Questions & Answers

What happens when white light passes through a hollow prism?(A) There is no dispersion and no deviation(B) Dispersion but no deviation(C) Deviation but no dispersion(D) There is dispersion and deviation both

Answer
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Hint : This question can be solved by the understanding of behaviour of light in the different media and the properties of a hollow prism where light encounters two inclined surfaces. We need to consider the medium outside the prism and inside the hollow prism are the same.

Formula Used: In solving this question, the following formula has been used,
$v = \upsilon \lambda$ where $\upsilon$ is the frequency, $v$ is the velocity of light and $\lambda$ is the wavelength of light.

Complete step by step answer
White light consists of several colours with different wavelengths and refractive indices. Upon passage through a prism, white light undergoes dispersion, the phenomenon in which light is separated into its constituent wavelengths of different colours which get refracted differently. These colours are arranged in a definite order according to their speeds in the medium of prism.
$v = \upsilon \lambda$ where $\upsilon$ is the frequency, $v$ is the velocity of light and $\lambda$ is the wavelength of light.
For a hollow prism, when white light is incident on the first wall of the prism, it enters a denser medium with a higher refractive index. As a result, the light will bend towards the normal, that is, it undergoes refraction. White light disperses inside the glass and are separated into constituent colours and the dispersed rays fall on the glass surface parallel to the surface the white light is first incident on. There is no deviation, but only dispersion in this case. Inside the prism, which is hollow, the media is the same as that, outside the prism. The light rays on leaving the prism surface enter a lighter medium and bend away from the normal. Again, when the light enters a denser medium, the slab surface on the opposite side, light rays bend towards the normal. The light rays bend away from the normal when they emerge out of the denser medium of the second slab.
$\therefore$ The net result is that there is neither any effective dispersion nor any evident deviation.
So the correct answer is option A.

Note
This problem can also be solved in another way. In a hollow prism, the inside of the prism is filled with air, thus resulting in the same external and internal media separated by the prism surfaces. Thus, the refractive index is the same on both sides of the prism surface. Light encounters two inclined walls, each of which behaves like a thin slab. All the colours travel with the same speed in the air inside a hollow prism. Under such circumstances, no dispersion can occur.
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