Refraction of Light Through a Prism

1.0Prism (Triangular Prism)

In a triangular prism, there are two triangular base and three rectangular lateral surfaces (refracting faces) [see figure]. These surfaces are inclined to each other at some angle. The angle between its two lateral surfaces is known as the angle of the prism.

Let the incident ray be PQ, QR be the refracted ray and RS be the emergent ray (see figure). The ray PQ enters from air to glass at the first refracting surface AB. The light ray after refraction, bends towards the normal (refracted ray QR). At the second surface AC, the ray QR enters from glass to air and bends away from the normal after refraction. The emergent ray RS is not parallel to the incident ray PQ due to the peculiar shape of prism.

The angle between the incident ray and the emergent ray is called ‘angle of deviation (δ)’.

Dispersion of White Light by a Prism

If a beam of white light is made to fall on one face of a prism, the light emerging out from the other face of prism consists of seven colours namely Violet (V), Indigo (I), Blue (B), Green (G), Yellow (Y), Orange (O) and Red (R). The deviation suffered by the red light is minimum and for the violet light, it is maximum (see figure).

The phenomenon of splitting up of white light into its constituent colours is called ‘dispersion of light’.

The beautiful, sparkling colours produced by ice crystals on a small branch of a tree in winter, the vibrant colours of a rainbow, and the brilliant flashes of colour you see when light passes through diamonds, all these are examples of the phenomenon known as ‘dispersion’.

Reason

The wavelengths of different colours of light are different and the refractive index of glass is different for different wavelengths. Higher the wavelength, lower will be the refractive index and thus, lower will be the deviation and vice-versa. Thus, deviation of red light is low as its wavelength is large. Similarly, deviation of violet light is high as its wavelength is small.

Initially, it was a matter of debate, whether the prism itself creates colours in some way or it only separates the colours already present in white light. Sir Isaac Newton settled the issue by performing a simple experiment. He put another similar prism, but in an inverted position, and let the emergent, separated beam fall on the second prism. The resulting emergent beam was found to be white light (see figure). The first prism separated the white light into its component colours, which were recombined by the inverted prism to give white light. Thus, white light itself consists of colours which can be separated by the prism.

2.0The Rainbow

The rainbow is the nature’s most spectacular display of the spectrum of white light. The required conditions for the appearance of the phenomenon are that Sun be shining in one part of the sky and the rain be falling in opposite part of sky. The observer’s back is towards the Sun.

A rainbow is a natural spectrum appearing in the sky after a rain shower. It is caused by dispersion of sunlight by tiny water droplets, present in the atmosphere. A rainbow is always formed in a direction opposite to that of the Sun. The water droplets act like small prisms. They refract and disperse the incident sunlight, then reflect it internally, and finally refract it again when it comes out of the raindrop. Due to the dispersion of light and internal reflection, different colours reach the observer’s eye. You can also see a rainbow on a sunny day when you look at the sky through a waterfall or through a water fountain, with the Sun behind you.

Rainbow : The sun rays incident on a water drop get refracted twice and reflected internally by a drop.

3.0Atmospheric Refraction 

The refraction of light caused by the earth’s atmosphere due to variable refractive index of air at different zones is called ‘atmospheric refraction’.

Twinkling of Stars

Twinkling of stars can be seen on a clear night. This is due to atmospheric refraction of light coming from the stars (star light). As the star light enters into the earth’s atmosphere, atmospheric refraction takes place due to gradually changing refractive index of the air. Since the physical conditions of the refracting medium (earth’s atmosphere) are not stationary, star light flux (luminous flux) entering the eye of an observer continuously fluctuates. This means luminous energy reaching our eyes per second from the star increases and decreases with time. Thus, the star sometimes appears brighter and at some other times fainter, causing the ‘twinkling of stars’.

Star appears slightly higher than its actual position

As the star light enters the earth’s atmosphere, it undergoes refraction continuously before it reaches the earth’s surface. This refraction occurs due to the gradually changing refractive index of air. As the star light enters from rarer medium to comparatively denser medium, it bends more and more towards the normal as it is reaching the earth’s surface. Thus, the apparent position of a star is slightly higher than its actual position when it is viewed from the earth’s surface. Also, this apparent position is not stationary but it changes with time because of variable physical conditions of the refracting medium (earth’s atmosphere).

Delayed Sunset and Advanced (Early) Sunrise

The sun is visible before actual sunrise and after actual sunset because of atmospheric refraction. Actual sunrise means the ‘sunrise on actual crossing of the horizon by the sun’. The refractive index of air with respect to free space or vacuum is 1.00029 (~1.0003). Due to this, sunlight bends towards the surface of Earth because of refraction. Thus, the sun appears to be raised above the horizon when it is slightly below the horizon (see figure). The apparent shift in the direction of sun is about 1/2° and corresponding time difference between actual and apparent sunrise (or sunset) is about 2 minutes. 

Thus, sun is visible to us about 2 minutes before actual sunrise and about 2 minutes after actual sunset.

Related Questions:

1. In the figure, a white light is incident on a triangular prism. Name the colour which is at third position from the top on the screen.

Explanation

Since the prism as shown in figure is inverted thus, the colour violet is at the top while colour red is at the bottom. So in seven colours starting from top (V I B G Y O R), the colour blue is on third position from the top.

2. Suppose all colours of light are travelling in glass. Which colour has maximum speed in glass? Which colour has minimum speed in glass?

Explanation

We know that in any transparent medium, 

speed of light is given by, $v=\frac{c}{n}$

i.e., $v\propto \frac{1}{n}$

Since, refractive index for red colour is least among the seven colours of light, speed of red colour light is maximum in glass. Refractive index of violet colour is maximum, thus its speed is minimum in glass.