Contents
Physics Topics can also be used to explain the behavior of complex systems, such as the stock market or the dynamics of traffic flow.
State the Cause of Refraction and Dispersion of Light Through the Prism
We have already studied the refraction of light through a rectangular glass slab. In a rectangular glass slab, the emergent light rays are parallel to the incident light rays because the opposite faces of a rectangular glass slab (where refraction takes place) are parallel to one another. We will now discuss the refraction of light through a glass object whose opposite faces (where refraction takes place) are not parallel to one another.
A triangular glass prism is such an object. A triangular glass prism is shown in Figure (a). The triangular glass prism is a transparent object made of glass having two triangular ends and three rectangular sides (or rectangular faces). Please note that the opposite faces of a triangular glass prism are not parallel to one another.
For example, in Figure (a), the opposite faces of the glass prism F1 and F2 (where the refraction of light takes place) are not parallel to one another. They are inclined at an angle to one another. The angle between its opposite faces is called the angle of the prism.
In Figure (a), angle QPR is the angle of this prism. Though an actual triangular glass prism looks like that shown in Figure 19(a), but for the sake of convenience in drawing ray-diagrams, a triangular glass prism is represented by drawing a triangle as shown in Figure (b). Please note that a ‘triangular glass prism’ is usually called ‘glass prism’ and sometimes even just ‘prism’.
As we will study after a while the refraction of light on passing through a glass prism is different from that in a glass slab. This is because in refraction through a glass slab, the emergent ray is parallel to the incident ray but in refraction through a glass prism, the emergent ray is not parallel to the incident ray.
The emergent ray of light in a glass prism is not parallel to the incident ray of light because the opposite faces of the glass prism (where refraction takes place) are not parallel to one another. Actually, in refraction through a glass prism, the emergent ray is deviated from its original direction by a certain angle. And we say that light rays get deviated on passing through a glass prism. We will now study the refraction of light through a glass prism in somewhat detail.
Refraction of Light Through a Glass Prism
When a ray of light passes through a glass prism, refraction (or bending) of light occurs both, when it enters the prism as well as when it leaves the prism. Since the refracting surfaces (PQ and PR) of the prism are not parallel, therefore, the emergent ray and incident ray are not parallel to one another (see Figure). In this case the ray of light is deviated on passing through the prism. Let us see how it happens.
In Figure, a glass prism PQR has been kept on its base QR. A ray of light AB is incident on the face PQ of the prism. The incident ray AB is going from air (rarer medium) into glass (denser medium), so it bends towards the normal BN’ and goes along the direction BC inside the glass prism. Thus, BC is the refracted ray of light which bends towards the base QR of the prism.
When the ray of light BC travelling in the glass prism comes out into air at point C, refraction takes place again (see Figure). Since the ray BC is going from glass (denser medium) into air (rarer medium), so it bends away from the normal MC and goes along the direction CD in the form of emergent ray.
Here also, the emergent ray of light CD bends towards the base QR of the prism. From this discussion we conclude that when a ray of light passes through a prism, it bends towards the base of prism, hi other words, when a ray of light passes through a prism, it bends towards the thicker part of the prism.
If we look carefully at Figure, we will see that the emergent ray CD is not parallel to the incident ray AB. There has been a deviation (or change) in the path of light in passing through the prism. Let us produce the incident ray AB upwards towards the point E by a dotted line.
Now, AE represents the original direction of the ray of light. Similarly, let us produce the emergent ray CD backwards by a dotted line so that it cuts the line AE at point O (see Figure). We can now say that the original direction of the ray of light is AE but after passing through the prism, it deviates from its path and goes in the direction OD.
The angle between incident ray and emergent ray is called angle of deviation. In Figure 20, the angle EOD is the angle of deviation. Please note that it is the peculiar shape (triangular shape) of the glass prism which makes the emergent ray bend with respect to the incident ray.
Dispersion of Light
In the year – 1665, Newton discovered by his experiments with glass prisms that white light (like sunlight) consists of a mixture of seven colours. By saying that white light is a mixture of seven colours we mean that white light is a mixture of lights of seven colours.
Newton found that if a beam of white light is passed through a triangular glass prism, the white light splits to form a band of seven colours on a white screen (see Figure). The band of seven colours formed on a white screen, when a beam of white light is passed through a glass prism, is called spectrum of white light.
The seven colours of the spectrum are : Red, Orange, Yellow, Green, Blue, Indigo, and Violet. The seven colours of the spectrum can be denoted by the word VIBGYOR where V stands for Violet, I for Indigo, B for Blue, G for Green, Y for Yellow, O for Orange and R for Red.
In Figure, a beam of white light AB is passed into a glass prism PQR. This beam of white light splits on entering the glass prism and forms a broad patch of seven colours on a white screen S placed on the other side of the prism.
Please note that when the glass prism is kept on its base as shown in Figure, then the red colour is at the top and violet colour is at the bottom of the spectrum.
The splitting up of white light into seven colours on passing through a transparent medium like a glass prism is called dispersion of light. The formation of spectrum of seven colours shows that white light is made up of lights of seven different colours mixed together. That is, white light is a mixture of seven colours (or seven coloured lights).
The effect of glass prism is only to separate the seven colours of white light. A similar band of seven colours is produced when a beam of white light from an electric bulb falls on a triangular glass prism. We can explain the dispersion of light by a glass prism as follows.
White light is a mixture of lights of seven colours : red, orange, yellow, green, blue, indigo and violet. The dispersion of white light occurs because colours of white light travel at different speeds through the glass prism. The amount of refraction (or bending) depends on the speed of coloured light in glass.
Now, since the different colours travel at different speeds, they are refracted (or bent) by different angles on passing through the glass prism (some colours are bent less whereas others are bent more). So, when white light consisting of seven colours falls on a glass prism, each colour in it is refracted (or deviated) by a different angle, with the result that seven colours are spread out to form a spectrum.
The red colour has the maximum speed in glass prism, so the red colour is deviated the least. Due to this the red colour forms the upper part of the spectrum. On the other hand, the violet colour has the minimum speed in glass prism, so the violet colour is deviated the maximum. Due to this violet colour appears at the bottom of the spectrum.
Please note that the seven colours of spectrum differ only in their frequencies. These colours in the order of increasing frequency (but decreasing wavelengths) are : Red, Orange, Yellow, Green, Blue, Indigo and Violet. Any light that gives spectrum similar to that of sunlight is called white light.
Re-Combination of Spectrum Colours to Give White Light
We have just seen that white light can be dispersed into its seven constituent colours. Newton showed that the reverse of this is also true. That is, the seven coloured lights of the spectrum can be recombined to give back white light. This can be done as follows.
A triangular glass prism PQR is placed on its base QR as shown in Figure, and another similar prism P’Q’R’ is placed alongside it in the inverted position on its vertex P’ so that its refracting surface is in the opposite direction.
When a beam of white light is allowed to fall on the first prism PQR, then a patch of ordinary white light is obtained on a screen S placed behind the second prism P’Q’R’ (see Figure). Newton explained these observations as follows.
The first glass prism PQR disperses (splits) the white light into seven coloured rays. The second glass prism P’Q’R’ receives all the seven coloured rays from the first prism and recombines them into original white beam of light which falls on the screen S.
The recombination of seven colours, produced by first prism, is due to the fact that the second prism has been placed in reversed position due to which the refraction produced by the second prism is equal and opposite to that produced by the first prism.
The Rainbow
One of the most beautiful examples of spectrum formed by the dispersion of sunlight is provided by nature in the form of rainbow. The rainbow is an arch of seven colours visible in the sky which is produced by the dispersion of sun’s light by raindrops in the atmosphere (see Figure ).
The rainbow is actually a natural spectrum of sunlight in the sky. The rainbow is formed in the sky when the sun is shining and it is raining at the same time. We can see the rainbow if we stand with our back towards the sun and rain in front of us. A rainbow is always formed in a direction opposite to that of the sun.
A rainbow is produced by the dispersion of white sunlight by raindrops (or water drops) in the atmosphere. Each raindrop acts as a tiny glass prism splitting the sunlight into a spectrum. This will become more clear from the following discussion.
The raindrops in the atmosphere act like many small prisms. As white sunlight enters and leaves these raindrops (or water drops), the various coloured rays present in white light are refracted by different amounts due to which an arch of seven colours called rainbow is formed in the sky.
The formation of rainbow can be explained with the help of a diagram shown in Figure. A ray of white sunlight AB enters the raindrop at point B and undergoes refraction and dispersion to form a spectrum. This spectrum undergoes total internal reflection at point C within the raindrop and finally refracted out of the raindrop at point D (see Figure).
This spectrum produced by the raindrops in the atmosphere is seen from the earth. The red colour of spectrum appears at the top of the rainbow whereas violet colour appears at its bottom.
The formation of seven-coloured rainbow in the sky shows that white sunlight consists of a mixture of seven coloured lights. We can also see a rainbow on a sunny day if we look through a spray of water from a fountain (or through a waterfall) with the sun behind us.