Question

If a glass plate is placed over VIBGYOR colours, which colours will appear to be least raised ?
(A) Violet
(B) Yellow
(C) Red
(D) Green

Answer 1

Hint: When a glass slab is placed over VIBGYOR colours all the colours get raised to unequal heights.
Find the relationship between Normal shift and wavelength of light used (which depends upon colour of light).

Complete step by step answer:
When a glass slab is placed over VIBGYOR colours all the colours get raised to unequal heights.
When an object is viewed through a glass slab it gets shifted towards the slab. This shift is called a normal shift. The normal shift depends upon the refractive index of the glass slab and its thickness.
$$\text{Normal Shift = t}\left(1-{\displaystyle \frac{1}{\mu }}\right)$$
From the above equation it is clear that smaller the refractive index smaller will be the normal shift. Also, the refractive index is inversely proportional to the wavelength of light used. So we conclude that larger the wavelength, smaller will be the refractive index.. and hence smaller will be the normal shift.
In VIBGYOR, red colour has largest wavelength and violet colour has least wavelength, and thus the normal shift will be least for the red colour and greatest for violet colour. Thus, the red colour will appear to be least raised.

So, the correct answer is “Option C”.

Additional Information:
The relationship between the refractive index of a material and the wavelength of the light is given by Cauchy’s expression:
$$\mu =a+{\displaystyle \frac{b}{{\lambda }^2}}+{\displaystyle \frac{c}{{\lambda }^4}}$$
From the above equation it is clear that refractive index of a material is inversely proportional to the wavelength of light used.

Note:
In VIBGYOR, red colour has the largest wavelength (least frequency) and violet colour has least wavelength (highest frequency).
So we conclude that larger the wavelength, smaller will be the refractive index.. and hence smaller will be the normal shift.