Refraction of Light through Plane Media

• Straight things often look bent whey they stand in water. The science behind

this illusion is called refraction. Light rays usually travel in straight lines, but

when they pass from one material to another they can bend. This happens

because light travels at different speeds in different materials (medium). For

example, when light moves from water to air, it changes speed and bend in a

new direction. This can make an object in water appear to be in a different

position

• Therefore; Refraction of light – Is the process by which the direction of a

ray of light changes when passes obliquely from one medium into another

• It is possible to observe refraction through a “set up” of the type described

below

Activity 1

• Take two coins and place one coin at the bottom of a beaker and another

alongside the beaker, now half fill the beaker with water.

• Next observe the two coins by looking vertically downwards from the beaker

Question

What do you observe about the position of the coin in the beaker compared with the

coin kept alongside the beaker?

 The coin in the beaker appears to be “raised up” with respect to the coin

alongside the beaker

Activity 2

• Dip a pencil in a glass of water at about 45⁰to the surface of the glass.

• Examine the appearance of the pencil when viewed at an angle to the surface

of the glass

Question

What do you observe about the appearance and shape of the pencil?

 The pencil appears “bent” near the surface of water due to change of direction

of rays of light at the boundary between water and air as shown above

All of the above activities (and many other similar phenomenon) can be easily

understood in terms of refraction of light

Angle of incidence and angle of refraction

• The angle of incidence is the angle between a ray of light which hits the

surface and the normal line. The ray of light is called the incident ray.

• The angle of refraction is the angle between the refracted ray and the normal

line. (see the figure below)

Laws of Refraction

When a beam of light travels from two medium then it follows two laws of refraction.

The laws state that: -

1. “At the point of incidence, the Incident ray, the normal and the refracted

ray all lie in the same plane”

2. The ratio between the Sine of the angle of incidence and Sine of the angle of

refraction is constant to the interference of the medium

Refractive Index (index of refraction)

• As described above, when light is traveling from air into another medium Snell’s

Law states the relationship between the angle of incidence and angle of

refraction is governed by the constant,

• Where

is the angle of incidence,

is the angle of refraction, and is the ratio

of the two Sines and is called the index of refraction or the refractive index.

• The index of refraction is also related to the relative speeds of light in a vacuum

and in the medium. That is called an absolute index of refraction that can be

measured for each material.

• For a light ray passing from a medium with refractive index

to a medium with

refractive index,

by

the angle of incidence

is related to the angle of refraction,

• When a light ray moves from air to a denser medium, the value of

can be

taken as approximately equal to 1. We can then write Snell’s law as

• Whereby

is the refractive index of the denser medium

• Therefore, Refractive index between air and the medium is given by

Worked Examples:

1. A ray of light travels from water to glass. What will be the angle of refraction in

glass if the angle incidence in water is 20⁰? If the refractive index of the glass

is 1.5 Soln:

Given:

= 20⁰

= ?

From:

,

2. What is the constant value if the angle of incidence is 50° and the angle of

refraction is given to be 30°?

Solution; From;

3. A ray of light travels from water to glass. The refractive index of water is 1.3 and

that of glass is

1.5. The angle of incidence is 60⁰. What would be the angle of refraction?

0

Solution; given

,

From;

, 48.63⁰



NB:

• Any material has its own refractive index due to the fact that each has

individual optical density

• When light rays pass through rarer to a denser medium, the light rays

bend towards the normal. Due to this the angle of refraction is smaller than

the angle of incidence. e.g. In the case when light rays pass from air to water

or from air to glass, it bends towards normal. It is because of the reason that

the speed of light rays reduces while passing from air to glass or water.

• When light rays pass from denser to rarer medium, the light rays bend

away from the normal. Due to this the angle of refraction becomes more than

the angle of incidence. e.g. In case when light rays pass from water to air or

glass to air, light rays bend away from the normal. The speed of light rays

becomes greater while passing from glass or water to air.

• The speed of light in a medium is low if the refractive index of the medium is

high and vice versa.

Refractive Index of Different Medium

Medium

Refractive Index Medium

Refractive Index

Diamond

2.417 Air (at s.t.p) 1.00029

Ethyl alcohol

Glass/crown

Quartz

1.360

1.520

1.553

1.333

Glycerin

Paraffin

1.47

1.44

Crown(flint) 1.65

Ice 1.31

Water (200⁰C)

Principle of Reversibility of Light

 The principle of reversibility of light states that the paths of light rays can

be reversed

 If the refractive index for a ray of light moving from air (a) to glass (g) is

represented as 풂휼_품and the refractive index for a ray moving from glass to air is

represented as 품휼_풂, then by principle of reversibility of light:

ퟏ

품휼_풂

=

풂휼

품

For Example;

The refractive index for a ray of light travelling from air to water is 1.33. What is the

refractive index for a ray travelling from water to air Answer:

Given: 풂휼_풘= 1.33

From:

Calculating the Refractive index by the real and apparent depth method

• We see the objects closer than their real depth to the surface. We see objects

only if the rays coming from them reaches our eyes. In the figure below, ray

coming from the object O reaches the observer’s eye after refraction. Thus,

observer sees the image of the object at the distance AI from the surface which

is the apparent depth of the Object. This is the result of the refraction of light.

• Consider a point object O kept at the bottom of a transparent medium (such as

water or glass) separated from air by the surface PQ.