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We,ve studied how light gets refracted through a rectangular glass slab.

For parallel refracting surfaces, as in a glass slab, the emergent ray is parallel to the incident ray.

However, it is slightly displaced laterally. How would light get refracted through a transparent prism? Consider a triangular glass prism.

It has two triangular bases and three rectangular lateral surfaces. These surfaces are inclined to each other. The angle between its two lateral faces is called the angle of the prism. Let us now do an activity to study the refraction of light through a triangular glass prism.

`ul"Activity 11.1"`

♦ Fix a sheet of white paper on a drawing board using drawing pins.
♦ Place a glass prism on it in such a way that it rests on its triangular base. Trace the outline of the prism using a pencil.
♦ Draw a straight line PE inclined to one of the refracting surfaces, say AB, of the prism.
♦ Fix two pins, say at points `P` and `Q`, on the line `PE` as shown in Fig. 11.4.
♦ Look for the images of the pins, fixed at `P` and `Q`, through the other face `AC`.
♦ Fix two more pins, at points `R` and `S`, such that the pins at `R` and `S` and the images of the pins at `P` and `Q` lie on the same straight line.
♦ Remove the pins and the glass prism.
♦ The line PE meets the boundary of the prism at point E (see Fig. 11.4). Similarly, join and produce the points R and S. Let these lines meet the boundary of the prism at `E` and `F`, respectively. Join `E` and `F`.
♦ Draw perpendiculars to the refracting surfaces `AB` and `AC` of the prism at points `E` and `F`, respectively.
♦ Mark the angle of incidence `(∠ i)`, the angle of refraction `(∠r)` and the angle of emergence `(∠e)` as shown in Fig. 11.4.

Here `PE` is the incident ray, `EF` is the refracted ray and `FS` is the emergent ray. You may note that a ray of light is entering from air to glass at the first surface `AB`.

The light ray on refraction has bent towards the normal. At the second surface `AC`, the light ray has entered from glass to air.

Hence it has bent away from normal. Compare the angle of incidence and the angle of refraction at each refracting surface of the prism. Is this similar to the kind of bending that occurs in a glass slab?

The peculiar shape of the prism makes the emergent ray bend at an angle to the direction of the incident ray. This angle is called the angle of deviation. In this case `∠D` is the angle of deviation.

Mark the angle of deviation in the above activity and measure it.


You must have seen and appreciated the spectacular colours in a rainbow.

How could the white light of the Sun give us various colours of the rainbow? Before we take up this question, we shall first go back to the refraction of light through a prism.

The inclined refracting surfaces of a glass prism show exciting phenomenon. Let us find it out through an activity.

`ul"Activity 11.2"`

♦ Take a thick sheet of cardboard and make a small hole or narrow slit in its middle.
♦ Allow sunlight to fall on the narrow slit. This gives a narrow beam of white light.
♦ Now, take a glass prism and allow the light from the slit to fall on one of its faces as shown in Fig. 11.5.
♦ Turn the prism slowly until the light that comes out of it appears on a nearby screen
♦ What do you observe? You will find a beautiful band of colours. Why does this happen?

The prism has probably split the incident white light into a band of colours. Note the colours that appear at the two ends of the colour band. What is the sequence of colours that you see on the screen?

The various colours seen are Violet, Indigo, Blue, Green, Yellow, Orange and Red, as shown in Fig. 11.5. The acronym `"VIBGYOR"` will help you to remember the sequence of colours.

The band of the coloured components of a light beam is called its spectrum. You might not be able to see all the colours separately. Yet something makes each colour distinct from the other. The splitting of light into its component colours is called dispersion.

You have seen that white light is dispersed into its seven-colour components by a prism. Why do we get these colours?

Different colours of light bend through different angles with respect to the incident ray, as they pass through a prism. The red light bends the least while the violet the most.

Thus the rays of each colour emerge along different paths and thus become distinct. It is the band of distinct colours that we see in a spectrum.

Isaac Newton was the first to use a glass prism to obtain the spectrum of sunlight. He tried to split the colours of the spectrum of white light further by using another similar prism.

However, he could not get any more colours. He then placed a second identical prism in an inverted position with respect to the first prism, as shown in Fig. 11.6.

This allowed all the colours of the spectrum to pass through the allowed all the colours of the spectrum to pass through the second prism. He found a beam of white light emerging from the other side of the second prism.

This observation gave Newton the idea that the sunlight is made up of seven colours.

A rainbow is a natural spectrum appearing in the sky after a rain shower (Fig. 11.7). 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 (Fig. 11.8).

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.


You might have observed the apparent random wavering or flickering of objects seen through a turbulent stream of hot air rising above a fire or a radiator. The air just above the fire becomes hotter than the air further up.

The hotter air is lighter (less dense) than the cooler air above it, and has a refractive index slightly less than that of the cooler air.
Since the physical conditions of the refracting medium (air) are not stationary, the apparent position of the object, as seen through the hot air, fluctuates.

This wavering is thus an effect of atmospheric refraction (refraction of light by the earth’s atmosphere) on a small scale in our local environment. The twinkling of stars is a similar phenomenon on a much larger scale. Let us see how we can explain it.

Twinkling of stars

The twinkling of a star is due to atmospheric refraction of starlight. The starlight, on entering the earth’s atmosphere, undergoes refraction continuously before it reaches the earth.

The atmospheric refraction occurs in a medium of gradually changing refractive index. Since the atmosphere bends starlight towards the normal, the apparent position of the star is slightly different from its actual position.

The star appears slightly higher (above) than its actual position when viewed near the horizon (Fig. 11.9). Further, this apparent position of the star is not stationary, but keeps on changing slightly, since the physical conditions of the earth’s atmosphere are not stationary, as was the case in the previous paragraph.

Since the stars are very distant, they approximate point-sized sources of light. As the path of rays of light coming from the star goes on varying slightly, the apparent position of the star fluctuates and the amount of starlight entering the eye flickers the star sometimes appears brighter, and at some other time, fainter, which is the twinkling effect.

Why don’t the planets twinkle? The planets are much closer to the earth, and are thus seen as extended sources.

If we consider a planet as a collection of a large number of point-sized sources of light, the total variation in the amount of light entering our eye from all the individual point-sized sources will average out to zero, thereby nullifying the twinkling effect.

`ul"Advance sunrise and delayed sunset"`

The Sun is visible to us about 2 minutes before the actual sunrise, and about 2 minutes after the actual sunset because of atmospheric refraction. By actual sunrise, we mean the actual crossing of the horizon by the Sun.

Fig. 11.10 shows the actual and apparent positions of the Sun with respect to the horizon. The time difference between actual sunset and the apparent sunset is about 2 minutes.

The apparent flattening of the Sun’s disc at sunrise and sunset is also due to the same phenomenon.