12.

5 Total Internal Reflection

When light travels from one medium into another, some of the light is reflected
and some is refracted. As you know, light slows down when it travels from air
into acrylic or water. This results in the light bending toward the normal.
Light, however, bends away from the normal when it speeds up at the
boundary of two media. (An example of this is when light travels from acrylic
into air.) In this situation, the angle of refraction is always larger than the angle of
incidence (Figure 1). In fact, the angle of refraction continues to increase as the
angle of incidence increases. Eventually, the angle of refraction will become 90°.
critical angle the angle of incidence that The angle of incidence at this point is called the critical angle. The critical angle
results in an angle of refraction of 90° is the angle of incidence that produces a refracted angle of 90°.

n1 > n2

air
n2 = 1.00

water
n1 = 1.33

Figure 1 Medium 1 (water) has an index of refraction that is greater than that of medium 2 (air).
So an incident ray in water speeds up as it goes into air.

If you increase the angle of incidence past the critical angle, the refracted
ray will no longer exit the medium. Instead, it will reflect back into the
medium. In other words, the refracted ray disappears; only a reflected ray is
total internal reflection the situation visible. This phenomenon is called total internal reflection (Figure 2).
when the angle of incidence is greater
than the critical angle

LEARNING TIP
Understanding Diagrams
It is often easier to understand a concept
from a diagram than from words. Total
internal reflection is a perfect example
of this. After looking at Figure 2, draw
your own diagrams to illustrate total
internal reflection. Show your diagrams
to a classmate and explain them. Figure 2 Total internal reflection of laser light in water

526 Chapter 12 • The Refraction of Light NEL

 Total internal reflection occurs when these two conditions are met:
1. Light is travelling more slowly in the first medium than in the
second.
2. The angle of incidence is large enough that no refraction occurs in To see some interesting simulations
the second medium. Instead, the ray is reflected back into the first for total internal reflection,

medium (Figure 3). GO TO NELSON SCIENCE

air Ray 1 air Ray 2 air Ray 3

water water water

critical
angle
(a) (b) (c)
Figure 3 Ray 1 is refracted as it passes from water into air. Ray 2 has an angle of refraction of 90°;
the angle of incidence is equal to the critical angle. Ray 3 is reflected internally back into water and does
not go into air. Note that in (a) and (b), some light is reflected internally but not as strongly as in (c).

Water has a critical angle of 48.8°. This means that an angle of incidence
greater than 48.8° would result in total internal reflection in the water. The
critical angle is a physical property of a medium. (Recall that the index of
refraction is another physical property.)

Diamonds Are Forever

One of the features that make diamonds so attractive in jewellery is the fact
that they sparkle. This “sparkling” is due to the cut of the diamond faces,
which, combined with the high index of refraction for diamond (n  2.42),
results in the total internal reflection of light. The high refractive index
means that diamonds have a very small critical angle: 24.4°. So a great deal of
incident light undergoes total internal reflection inside the diamond. A light
To learn more about how
ray can bounce around several times inside the diamond before eventually jewellers and gem cutters use
exiting through a top face of the gemstone (Figure 4(a)). This causes the optics in their work,
“sparkling” effect that makes diamonds so appealing (Figure 4(b)). GO TO NELSON SCIENCE

READING TIP
Evaluating
Examine illustrations and captions
carefully to determine how they increase
your understanding of a text. Make
connections to what you already know
about the topic. For example, you might
have seen pictures of diamonds that
(a) (b) appear to support the explanation for
Figure 4 (a) Many light rays undergo two total internal reflections inside a diamond. why diamonds sparkle.
(b) This is what makes a diamond “sparkle.”

NEL 12.5 Total Internal Reflection 527

 Fibre Optics
Fibre optics is a technology that uses light to transmit information along a
glass cable. The light must not escape as it travels along the cable. To achieve
this, the cable must have a small critical angle so that light entering it will
have an angle of incidence greater than the critical angle. Substances that
have a small critical angle include high-purity glass and special types of
plastics, such as Lucite (Figure 5).

(a) (b)
Figure 5 (a) A laser beam undergoes total internal reflection in a Lucite rod. (b) In close-up,
you can see the point at which total internal reflection occurs.

READING TIP Fibre optics is used extensively in the communications industry for
Evaluating phones, computers, and TVs. Fibre optics also plays a major role in the
Check a text for clues of bias. Are movie industry. Science fiction films sometimes make use of fibre-optic
advantages and disadvantages cables to represent small windows in “giant” spaceships (Figure 6). The
described? If only advantages are given,
automotive industry uses optical fibres to transmit light to the instrument
can you think of any disadvantages? For
example, in a text about the applications panel in cars. As you learned in Chapter 2, medical professionals use fibre-
of fibre optics, does the author treat the optic technologies to see into parts of the human body that would otherwise
topic in a balanced way? Are both pros be inaccessible. An endoscope is a fibre-optic device that allows doctors
and cons described? If not, does the to check the health of various internal organs (Figure 7). The endoscope
text show a bias toward one side of the
consists of two separate fibre-optic bundles. One bundle shines light into the
issue?
body. The second bundle carries the reflected light back to the instrument.
To learn more about careers in A colonoscopy, for example, is now a very common procedure among males
fibre optics, over 50 years of age. In this procedure, doctors use an endoscope to check
GO TO NELSON SCIENCE for growths that could develop into colon cancer.

Figure 6 Light travels along optical fibres and Figure 7 An endoscope is an important fibre-
then emerges at the ends. optic device used for medical diagnoses.

528 Chapter 12 • The Refraction of Light NEL

The Triangular Prism
A triangular prism also exhibits total internal reflection. The critical angle
for glass is about 41.1°. If a prism is oriented in such a way that the angle of
incidence is greater than 41.1°, total internal reflection will result. Prisms
are much more useful to reflect light than mirrors because a prism reflects
almost 100 % of the light internally. Mirrors reflect most incident light
but lose a little through absorption. Also, the silvered surface of mirrors
deteriorates over time. For these reasons, most optical devices, such as
cameras and binoculars, use prisms instead of mirrors. The emergent ray
can be either 90° or 180° relative to the incident ray, depending on the
placement of the prism (Figure 8).

45°
45°
45°
45°

45°
45°

(a) (b)

Figure 8 By changing the orientation of the prism, you can change the direction of the emergent
ray by either 90° or 180°. In (a) the light ray goes through just one reflection. In (b) it goes through
two reflections.

In Chapter 11, you learned that plane mirrors could be used to make
a simple periscope. A more complex periscope uses triangular prisms to
change the direction of light by 90° (Figure 9). Each triangular face has
angles of 45°, 45°, and 90°. A pair of binoculars uses two such prisms to
change the direction of light by 180° (Figure 10).

triangular prisms

prisms

Figure 9 A periscope uses triangular prisms to Figure 10 Binoculars use two triangular prisms
change the direction of light by 90° twice. to change the path of light.

NEL 12.5 Total Internal Reflection 529

 Retro-reflectors and Prisms
retro-reflector an optical device in which A retro-reflector is an optical device that returns any incident light back
the emergent ray is parallel to the incident in exactly the same direction from which it came. The prism orientation in
ray
Figure 8(b) on the previous page is an example of a retro-reflector because
the emergent ray is parallel to the incident ray as a result of two total
internal reflections.
If you cut off the corner of a glass cube, you would produce a corner cube
retro-reflector. This type of retro-reflector has three perpendicular faces (like
the corner of a room) (Figure 11). It will reflect an incident ray coming from
any direction back along its original direction.

Figure 11 (a) and (b) A corner

cube retro-reflector is created by
cutting off the corner of a cube.
(c) The resulting corner cube
retro-reflector after three corners
have been ground down. (a) (b) (c)
(a) (b) (c)

The Laser Ranging Retro-Reflector (LR³ or “LR-cubed”) left on the Moon

by the Apollo 11 astronauts is an example of this type of retro-reflector. The
LR³ is an array of 100 corner cube retro-reflectors set up in a 10 × 10 grid
mounted on a square aluminum panel that is 46 cm long, about the size of
a large pizza box. These 100 corner-cubed prisms on the Moon are made of
quartz. With this device, scientists on Earth have been able to shine a very
powerful laser beam at the Moon and bounce it off the LR³. This enabled
scientists to determine the Earth–Moon distance with an accuracy of 3 cm.
The LR³ is still working, and recent laser measurements have refined the
C12-F31-UDOS10SB.ai
Earth–Moon distance even further, down to within a few millimetres.
You may not have heard of retro-reflectors before, but you have almost
To learn more about the LR³ on
the Moon and retro-reflectors certainly seen them. They are built into bike reflectors and the reflective
in general, strips on clothing and helmets. Road signs also contain tiny retro-reflectors
GO TO NELSON SCIENCE in the paint so that you can see the signs at night (Figure 12).

Ontario Science 10 SB
0-17-635528-6
FN C12-F31-UDOS10SB
CO CrowleArt Group
Deborah Crowle
Pass 3rd pass
Approved
Not Approved

Figure 12 Retro-reflectors on road signs help you see the signs at night.

530 Chapter 12 • The Refraction of Light NEL

 UNIT TASK Bookmark
You can apply what you learned about total internal reflection as you plan what optical
device you will construct for the Unit Task described on page 588.

IN SUMMARY
• The critical angle is the angle of incidence for • Optical devices such as periscopes, binoculars,
which the angle of refraction is 90°. This occurs and fibre-optic cables make use of total internal
only when light passes from one medium into reflection.
another with a lower index of refraction. • A triangular prism, depending on its orientation, can
• Total internal reflection occurs if the angle of change the direction of light by 90° (one total internal
incidence is greater that the critical angle. reflection) or 180° (two total internal reflections).

CHECK YOUR LEARNING

1. What two conditions must be satisfied in order for total
internal reflection to occur? K/U
2. Why does total internal reflection occur only when light
medium A
medium
travels more slowly through the first medium than in medium A
A
the second and not the other way around? Include a ray
diagram with your answer. T/I mediumBB
medium
medium B
3. The critical angle for sapphire is 34.4°. For each angle
of incidence, determine if it would result in total internal
reflection in a sapphire. K/U
(a)
(a) 23.7° (b) 34.7° (c) 53.4° (d) 31.5°
4. What is the advantage of using triangular prisms over
plane mirrors in optical devices requiring the reflection of
light? K/U A
medium A
medium
5. Will you get more total internal reflection with a medium medium A
A
that has a small critical angle or with one that has a large
critical angle? Explain. K/U mediumBB
medium
medium B
6. Brainstorm to create a list of suggestions for using
retro-reflectors to improve road safety on a winding, dark,
country road. A (b)
7. Briefly describe three applications that make use of the
total internal reflection of light. A
8. Figure 13 shows light travelling through two different
media. In which diagrams would total internal reflection be
possible if the angle of incidence were increased? T/I medium A
medium
medium A
A
9. Look again at Figure 13. For each diagram, in which
medium would total internal reflection occur? Explain your
answers. T/I
medium B
medium
medium B
B
(c)

Figure 13

NEL 12.5 Total Internal Reflection 531