CAPS

Physical Sciences
Grade 11
Waves, Sound & Light I

Geometrical Optics
Copyright of the GMMDC© 2020
Exam Guidelines: Waves, Sound & Light

WAVES, SOUND & LIGHT, is examined in Paper 1 (3 hr)

Exam Weighting -
• 32 marks out of 150 – 21%

Examinable Materials
• Geometrical Optics (Waves, Sound & Light I)
• Refraction, critical angles and total internal reflection
• 2D & 3D Wavefronts (Waves, Sound and Light II)
• Diffraction
 Reflection Review
Reflection may be defined as ..
… the change in direction of a wave/ray at the
boundary between two different media so that the
wave/ray returns into the medium it came from.

Here is some VIT – very important terminology …

A reference line perpendicular to the
angle of incidence the normal reflecting surface at the point of reflection
angle of reflection
incident ray
light approaching reflected ray
a surface or light leaving
boundary (moving away
𝜃𝑖 𝜃𝑟 from) a surface or
Note: the angle of incidence (𝜃𝑖 ) is always boundary
boundary equal to the angle of reflection (𝜃𝑟 ) or interface or
between mediums reflecting surface
The Law of Reflection
There is one further point to be made: the incident ray, the normal
and the reflected ray all lie in the same vertical plane (the PLANE
OF INCIDENCE).

THE LAW OF REFLECTION …

The angle of incidence is equal to the
angle of reflection (𝜃𝑖 = 𝜃𝑟 ), with the
normal, the incident & reflected rays,
all lying on the same vertical plane.

The SPEED OF LIGHT …

• is the speed at which light travels in a particular medium.
• light travels at a constant speed in a particular medium
• the denser the medium, the slower the speed of light in it.
• light travels fastest in a vacuum: at 3×108 m·s-1: this value is
denoted by the symbol c
Some Definitions
REFRACTION
• refraction of light is defined as the change in direction of a
light ray due to a change in speed when light travels from
one medium into the other of different optical density
OPTICAL DENSITY
• optical density is defined as a measure of the refracting
power of a medium. The higher the optical density, the more
the light will be refracted or slowed down as it moves through
the medium.
REFRACTIVE INDEX (n)
• the refractive index (n) of a material is defined as the ratio of
the speed of light in vacuum (c) to the speed of light in a
material (v); as formula: n = c / v
• note that materials with a high refractive index have a high
optical density
 Refraction
Angle of incidence – the Angle of reflection – the angle between the
angle between the incident reflected ray and the normal
ray and the normal
reflected ray – travelling at 3×108
incident ray m·s-1 (note: a percentage of the
– in air, travelling at the incident light will be reflected –
speed of light, c, 3×108 m·s-1 how much depends on the
(the speed depends on air angle of incidence)
the type of medium)
normal
boundary (transparent –
REFRACTION (bending allowing light through)
of light) occurs at
the boundary between glass refracted ray – passing into a denser
two different media medium, the light slows down, and is bent
when light travels from one medium towards the normal. (some of the incident light is
refracted: reflected + refracted light = 100% of incid.
into the other and its speed changes.
Angle of refraction – the angle between the
Note: its speed changes, and its
refracted ray and the normal
wavelength, but not its frequency.
Away From or Towards The Normal
When light crosses a boundary from …
a less dense medium (e.g. air)
a more dense medium (e.g. water, glass), it
• slows down, and is ….
• refracted towards the normal.
When moving in the opposite direction, i.e. from a more dense
to a less dense medium, light will …
• speed up (move faster), and be ….
• refracted away from the normal.

The degree to which light is refracted

depends on the change in the velocity of the
light as it enters a new medium. This is given by a material’s
REFRACTIVE INDEX (symbol 𝒏).
The refractive index is the ratio of the speed of light in a vacuum
(i.e. c = 3×108 m·s-1) to its speed in the material. As formula ….
Refractive Index
where 𝑛 = refractive index (as ratio, it has no units),
𝑐 = speed of light in a vacuum (3×108 m·s-1),
𝒄
𝑛= 𝑣 = speed of light in the given material, also
𝑣 in m·s-1.
The refractive index of a vacuum is equal to 1 (𝑛 = 𝑐 Τ𝑐) (its
smallest value). A higher refractive index indicates that, for that
material, light travels at less than 3×108 m·s-1 through it.
The refractive index can then be used
to compare the speed at which light
travels through various media.
The higher the value of 𝑛, the slower it
travels.
𝑛 is important for calculations.
Optical Density
OPTICAL DENSITY is a measure of the refracting power of a
medium, i.e., the degree to which a medium slows down light
waves relative to the speed of light, c.
• The greater the optical density of a material, the slower light
will move through that medium. It is directly related to the
refractive index for that material.

A light ray being refracted

as it enters a new medium

The light ray is refracted towards the normal, thus the medium it
is entering must have a greater optical density.
Snell’s Law

the ratio of the sin of the angle of incidence in one medium to the
sine of the angle of refraction in the other medium is constant.
As formula:
𝑛1 sin 𝜃1 = 𝑛2 sin(𝜃2 )
where
n1 = refractive index of material 1,
n2 = refractive index of material 2
𝜃1 = angle of incidence, and 𝜃2 = angle of refraction

manipulating Snell’s law …

sin(𝜃1 ) 𝑛2
𝑛1 sin(𝜃1 ) = 𝑛2 sin(𝜃2 ) , ∴ =
sin(𝜃2 ) 𝑛1 Note the
𝑐 𝑐
but since 𝑛1 = 𝑎𝑛𝑑 𝑛2 = subscripts
𝑣1 𝑣2
𝑛2 𝑐 𝑐 𝑐 𝑣1 𝑣1 𝑛2 𝑣1
∴ = ÷ = × = =
𝑛1 𝑣2 𝑣1 𝑣2 𝑐 𝑣2 𝑛1 𝑣2

Now 𝑣 = 𝑓 × 𝜆, and since frequency is unchanged by refraction, ….

Examples of Refraction
𝑣1 = 𝑓 × 𝜆1 and 𝑣2 = 𝑓 × 𝜆2
𝑣1 𝑓 × 𝜆1 𝜆1
Therefore …. ∴ = =
𝑣2 𝑓 × 𝜆2 𝜆 2
sin(𝜃1 ) 𝑛2 𝑣1 𝜆1
= = = Pay close attention to the subscripts – and
sin(𝜃2 ) 𝑛1 𝑣2 𝜆2 the ‘inversion’ of the refractive indexes.

Examples of refraction …
• The spoon appears bent, even broken. The light from the spoon is refracted
more by water than by air, hence the strange appearance of the spoon.
• Wavefronts from a point source in the context of Snell’s law. The region below
the grey line has a higher index of refraction, and proportionally lower speed
of light, than the region above it.
• When air cools over water at night, sound is refracted towards the
ground and so is heard much more clearly than during the day.
Total Internal Reflection
n1 n2 When light crosses a boundary
θi > θc (n2 < n1) into a less dense medium (with
a lower refractive index), it is …
θc refracted away from the normal.
θi normal
As the angle of incidence is
increased …
it reaches a point where the
θr = 90°
angle of refraction is 90°.
The angle of incidence for which
more dense less dense the angle of refraction is 90° is
known as the …
critical angle (θc) When the angle of incidence is increased
even further, the light is reflected off the interface back into the
original medium.
This phenomenon is known as total internal reflection
Definitions …
The relationship between the angles of incidence and refraction for
light moving from one medium to different medium (i.e. with a
different refractive index) is given by SNELL’S LAW …
n1·sin(θ1) = n2·sin(θ2)
The CRITICAL ANGLE (θc) is the angle of incidence in the optically
denser medium for which the angle of refraction in the optically
less dense medium is 90°.
n1·sin(θc) = n2·sin(90°) applies only if n1 > n2

When (i) the angle of incidence > critical angle, and (ii) light moves
towards an optically less dense medium, i.e. n1 > n2
then the light will not leave the first medium, and be totally
reflected …
total internal reflection
Another Diagram

medium 2 (n2 < n1) refracted

rays
interface

medium 1 (n1)
θc
critical angle total internal
source reflection

Note: the refractive index may be calculated using Snell’s law and
the critical angle ..
Alternately, use sin(𝜃1 ) for light moving
1 from a vacuum 𝑛= (or air) to the
𝑛= sin(𝜃2 )
sin(𝜃𝑐 ) medium.
Fibre Optics
The phenomenon of total internal reflection has proved extremely
useful in the field of fibre optics – allowing light to easily travel
through a (not necessarily straight) glass fibre.

An optical fibre is a thin (thinner than a human hair), transparent

“tube” (glass or plastic) that can transmit light. If light enters the
fibre at an angle greater than the critical angle, the light will be
“trapped” or “confined” within the fibre and through total internal
reflection, will be transmitted to the other end.
A very significant advantage of fibre optics for the transmission of
data is that unlike the traditional copper wire, the fibre offers no
(or very little) resistance to the movement of light. Since it is light,
not electric current, moving, a major danger is avoided.
Medical Applications

Fibre optics are also very useful in the

medical field.

In the medical field, an

endoscope is inserted into the
patient’s body and used to do
internal examination.
Some internal operations can also
be performed by pushing an
endoscope through a small incision
(cut) without the need for open
surgery.

A medical examiner using an endoscope to look for

abnormalities in the patient’s airways during a bronchoscopy
Exercises – Understanding: The End

Having studied this section on Geometrical Optics, work through

as many of the associated exercises as possible.
Remember, practice (and more practice) makes perfect.
Where you are uncertain about something, consult with your
teacher, or your classmates. Always try to clarify difficulties as
soon as possible.
And remember too: is
key – the right answer will then take care of itself.