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Background

In earlier topics, we learnt that light is a form of energy which travels in a straight line. Light is also reflected when it strikes a smooth surface. In this topic, we are going to learn what happens when light travels from one medium to another.

Objectives

By the end of this topic, you should be able to:

-Describe refraction of light

-Explain total internal reflection and its effects

-State the applications of total internal reflection

-Describe experiments to illustrate dispersion of white light













Introduction

When you put a cooking stick in water, it appears bent. A swimming pool appears shallower than it actually is when viewed by an observer from above. When there is a drizzle and the sun shines at the same time, the rainbow appears. These are some of the phenomena that do occur due to refraction of light when it passes through different media. Click the play button to see some of these phenomenon.

Refraction

The animation below shows a ray of light crossing an air-glass interface (boundary). Play the animation below and observe what happens to the ray before and after crossing the boundary.

Discussion

When a ray of light travels from a less optically dense medium to a more optically dense medium, it bends towards the normal due to change in the speed of light across the boundary. This bending of light is referred to as refraction. Snell's law states that sin i/sin r is equal to a constant for all angles of incidence and their corresponding angle of refraction for a given pair of media. Therefore the ratio of the sine of angle of incidence, i to the sine of the angle of refraction, r, is known as the refractive index,N.

N =sin i/sin r also, the ratio of velocity of light in air, c, to velocity of light in glass, v is the refractive index, N.

N = c/v where v is the velocity of light in the material medium.

Critical angle
When light travels from an optically denser medium to an optically less dense medium, it is refracted. The animation below shows what happens when the angle of incidence is varied. Play the animation by increasing the angle of incidence until the angle of refraction is 90o.


Observation
When the angle of incidence was increased to 42o,the ray was refracted with an angle of refraction equal to 90o.

Discussion

If we apply the Snell's law in this case, we have;

gNa = sin C/sin90o = sin C/1

gηa = sin C.............................................i From the principle of reversibility of light aηg = sin90o/sin C

aηg = 1/sin C...........................................ii

From i and ii, we've gηa = 1/ aηgwhere aηg refer to refractive index of glass when the ray travels from air to glass. gηa is the refractive index of the glass when the ray travels from glass to air.
Conclusion
Critical angle is the angle of incidence in the optically denser medium whose angle of refraction is 90o
. It is denoted by C.

Total internal reflection

A ray of light travelling from a medium of higher refractive index to one of lower refractive index will not undergo refraction at every angle of incidence. The animation below shows what takes place when the angle of incidence is: (i) equal to the critical angle and (ii) greater than the critical angle. Play the animation to observe the ray's behavior in both cases.

Discussion

We learnt that when the angle of incidence, i is equal to the critical angle, C, of glass-air boundary, the refracted ray moves along the boundary. When the critical angle, C, is exceeded, there will be no refraction but the ray will be totally internally reflected.

Application of total internal reflection

The following are some of the applications of total internal reflection:

  • Prism periscope
  • Optical fibre

Prism periscope

Periscopes are used to see over the top of an obstacle. A prism periscope consists of two right angled isosceles prisms. It produces a virtual, upright image. Play the animation below to see how this device works.

Optical fibre

This is a flexible transparent cable used to transmit light energy carrying signals such as images or messages. Inside the cable loss of light energy is prevented by multiple total internal reflections. Play the animation below to see how reflection occurs.

 

N.B. Other than communication systems, optical fibres are also used in medicine to view internal organs of the body.

Dispersion of light

Play the animation below to observe how light is dispersed.


Observation

White light is separated into strips of different colours.

Discussion

White light consists of seven different colours which travel at different speeds in different media other than vacuum. When white light moves from A to B, each of these constituent colours is refracted at different angles due to differences in speed. On passing the second boundary, further deviation takes place as observed and a spectrum of all the seven colours is displayed on the screen.

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