REFRACTION OF LIGHT WAVES

SPECIFIC OBJECTIVES

â€¢ By the end of the lesson, the students should be able to:

â€¢ Explain how the direction of light changes as it travels from one medium to another,

â€¢ Deduce the value of the refractive index of a given material from the measurement of angles of incidence and refraction,

â€¢ State Snell’s law of refraction

â€¢ Trace light rays through a triangular glass prism and obtain graphically the value of the angle of minimum deviation.

REFRACTION OF LIGHT WAVES

The phenomenon of refraction is responsible for: the bottom of a river appearing shallower than it really is and a rod or spoon or pencil appears bent or broken when it’s partially immersed in water. Let us consider a ray of light traveling from a medium A and B.

Fig. the bending of light rays

ANGLE OF INCIDENCE (i):Â is the angle the incident ray makes with the normal to the surface at o.

ANGLE OF REFRACTION (r): is the angle between the reflected ray and the normal to the surface.

Refraction through rectangular glass block or prism

We can study the refraction of light at the air to glass using a rectangular glass prism ABCD is placed horizontally on a thick sheet of paper and the outlines of the prism are drawn with a pencil. Viewing through another side through which the ray was refracted, the angle of emergent emerge.

LAWS OF REFRACTION

1. The incident ray, the refracted ray, and the normal at the point of incidence all lie on the same plane.

2. The ratio of the sine of the angle of incidence to the sine of the angle of refracted is a constant for a given pair of media also known as Snell’s law.

Refractive Index (n) = sin i/ sin r

REFRACTIVE – INDEX(n): it is a number that gives a measure of refraction or bending of light as it travels from one medium to another. If the light is traveling from air to glass,Â it’s given as:

a n g = sine of angle of incidence in air/ sine of angle of refracted in glass

since refraction deals with change in speed and direction as it travels from one medium to another

THE REAL AND APPARENT DEPTH

The depth of a river or swimming pool always appears shallower than it actually is. When a glass block is placed on top of an object e.g. a pin or a mark on a piece of paper, the object appears nearer to the top. This is called APPARENT DEPTH caused by refraction o plane surfaces.

Thus, the real depth is the actual distance between the bottom of the trough and the surface of water. The real depth, apparent depth, and refractive index are related by

N = real depth (D) /apparent depth (d)

Example 1:

What is the real depth of a swimming pool, which appears to be 10m deep when viewed directly from above its surface? Take n = 4/3

Solution

Given that: n = 4/3, d = 10m, thus using that

N = D / d

4/3 = D/10

40 = 3D

D = 40/3 = 13.3m

REFRACTION OF LIGHT USING A TRIANGULAR BLOCK/PRISM

A triangular prism is an optical device or instrument made up of a piece of glass which is combined in such a way that at least one of its cross-sectional areas is triangular. There are various forms of prism like equilateral triangular one, isosceles right angular triangular prism etc. a prism is capable of reflecting light rays. Refer to a physics textbook for a diagram of a triangular glass prism

ANGLE OF DEVIATION: this is the angle between the incidence ray and emergent ray. Angle of deviation varies with the angle of incidence.

Minimum deviation (dm): this occurs when the angle of incidence and the emergent angle are equally inclined to their respective surface i.e. (i = e).

Using the angle of prism (A) and the minimum deviation (m), the refractive index of glass ng =

Ng = sin1/2 (dm + A)/ sin 1/2A

TOTAL INTERNAL REFLECTION

When light travels from an optically denser medium e.g. glass to less denser medium say air, the refraction is such that the refracted ray moves away from the normal. As the i increases, at a certain value of the i, the r would have been normal on the boundary and as such, the r angle is 900. Therefore,when the incidence angle equals the critical angle (C) is 900.

NB: critical angle is the angle of incidence in the denser medium for which the angle of refraction in the less medium is 900. On reversing the direction of light, the angle of incidence becomes 90 and the refracted angle becomes the critical angle (r = c)

Thus, a n g = sin i/sin r

= sin 90/sin C, since sin 90 = 1, then

n = 1/sin C.

If the incidence angle is increased beyond the critical angle, then all the refracted ray would become reflected as shown below:

Refer to physics text book for figure

Mirage formation and short periscope are the applications of total internal reflection. Mirage simply means illusion.

Example 2

What is the critical angle for light travelling from water to air (n of water = 4/3).

Solution

Using that n = 1/sin C

n = 4/3, then

4/3 = 1/sin C

3 = 4sinC

SinC = 3/4 = 0.75

C = Sin 0.75 = 480.

Therefore, a mirage is a natural effect caused due to total internal reflection occurring at the boundary of hot air and cooler air.

SUMMARY

When a ray of light travels from one medium to a denser medium, the ray will be refracted toward the normal. The refractive index of a medium is defined as :

N = sin of i in air/sin of i in glass or vacuum.

Refractive index is a number that gives a measure of refraction or bending of light as it travels from one medium to another.