Question

Refractive index of a medium _________ with increase in wavelength of light.
(A) Increases
(B) Decreases
(C) Remains same
(D) Can't say

Answer 1

Hint: When white light passes through a prism, the violet light bends the most and red light bends the least.

Complete step by step solution:
According to cauchy’s relation between refractive index and wavelength of light.
$\mu = A + \dfrac{B}{{{\lambda ^2}}}$
Where μ denotes the refractive index of the medium, and λ denotes the wavelength of light.
Here A and B are constants, which depend on the material through which light is passing.
From this relation, it is clear that when λ increases, the value of the refractive index will decrease.

Therefore, the correct answer to the question is option : B

Additional information:
Like Cauchy’s relation, there are other scientists who have given the relation between refractive index and wavelength based on other constants. All such relations denote the same result, that the refractive index of any material decreases with increase in wavelength of light passing through it. This is true for the whole spectrum i.e. Infrared light, visible light, ultraviolet light, X rays, microwaves etc.
When we talk about visible light, the wavelength of red light is highest and wavelength of violet light is the lowest. The wavelength increases as we move along “V I B G Y O R”, in which each letter symbolizes a colour. Hence refractive index will decrease as we move along “V I B G Y O R”. Due to high refractive index, violet light bends the most and due to low refractive index red light bends the least on passing through a prism.

Note: For simplicity, we can consider that refractive index of a material is inversely proportional to the wavelength of light, $\mu \propto \dfrac{1}{\lambda }$, and then derive the increase or decrease of refractive index through this relation.