Question

The refractive index of glass is $1.520$ for red light and $1.525$ for blue light. Let ${D_1}$ and ${D_2}$ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then:
(A) ${D_1}$ can be less than or greater than ${D_2}$ depending upon the angles of prism
(B) ${D_1} > {D_2}$
(C) ${D_1} < {D_2}$
(D) ${D_1} = {D_2}$

Answer 1

Compare both the refractive index of the red light and the blue light. Use the formula of the minimum angle of deviation, and find the relation between it and the refractive index. From that link with the refractive index to find the relation of the angle of deviation.
Useful formula:
The formula of the angle of the minimum deviation is given by
$D = \left( {\mu - 1} \right)A$
Where $D$ is the angle of the minimum deviation, $\mu$ is the refractive index of the glass and $A$ is the angle of the prism.

Complete answer:
It is given that the
The refractive index of glass for the red light, ${\mu _r} = 1.520$
The refractive index of glass for the blue light, ${\mu _b} = 1.525$
The angle of the deviation is defined as the angle between the angle of the incidence and the angle of the refraction when the light passes from one medium to the other medium. Let us consider the formula of the angle of the minimum deviation.
$D = \left( {\mu - 1} \right)A$
From the above formula, it is clear that the angle of the minimum deviation is directly proportional to that of the refractive index .
$D \propto \mu$
From the given data, it is clear that the refractive index of the blue light is greater than that of the refractive index of the red light. Since the angle of the minimum deviation is directly related to that of the refractive index, the angle of the minimum deviation of the blue light is greater than that of the red light.
${D_1} < {D_2}$

Thus the option (C) is correct.

Note:
The angle of the minimum deviation mainly depends upon the angle of the incidence of the light, wavelength of the light, apex angle of the prism, cut angle of the prism and the material in which the prism is made up of. Hence the red light deviates less and the violet light deviates more in the rainbow.