light?
2. Explain how a rearview mirror works. Review Figure 11.13 if
necessary. In your explanation, include why many rearview
mirrors have two settings.
3. If you were sitting on a riverbank, holding a fishing rod, a fish
in the river would probably not be able to see you. Explain why.
4. Describe an example in your everyday life that demonstrates
that both reflection and refraction occur at a boundary between
two media with different indices of refraction. Figure 11.15 The water is clear,
but you can see objects under
the water only when they are
Refraction: Water to Air close to you.

If you were standing in shallow water at the edge

of a clear lake, as in Figure 11.15, you would be
able to see stones on the bottom of the lake or fish
swimming in the water that were very near you.
As you look farther away, objects underwater are
more difficult to see. At a great enough distance,
you cannot see anything below the surface of the
water. You know that the water is clear and that
there is plenty of light. Why is it not possible to
see objects underwater?

Chapter 11 Refraction • MHR 461

 The Critical Angle
For you to see an object underwater, light must hit the object, reflect off
Suggested Investigation
it, and travel to your eyes. Figure 11.16A shows two separate incident
Inquiry Investigation 11-D,
Investigating Total Internal rays travelling toward the boundary between air and water, at relatively
Reflection in Water, on small angles of incidence. Because the incident rays are going from
page 480 water to air, the refracted rays bend away from the normal. As you can
see, as the angle of incidence increases, the angle of refraction increases
more rapidly.
As the angle of incidence continues to increase, the angle of refraction
will eventually reach 90°, as shown in Figure 11.16B. At this angle of
incidence, the refracted ray lies along the boundary between the two
critical angle the angle of media. No light passes into the second medium, which is air in this
incidence that produces an
angle of refraction of 90°
example. The angle of incidence that produces a refracted ray at an angle of
90° from the normal is called the critical angle, and is symbolized by ∠c.
Total Internal Reflection
The size of the critical angle depends on the indices of refraction of the
total internal reflection
two media. When the angle of incidence is larger than the critical angle,
the phenomenon in which
incident light is not refracted
the angle of refraction cannot get any larger because the refracted ray
but is entirely reflected back would no longer be in the second medium. So, at angles of incidence
from the boundary; occurs that are greater than the critical angle, no refraction occurs. All the light
when light travels from a is reflected back into the first medium, as shown in Figure 11.16C. This
medium in which its speed is
phenomenon is called total internal reflection. Note that total internal
lower to a medium in which
its speed is higher
reflection happens only when light travels from a medium in which its
speed is lower to a medium in which its speed is higher.

A normal normal B normal C normal

R refracted refracted
R
ray ray R
air refracted ray
water
incident c i r
i r
ray r
i
r

incident ray reflected ray incident ray reflected ray

reflected ray
reflected ray
incident ray

Figure 11.16 A When the angle of incidence is smaller than the critical angle, both
refraction and reflection occur at the boundary between the two media. B When the
angle of refraction reaches 90°, the refracted ray lies along the boundary between the
two media. C When the angle of incidence is larger than the critical angle, all the light is
reflected back into the first medium.

462 MHR • Unit 4 Light and Geometric Optics

Activity 11–3
The Fountain of Light
What is happening in the diagram on the right? In this
activity, you will observe total internal reflection within
a stream of water in a darkened room.

Materials
• clear plastic bottle (remove • water
the label if necessary) • bucket (or use a sink)
• duct tape (about 5 cm) • flashlight Set up the apparatus as shown here to
• thumbtack see the light in the stream of water.
• scissors
• masking tape (about 3 cm)
5. Look for the spot where total internal reflection
Procedure suddenly occurs. Try to measure the critical angle.

1. Place a short piece of duct tape on a part of the bottle 6. Empty the water from the bottle. Use the point of the
that is clear on both sides, about 6 to 8 cm from the scissors to make the hole larger, and cover the hole
bottom of the bottle. with masking tape. Repeat steps 3 to 5.

2. Use the thumbtack to make a small hole in the centre

Questions
of the duct tape. Cover the hole with a small piece of
1. Total internal reflection occurs when light in water hits
masking tape.
the water—air surface at an angle of incidence that is
3. Fill the bottle with water. Perform the rest of this greater than 49°. Compare 49° with your measurement
activity over a bucket or sink. in step 5.
4. Have your partner shine the light from a flashlight 2. When did you observe the greater amount of total
through the bottle from the side that is opposite the internal reflection: when the stream of water fell far
hole. Remove the masking tape, and observe the from the bottle, or when the stream of water fell close
stream of water as it exits the hole, as well as the to the bottle? Explain your observation using a diagram.
height of the water in the bottle as it nears the hole.

Making a Difference
Michael Furdyk uses Internet communications technology to make a difference.
He is co-founder and director of technology for TakingITGlobal.org, an on-line
community for youth interested in positive change. More than five million
users from 200 countries have visited TakingITGlobal.org to learn about and
engage in global issues, such as education and sustainable development.
Michael started his first computer business when he was 8. At 15, he
formed a company called MyDesktop.com with Michael Hayman, an Australian
friend. The website had more than 500 000 users monthly, and Michael and his
friend eventually sold it. In 2000, Michael co-founded the non-profit
TakingITGlobal.org with another friend, Jennifer Corriero.
Michael has advised many organizations on how to engage today’s youth.
He speaks at conferences around the world and was named one of Teen
People’s “20 teens that will change the world” in 2000.
How could you use the Internet and other communications
technologies to make positive changes in your community?

Chapter 11 Refraction • MHR 463

 Changing the Direction of a Light Ray
A glass prism can change the direction of light by creating the conditions
Study Toolkit for total internal reflection. The critical angle between glass and air is less
Summarizing It may be than 45°. Therefore, light hitting an inner surface at exactly 45° will be
helpful to summarize the totally reflected inside the glass.
information in the first three Figure 11.17A shows how a glass prism that is shaped like an isosceles
paragraphs on this page right triangle can change the direction of a light ray by 90°. When light
in a table like the one on
enters the prism perpendicular to one of the short sides of the prism,
page 448.
the angle of incidence is zero. Thus, there is no refraction at this surface.
The light travels straight through the prism to the inside of the long side
of the prism. At the long side of the prism, the angle of incidence is 45°,
so the angle of reflection is also 45°. The total change in the direction of
the ray is 90°. In comparison, when light enters the prism perpendicular
to the long side of the prism, as shown in Figure 11.17B, it is reflected off
both short sides, changing direction by 90° each time. The total change in
direction is therefore 180°.
When light enters the long side at any angle, as shown in Figures 11.17B
and C, the reflected light is reflected by 180°, or directly back in the direction
that it came from. When the angle of incidence into the prism is not 0°, the
light will be refracted. However, after the light has reflected off both inner
short sides and then leaves the prism, it will refract at the same angle.

Figure 11.17 A The direction A normal B

of light is changed 90°. B The
45°
direction of light is changed 45°
normal
180°. C Regardless of the angle
45°
of incidence at the long side of
45°
the prism shown, the refracted
45°
and reflected rays will go back in
exactly the same direction from 45°
45°
which they came.
normal
45°

45°
normal
normal

normal
normal
eyepiece
45°

prism

Applications of Total Internal Reflection

objective Figure 11.18 shows how binoculars use total internal reflection. See how
the path of light in the binoculars is lengthened and moved to the side.
Figure 11.18 The direction of
the light is reflected twice in
When you study lenses in Chapter 12, you will find out why the long path
binoculars to make the path of length is important.
the light longer.

464 MHR • Unit 4 Light and Geometric Optics

Retroreflectors
The ability to change the direction of light by 180° has some very useful
applications. One of these applications is retroreflectors, which look like
small plastic prisms. For example, the reflectors on the back of a bicycle
are retroreflectors, as shown in Figure 11.19A. Regardless of the direction
that light from headlights hits the reflectors, the light is always reflected
directly back to the car so the driver can see the bicycle, as shown in part B.

A B Figure 11.19 A Look closely at

this bicycle reflector. You will see
small circles or hexagons. B Each
circle or hexagon is a cut in the
plastic. It functions like a prism to
reflect light directly back in the
direction it came from.

Optical Fibres
Fibre optics has revolutionized all forms of communication, including the
Internet. Optical fibres are made from a glass core, which is surrounded
by an optical cladding. A cladding is a covering, much like a sleeve but
completely closed. In this case, the fibre core is made of one type of glass,
and the cladding is made of another type of glass. The material that makes
up the cladding must have a lower index of refraction than the core to
facilitate total internal reflection. See Figure 11.20A. When light enters
the end of the fibre in a direction that is almost parallel to the axis of the
fibre, it hits the boundary between the core and cladding at an angle that
is larger than the critical angle, as shown in Figure 11.20B. Even when the
fibre is bent, the light is totally internally reflected along the entire fibre
until it reaches the other end.
Individual fibres are somewhat fragile. Therefore, they are coated for
strength and protection. Groups of fibres are then bundled together into
a cable, as shown in Figure 11.20C. Depending on their use, the cables can
be as short as a metre or as long as several kilometres.

A optical cladding n  1.47 B C

c c total internal
reflection
optical
fibre
core n  1.50

optical cladding
light

Figure 11.20 A Total internal reflection will occur each time the light hits the boundary
between the core and cladding in an optical fibre, regardless of the amount of bending of
the fibre. B The light is totally internally reflected along the optical fibre until it reaches
the other end. C A fibre optics cable can carry hundreds of telephone conversations,
cable television signals, or data.

Chapter 11 Refraction • MHR 465

 Fibre Optics in Telecommunications
Copper wire cables have been used in the past to carry information. But
fibre optic cables are rapidly replacing them. There are three main ways
that fibre optics cables are superior to copper wire cables:
• The signals are not affected by electrical storms, as they would be in
copper wire cables.
• Fibre optics cables can carry many more signals over long distances,
losing less energy than copper cables.
• Fibre optics cables are smaller and lighter than copper cables.
Figure 11.21 The small
Figure 11.21 shows a fibre optics cable and a copper cable that carry the
optical fibres can carry as much
information as the large copper
same amount of information.
cable on the right.
Fibre Optics in Medicine
The use of optical fibre bundles has transformed many surgical procedures.
An instrument called an endoscope uses optical fibre bundles. The
surgeon inserts the endoscope in a small incision. One bundle of optical
Study Toolkit
fibres in the endoscope carries light into the area where the surgery is
Making Inferences Read
needed. Another bundle of optical fibres carries an image of the area back
the text under the to a monitor. The surgeon watches the monitor while manipulating the
heading “Fibre Optics in instrument to complete the surgery. Before this technique was available, a
Telecommunications.” What large incision was necessary, making the recovery time several weeks long.
prior knowledge do you have
Traditional surgery also increases the possibility of infection.
about copper wire cables?
Doctors also use endoscopes to help diagnose problems in their
patients. In Figure 11.22, the doctor has fed an endoscope down her
patient’s esophagus and can view the inside of the patient’s stomach
on a computer monitor. The doctor in the middle, holding the white
instrument, is taking a tissue sample from the stomach. By being able
to see the inside of the stomach and take a tissue sample, the doctor may
be able to diagnose any problems, such as an ulcer or cancer.

Sense of
Fibre optics are not a recent
invention. Sponges, which
are the oldest multicellular
organisms, transmit light
inside their bodies using
silica structures. The silica
structures are basically
glass rods.

Figure 11.22 The doctor has inserted the flexible, fibre optic end of the endoscope
down the patient’s throat and is watching the image of the stomach on a monitor.

466 MHR • Unit 4 Light and Geometric Optics

Section 11.2 Review

Section Summary
• When light strikes a boundary between two than the angle of incidence. Therefore, an angle of
transparent media that have different indices of incidence that results in a 90° angle of refraction
refraction, some light reflects off the boundary is eventually reached. This angle of incidence is
and some light refracts through the boundary. called the critical angle.
This phenomenon is called partial reflection • When the angle of incidence is larger than the
and refraction. critical angle, no refraction occurs. All the light is
• At a small angle of incidence, more light refracts reflected from the boundary. This phenomenon is
than reflects. As the angle of incidence increases, called total internal reflection.
more and more light reflects than refracts. • Total internal reflection has many practical
• When light travels from a medium with a higher applications, such as binoculars, retroreflectors,
index of refraction to a medium with a lower and optical fibres in telecommunications and in
index of refraction, the angle of refraction is larger surgical instruments.

Review Questions
C 1. Using diagrams, define the terms critical angle and total
internal reflection. A
K/U 2. Under what conditions will nearly all the light that reaches
a boundary between two different media be refracted?
K/U 3. What two conditions must exist for total internal
reflection to occur?
K/U 4. Describe the structure of optical fibre cables.

A 5. The diagrams on the right show rearview mirrors at two B

different settings. Which rearview mirror is set for daytime
driving, and which is set for nighttime driving? Explain
your reasoning. Review Figure 11.13 if necessary.
T/I 6. Refer to Figure 11.17. If the light enters one of the short
sides of the prism at an angle of incidence of 40°, will the Use these diagrams for question 5.
light change direction by 90°? Explain your answer.
A 7. Evaluate the impact of the development of optical fibres.
Which type of application do you think has the greatest
impact on our lives?
T/I 8. Diamonds have a large index of refraction of 2.42, and they
are cut with many facets. Based on what you know about
refraction, explain why cut diamonds sparkle more than
any other cut stones.

A facet on a diamond
is a small, flat area.

Chapter 11 Refraction • MHR 467

 Key Terms
rainbow
apparent depth
shimmering 11.3 Optical Phenomena in Nature
mirage
The double rainbow in Figure 11.23 is an excellent natural example of
the refraction and dispersion of light. Your new understanding of the
behaviour of light will allow you to analyze the paths of the light rays
that bring this double rainbow to your eyes.

Rainbows
The Sun must be behind you if you are to see a rainbow. It must also
rainbow an arc of colours
of the visible spectrum
reflect off something for it to return to your eyes. After a rainstorm,
appearing opposite the the sky is filled with tiny water droplets. The sunlight reflects off these
Sun, caused by reflection, water droplets.
refraction, and dispersion of Now consider the sequence of colours in the two parts of the double
the Sun’s rays as they pass
rainbow. Red is the top colour of the inner rainbow, but it is the lowest
through raindrops
colour of the secondary rainbow. Notice that much more light is coming
from the area inside the inner rainbow than the area outside the inner
rainbow. All of these factors can be explained by the reflection, refraction,
and dispersion of light in raindrops. A secondary rainbow is caused
when sunlight reflects twice inside rain droplets. This explains why the
secondary bow is less bright, with red at the bottom and blue at the top.

Figure 11.23 Notice how red is at

the top of the inner rainbow but at
the bottom of the secondary rainbow.

468 MHR • Unit 4 Light and Geometric Optics

Formation of a Rainbow
A rainbow forms when sunlight enters a water droplet and refracts,
reflects off the inner surface of the droplet, and then refracts again when
leaving the droplet. The two refractions result in dispersion of the light.
Notice in Figure 11.24A that within the droplet itself, the different colours
cross each other, and then spread out as they leave the droplet.
Compare the colours leaving the single water droplet in Figure 11.24A
with the colours in the inner rainbow in Figure 11.23. Notice that the red
light leaving the water droplet is the lowest colour, but red is the top colour
in the inner rainbow. Although this seems be a contradiction, it is correct.
When you see a rainbow, the colours that you see come from different
droplets. Because the red light is directed downward more than the other
colours of light, you can only see the red light that is coming from droplets
higher in the sky. Figure 11.24B shows which colours you see from droplets
at different heights in the sky.

A B

white light
from the Sun

water droplet

Figure 11.24 A The index of refraction is different for each colour of light. When white
light leaves a water droplet, refraction causes the colours to disperse. B You see the
different colours in a rainbow coming from water droplets at different heights in the sky.

Sundogs
At the beginning of this chapter, you saw a photograph of the spectacular
atmospheric phenomena known as sundogs, which are bright spots on
both sides of the Sun. They are sometimes called “mock suns” for that
reason. Their technical name is parhelia. Sundogs have something in
common with rainbows, but there is a difference. Rainbows are a result
from sunlight interacting with water droplets in the atmosphere. Sundogs,
however, occur when ice crystals in the atmosphere refract sunlight.
The most stunning sundogs occur on cold, clear sunny mornings and
evenings, when there are ice crystals in the air, such as in cirrus clouds.
(Cirrus clouds are at a high altitude, over 6000 m. They are composed of
ice crystals.) Sundogs occur when the Sun is low, near the horizon. These
phenomena have been photographed in many provinces and territories of
Canada, including Ontario.

Chapter 11 Refraction • MHR 469

 The Illusion of Apparent Depth
Just as an image is formed by reflection in a plane or a curved mirror,
apparent depth an optical
effect in which the image of
an image is formed by the refraction of light. Using ray diagrams, you can
an object appears closer than determine where the refracted image is located when it is viewed from the
the object air. Light rays from the object, like the box at the bottom of the pool in
Figure 11.25, travel to your eyes. The rays have refracted at the surface of the
water. As in Chapter 10, you can draw a ray diagram to locate the image of
the object. Locate the image of the box by tracing the rays backward until
they meet. Note that the box on the bottom of the pool looks like it is higher
and closer to the observer than it actually is. In fact, the bottom of the pool
is deeper than it appears to be. The level at which the object or the bottom
of the pool appears to be is called the apparent depth.

Figure 11.25 The solid lines from air

the box to the observer show water
the actual path of the light rays. apparent
The dashed lines show where the depth
observer’s brain interprets the actual
depth
path to be.

After analyzing Figure 11.25, you can understand why a fish in a pond is
lower in the water than it appears to be. So, how do water birds, such as
the pelican in Figure 11.26, actually catch the fish they dive for? A pelican
will spot a fish while flying above the water and start into a dive. It will hit
Figure 11.26 Water birds, such
the water forcefully, continue into the water, and catch the fi sh without
as the pelican, dive deeper for a
fish than the fish appears in the difficulty. The pelican has found a way to account for the illusion of
water to a human observer. apparent depth.

Learning Check
1. Explain why red is at the top of a single rainbow. Review
Figure 11.24.

2. What is a sundog?

3. If you are trying to spear a fish underwater, should you aim

above the fish, below the fish, or at the fish? Use your knowledge
of apparent depth to explain.
4. Draw a diagram to show how a double rainbow forms.

470 MHR • Unit 4 Light and Geometric Optics

Activity 11–4
Apparent Depth
How does the location of an object appear to change when 3. Place a pin at positions A and B, as shown in the diagram
you observe it through a plastic block? In this activity, you on the left.
will demonstrate the phenomenon of apparent depth.
4. Look in the direction shown in the diagram until pin B and
the pin at O appear in a straight line. Place pin C so that all
Materials
do three pins appear in a straight line. Similarly, place pin D
• rectangular plastic C so that the pins at D, A, and O appear in a straight line.
di
block
5. Remove the block, and draw dashed lines to show where
• thick piece of
B the lines CB and DA intersect inside the block
cardboard O
at the image of pin O. Measure di and do.
• sheet of blank A
paper 6. Make a ray diagram to illustrate your observation.

• 5 straight pins 7. Switch places with your partner, and repeat steps 3 and 4.
D
• ruler
Questions
Place the plastic block
1. Where do the rays intersect?
and pins as shown here.
Procedure
2. Explain your observations.
1. Place the cardboard on the desk. Place a sheet of
paper on top of the cardboard and the plastic block 3. Suppose you used a clear container instead of a plastic
on the paper. block. You then positioned the pins before filling the
container with water. Predict how your observations
2. Place a pin at position O shown in the diagram above. would change compared with your observations above.
The pin should be touching the plastic. Test your prediction.

Shimmering and Mirages

Shimmering and mirages are caused by the refraction
of light in unevenly heated air. When light travels through
air at different temperatures, it refracts because hot air
is less dense than cooler air. Because there is no distinct
boundary between sections of air at different temperatures,
the light does not bend at one specific point. Instead, it
travels along a curved path. Also, because air is usually
moving, the direction and the amount of the bending
are constantly changing.
Shimmering
You can see shimmering in air above any very hot surface.
For example, the air above the hood of a car that has been Figure 11.27 When you look through the hot air
travelling for a long time or hot asphalt being laid can around the engine at the distant plane in the middle
of the photograph, the distant plane looks wavy.
become very hot, due to contact with the hot surface. When
you look through the hot air, objects look wavy, as shown in
Figure 11.27. Objects often look like they are moving, as well. shimmering the apparent
This apparent movement of objects is called shimmering. movement of objects in hot
air over objects and surfaces

Chapter 11 Refraction • MHR 471

 Mirages
A mirage occurs on a much larger scale than shimmering. The most
common place to see a mirage is in a very hot desert or on a highway. The
sand or paved surface becomes extremely hot after being in sunlight for
several hours. The hot ground heats the air just above it, making the lower
layer of air much hotter than the higher air. When sunlight reaches the
hot air near the ground, the sunlight is refracted upward.
Because you are accustomed to assuming that light travels in a straight
mirage an optical effect
line, you interpret the origin of the light as being on the ground. An object
caused by the bending of light
rays passing through layers that appears to be on the ground but is not really there is called a mirage
of air that have extremely [pronounced mi-RAHJ]. Figure 11.28A shows how a mirage forms. The
different temperatures solid line shows the real path of the light. The dashed line shows where
the blue light from the sky appears to have originated. Figure 11.28B is a
photograph of a mirage on a highway formed in this way.

E Case Study
STSE
Protecting Your Eyes from UV Radiation
You may wear sunglasses for style and protection from the UV Radiation
Sun. Whatever the reason, it may surprise you to learn that UV radiation is one of the more energetic types of light in
your sunglasses could be letting through radiation that is the electromagnetic spectrum. UV radiation causes your skin
harmful to your eyes. to tan. If you expose your skin to sunlight for too long, you
The brightness of light is illustrated in the bar graph on will get a sunburn. Imagine, therefore, what UV radiation can
page 473. Sunglasses are tinted to reduce the amount of do to your eyes!
visible light that reaches your eyes. The tinting, which is
applied as a coating on the lens, is made up of light-absorbing
molecules. The thicker the coating is, the darker the lens is. Effects of UV Radiation
The coating does not block ultraviolet (UV) radiation, however. • Long-term exposure to UV radiation can damage
your eyes.
• Damage from UV radiation cannot be reversed.
• Exposure to UV radiation can contribute to the
development of cataracts (a clouding of the natural
lens of the eye), cancer, and snow blindness. Snow
blindness is a temporary but painful sunburn on the
surface of the eyes.

When you buy sunglasses, check the tags to see

how much light is blocked. Look for sunglasses
that block 99 to 100 percent of UV radiation
and 75 to 90 percent of visible light.

472 MHR • Unit 4 Light and Geometric Optics

 A B

hot air

mirage

Figure 11.28 A The solid, curved line shows the path of light from
the sky. The dashed line shows how your brain interprets the scene.
B The watery area on the road is really a mirage.

Wraparound sunglasses offer even more protection

Brightness of Light
because they protect your eyes from UV radiation that enters
14 000 from the side. Wraparound sunglasses are particularly useful
Brightness (lumens)

12 000
when skiing and when at the beach, where the reflection of
10 000
sunlight is particularly strong.
8 000
6 000 Over to You
4 000
1. According to the bar graph on the left, how bright is
2 000
light reflected from snow? Is that level of brightness
0
Indoor Outdoor Outdoor Snow comfortable for your eyes?
shade sunlight
2. Survey your friends and family members to find out
how many wear sunglasses and when. What argument
The brightness of light is measured in lumens. Your
could you make to persuade people who do not wear
eyes are comfortable up to 4000 lumens. After that,
you begin to squint. Sunglasses allow an acceptable sunglasses to buy a pair to protect their eyes?
amount of light to reach your eyes. 3. The lenses of some eyeglasses have features that
provide enhanced eye protection. These features include
How can you protect your eyes from UV radiation? By anti-glare coatings, anti-reflective coatings, polarization,
simply wearing a cap or a wide-brimmed hat, you can prevent and photochromic lenses. Choose one of these features.
50 percent of the UV radiation from reaching your eyes. Research how it protects the eyes. Then design a
Wearing sunglasses with a special coating will prevent even brochure for an optometrist’s office to encourage clients
more UV radiation from reaching your eyes. UV-filtering to buy prescription sunglasses that have this feature.
lenses are coated with special chemicals. These chemicals
have a structure that allows visible light to pass through
them while reflecting UV radiation away from your eyes.

Chapter 11 Refraction • MHR 473

 Mirages and Temperature Inversions
Although much less common, a mirage can also be caused by the opposite
combination of temperatures. Sometimes, a wind brings warm air over a
very cold ocean. This weather condition is called a temperature inversion.
Light from an object on the ground starts to travel upward, but it curves
and starts back down when it reaches warmer air. The light that reaches
an observer can even come from beyond the horizon. When this type of
mirage occurs, you think that you are seeing the object in the air. People
have seen ships and icebergs, and even buildings from a distant city that
appear to be sitting above the ocean.
Depending on the exact paths of the light through the different
temperatures of air, part of the object sometimes appears to be upside
down. Figure 11.29 shows a diagram and a mirage in which the object
appears to be upright, as well as a diagram and a mirage in which part
of the object appears to be upside down.

A B
warm air

cold air

C D
warm air

cold air

Figure 11.29 A The solid, curved lines show the path of light from an object, such as an
iceberg. The dashed lines show where the object seems to be. B The mountains in this hot
desert are a mirage. C The curved, solid lines show the path of light from an object, such
as a boat. The atmospheric conditions caused the light rays to cross, so the boat appears
to be upside down. D In this photograph, it looks like the animals are reflected in water,
but there is no water. This is a mirage.

474 MHR • Unit 4 Light and Geometric Optics

Section 11.3 Review

Section Summary
• A rainbow is formed by the refraction and total • Shimmering is the apparent movement of
internal reflection of light and the resulting objects seen through air that is unevenly heated
dispersion of the light by spherical water droplets and moving.
in the sky. • A mirage is the appearance of water or another
• As a result of the refraction of light at the surface object that is not really there. A mirage is caused
of water, objects under the water are not where by light being continuously refracted by layers of
they appear to be when you are looking at them air that are at extremely different temperatures.
from above the water. The level at which they
appear to be is called their apparent depth.

Review Questions
K/U 1. Under what atmospheric conditions are sundogs likely
to appear, and where would they be in the sky?
K/U 2. Use Figure 11.24B to explain the sequence of colours that
you see in a rainbow.
C 3. Sketch all the conditions that are necessary for you to see
a single rainbow. Include the position of the Sun relative
to your position.
C 4. Review Figure 11.25. Sketch the apparent depth of a fish
in a pond when you are looking at the fish from above
the water and to the side, at an angle. Explain your sketch.
A 5. An archer fish catches an insect by spitting a stream of water
at it to knock it off an overhanging branch. The insect then
falls in the water, and the fish eats it. The eyes of the fish
remain underwater when it hunts. Only the fish’s mouth
projects out of the water. Draw a ray diagram based on the
photograph on the right to show where the fish must aim to
strike the insect.
K/U 6. Explain how understanding the properties of light allows
you to explain shimmering images.
K/U 7. What conditions are necessary for a mirage to appear?

C 8. Suppose you are in a hot desert and you see a mirage

in which the object is upside down. Sketch the mirage.
Show the path that the light rays actually take as well as
the path that you assume the light rays take. Refer to
Figure 11.28. Use this photograph to answer
question 5.

Chapter 11 Refraction • MHR 475

 Inquiry Investigation 11-A
Skill Check Investigating Refraction, from Air to Water
Initiating and Planning
In this investigation, you will compare the angle of incidence and the
✓ Performing and Recording angle of refraction when a light ray travels from air into water.
✓ Analyzing and Interpreting
Question
✓ Communicating
What is the relationship between the angle of incidence and the angle
of refraction when light passes from a medium where its speed is
Safety Precautions
greater into a medium where its speed is lower?
• Be careful not to spill any water. Procedure
1. Design a table or a spreadsheet to record the angle of incidence
Materials
(∠i) and the angle of refraction (∠R) for eight sets of data. Give
• tap water
your table a title.
• clear, semicircular plastic
2. Put tap water in the container. Dissolve a very small amount of
container
non-dairy creamer in the water. This will make light rays visible in
• non-dairy creamer or chalk dust
the water.
• stir stick
3. Position the container so that the centre of the flat edge is at the
• ray box
centre of a sheet of polar graph paper. A line joining the 0° to
• polar graph paper 180° markings should be a normal at the centre of the flat edge of
the container.
Math Skills
Go to Math Skills 4. Place a single slit in the ray box. Shine the light ray toward the
Toolkit 3 to learn
more about making
centre of the container, as shown in the diagram on the left.
graphs.
5. Shine the light ray along the normal, toward the flat edge of
the container, so the angle of incidence is 0°. Record the angle
of refraction.
6. Increase the angle of incidence in 10° steps, up to 70°. Record
rays from the angle of refraction for each angle of incidence.
ray box

Analyze and Interpret

1. Create a graph with the angle of incidence on the y-axis and the
less angle of refraction on the x-axis. Give your graph a suitable title.
refractive
(air) Plot your results, and draw a smooth curve of best fit.
more 2. Describe and explain the shape of your graph.
refractive
(liquid)
Conclude and Communicate
semicircular 3. Summarize the answer to the investigation question.
container
Extend Your Inquiry and Research Skills
Shine the single beam toward
the centre of the semicircular 4. Research Research the principle of reversibility. Explain the
plastic container. principle in your own words.

476 MHR • Unit 4 Light and Geometric Optics

 Inquiry Investigation 11-B
Skill Check Analyzing the Index of Refraction
Initiating and Planning
In this investigation, you will investigate the refraction of light as it
✓ Performing and Recording passes through media with different refractive indices and determine
✓ Analyzing and Interpreting whether there is a trend.

✓ Communicating Question
How do the angles of refraction and incidence change in media with
Safety Precautions
different indices of refraction?
• Be careful not to spill Procedure
any liquids.
1. Make a table like the one below. Give your table a title.
• Ethyl alcohol is volatile. Keep
the classroom well ventilated, Angle of Angle of Index of
Material Incidence, ∠i Refraction, ∠R Refraction, n
and keep the container with
ethyl alcohol covered. Air

Water
Materials
Ethyl alcohol
• marker
Glycerol
• masking tape
Glass block
• 4 semicircular plastic
containers
2. Label a semicircular container for each material in the table
• cover for one container
except for the glass block. Pour water, ethyl alcohol, and glycerol
• water into the containers you labelled for them. Place a cover over the
• ethyl alcohol container containing ethyl alcohol.
• glycerol 3. Point a single ray from a ray box into each material listed in your
• glass block table. Measure and record the angles of incidence and refraction.
• ray box 4. Refer to Table 11.1 on page 454. Find the indices of refraction for
• protractor the materials you tested, and record them in your data table. For
the glass block, use the index of refraction for crown glass.

Analyze and Interpret

1. How do the angles of refraction and incidence change in media
with different indices of refraction?

Conclude and Communicate

2. Summarize your findings in a statement explaining the trend
you observed.

Extend Your Inquiry and Research Skills

3. Research Research refractometers. Explain what a refractometer
is and how refractometers are useful to society.

Chapter 11 Refraction • MHR 477

 Real World Investigation 11-C
Skill Check Saving Time
Initiating and Planning
A lifeguard hears cries of distress from someone in the water. To reach
✓ Performing and Recording the drowning victim as soon as possible, the lifeguard must take one
✓ Analyzing and Interpreting of the three paths shown in the diagram below. Each of the three
paths has two parts. First, the lifeguard runs on the sand at 5 m/s.
✓ Communicating Then the lifeguard swims in the water at 2 m/s. How is the time taken
to reach the victim related to the time spent running and the time
spent swimming?
Materials
• calculator
victim
water: swimming speed = 2.0 m/s

17 m
8.5 m
12 m

15 m
11 m
20 m

sand: running speed = 5.0 m/s

lifeguard

There are three different paths that the lifeguard could take.

Question
How does this analogy illustrate Fermat’s principle?

Prediction
Predict which path the lifeguard should take to reach the victim in the
shortest amount of time. Explain your prediction.

Organize the Data

1. The formula for speed is
distance travelled
speed = __
time taken
Rearrange this formula to show how you can calculate the
time taken.

478 MHR • Unit 4 Light and Geometric Optics

 2. Copy the following table into your notebook. Give your
table a title. Enter the distance data from the diagram.

Sand Water

Distance Time Speed Distance Time Speed Time to Reach

Path (m) Running (s) (m/s) (m) Swimming (s) (m/s) Victim (s)

Green

Red

Blue

3. Calculate the time taken to run and swim along

each of the three paths. Show your work, and
enter your results in your table.

Analyze and Interpret

4. Which path takes the least time for the lifeguard
to rescue the swimmer?

Conclude and Communicate

5. Explain how this analogy illustrates
Fermat’s principle.
6. Evaluate the analogy.

Extend Your Inquiry and Research Skills

7. Inquiry How much time would be lost if the
lifeguard chose the blue path, which is a
straight line to the victim?
8. Research Research the French
mathematician Pierre de Fermat
(1601–1665), who developed
this principle.

A lifeguard has to reach the

victim as soon as possible.

Chapter 11 Refraction • MHR 479

 Inquiry Investigation 11-D
Skill Check Investigating Total Internal Reflection
Initiating and Planning in Water
✓ Performing and Recording
In this investigation, you will investigate the relationship between the
✓ Analyzing and Interpreting angle of incidence and the angle of refraction when a light ray travels
✓ Communicating from water into air.

Procedure
Safety Precautions 1. Design a table or a spreadsheet to record the angle of incidence
• Be careful not to spill (∠i), the angle of reflection (∠r), and the angle of refraction (∠R)
any water. for several sets of data. Give your table a title.
2. Put tap water in the plastic container. Dissolve a very small
Materials
amount of non-dairy creamer in the water.
• tap water
3. Position the container on the polar graph paper, as shown in the
• clear, semicircular plastic
diagram on the left. The flat edge of the container must be on the
container
horizontal 90°–90° line, with its centre on the 0°–0° line.
• non-dairy creamer or
4. Use the ray box to shine a single light ray toward the centre of
chalk dust
the straight edge, directly along the normal. Record the angles of
• stir stick
incidence, reflection, and refraction.
• ray box
5. With the light ray directed toward the centre of the straight edge,
• polar graph paper
increase the angle of incidence by increments of 5°. Record the
angle of reflection and the angle of refraction. Note the brightness
of the reflected and refracted rays relative to each other.
6. When the angle of incidence results in a refracted ray that is close
to the flat edge of the container, increase the angle of incidence by
increments of 1°. Record the critical angle and your observations
rays from when the angle of incidence is greater than the critical angle.
ray box

Analyze and Interpret

1. Does the incident ray bend when it enters the curved side of the
plastic container? Explain your observation.
2. What is the critical angle for light travelling from water into air?
R What is the angle of refraction at the critical angle?

Conclude and Communicate

semicircular 3. What happens when the angle of incidence is greater than the
container critical angle?
The curved side of the semicircular
Extend Your Inquiry and Research Skills
plastic container must face toward
the light source. 4. Inquiry Design a periscope that uses prisms and total
internal reflection.

480 MHR • Unit 4 Light and Geometric Optics

Chapter 11 Summary

11.1 Refraction of Light

Key Concepts
• Light rays refract when they cross a boundary between • The index of refraction of a medium is
media in which the speeds of light are different. the ratio of the speed of light in a vacuum
• If a light ray goes from a medium in which its speed is to the speed of light in the medium. A ratio
higher (such as air) into a medium in which its speed greater than 1 results.
is lower (such as water), the refracted ray bends toward • Dispersion is the separation of the various colours of light
the normal. when white light crosses the boundary between different
• If a light ray goes from a medium in which its speed is media at an angle.
lower (such as water) into a medium in which its speed • The speed of each wavelength of light is different in any
is higher (such as air), the refracted ray bends away given medium. The speed of all wavelengths of light is
from the normal. 3.00 × 108 m/s in a vacuum.

11.2 Partial Refraction and Total Internal Reflection

Key Concepts
• When light strikes a boundary between two transparent Therefore, an angle of incidence that
media that have different indices of refraction, some light results in a 90° angle of refraction is
reflects off the boundary and some light refracts through eventually reached. This angle of incidence is
the boundary. This phenomenon is called partial reflection called the critical angle.
and refraction. • When the angle of incidence is larger than the critical
• At a small angle of incidence, more light refracts than angle, no refraction occurs. All the light is reflected
reflects. As the angle of incidence increases, more and from the boundary. This phenomenon is called total
more light reflects than refracts. internal reflection.
• When light travels from a medium with a higher index of • Total internal reflection has many practical applications,
refraction to a medium with a lower index of refraction, the such as binoculars, retroreflectors, and optical fibres in
angle of refraction is larger than the angle of incidence. telecommunications and in surgical instruments.

11.3 Optical Phenomena in Nature

Key Concepts
• A rainbow is formed by the refraction and total internal • Shimmering is the apparent movement of
reflection of light and the resulting dispersion of the light objects seen through air that is unevenly
by spherical water droplets in the sky. heated and moving.
• As a result of the refraction of light at the surface of • A mirage is the appearance of water or another
water, objects under the water are not where they appear object that is not really there. A mirage is caused by light
to be when you are looking at them from above the being continuously refracted by layers of air that are at
water. The level at which they appear to be is called their extremely different temperatures.
apparent depth.

Chapter 11 Refraction • MHR 481

Chapter 11 Review
11. When light crosses the boundary between
Make Your Own Summary two substances that have different indices of
Summarize the key concepts of this chapter using refraction, what determines the amount of
a graphic organizer. The Chapter Summary on the refraction that will occur compared with the
previous page will help you identify the key concepts. amount of reflection?
Refer to Study Toolkit 4 on pages 565–566 to help
you decide which graphic organizer to use. 12. A light ray is travelling from a medium with
a larger index of refraction to a medium with
a smaller index of refraction. Describe what
Reviewing Key Terms happens as the angle of incidence gets larger
1. The ratio of the speed of light in a vacuum to and larger. Include the concept of the critical
the speed of light in a medium is the angle in your discussion.
of the medium. (11.1) 13. The colours of light can be separated
2. is the separation of white with a prism. What property of light makes
light into its colours. (11.1) this possible?

3. The angle of incidence for which the angle of 14. Use a Venn diagram to show the similarities
refraction is 90° is called the . and differences between sundogs and rainbows.
(11.2) 15. Imagine that you are standing in the shallow
4. is the apparent movement of end of a swimming pool. You look ahead, at the
objects seen through hot air over objects and bottom of the pool, and see a coin. Describe the
surfaces. (11.3) difference between where the coin appears to be
and where it actually is.
5. When you think that you are seeing an object
but it is not really there, you are seeing a Thinking and Investigation T/I
. (11.3)
16. A clear plastic cube, with exactly the same
index of refraction as water, is placed in a
Knowledge and Understanding K/U
container of water. Would you be able to see the
6. Explain what happens to a light ray when it plastic cube in the water if you looked at it from
goes from air into water at an angle. an angle? Explain why or why not.
7. The speed of each colour (wavelength) of light 17. Complete the following calculations. Refer to
is different in any given medium. How, then, Table 11.1 on page 454 when necessary.
can a specific index of refraction be reported for
a. The speed of light in a solid is 1.96 × 108 m/s.
a certain substance, such as quartz?
Calculate the index of refraction for the solid.
8. Draw a simple diagram of a light ray travelling b. Calculate the speed of light in diamond.
from one medium into another. Include the
c. Calculate the speed of light in ethyl alcohol.
following labels: incident ray, normal, refracted
ray, angle of incidence, angle of refraction. d. The speed of light in a solid is 1.56 × 108 m/s.
Calculate the index of refraction, and
9. How would you predict whether an angle of identify the solid.
refraction is larger or smaller than the angle
of incidence? 18. Why is a small critical angle desirable for
optical fibres? What problems could be caused
10. What information must be included in a table if the critical angle were increased?
that lists indices of refraction? Why must this
information be present?

482 MHR • Unit 4 Light and Geometric Optics

19. The following diagram shows a beaker that 24. Using a sketch, explain how a retroreflector
contains water and cooking oil. The oil has a can reverse the direction of a light ray.
higher index of refraction than the water. A light
25. Imagine that you and a friend are hiking across
ray is about to enter the cooking oil. Copy the
a hot desert. Your friend believes that he sees
diagram, and show the refracted ray in the oil
a pool of water and starts to run toward the
and then in the water. Ignore the reflected rays.
water. How could you convince your friend
not to exert himself unnecessarily? In your
explanation, include a description of the
different indices of refraction of the layers of air
of different temperatures.
26. In the following diagram, wave fronts are
oil
Use this diagram travelling across the boundary between air and
for question 19.
water water. Explain the significance of the change
in the distance between the wave fronts where
the light passes from air into water. Draw a
similar diagram, but have the light approaching
20. Some of the astronauts who landed on the the boundary along a normal, so the angle
Moon placed retroreflectors there like the one of incidence is zero. Show and explain what
shown below. What properties of light would happens when the wave fronts are parallel to
you have to know and use if you wanted to the boundary as the light crosses the boundary.
determine the exact distance between Earth
and the Moon? incident normal
light ray

light
wave fronts

air
water

refracted
light ray
This retroreflector is on the Moon.
27. Review your observations for Activity 11-1,
21. Review Investigation 11-D. The method you
The Re-appearing Coin, on page 447. Based on
used to determine the critical angle of water what you have learned in this chapter, explain
only works for some liquids. Explain how your observations.
you could determine the critical angle of a
flat piece of glass. Application A

28. Identify two careers related to optics from

Communication C
this chapter.
22. Society has benefited from the
development of a range of optical 29. Astronomers can learn a lot about stars by
devices and technologies. Give two examples. studying the wavelengths of light that are
emitted by stars. Some of the early instruments
23. Using a sketch, explain how a rearview
that were used to analyze starlight contained
mirror can be set for daytime driving and prisms. Explain what you think the function
nighttime driving. of these prisms is.

Chapter 11 Refraction • MHR 483