Question

When a ray of light enters from air to water, then its wavelength
(A) Decreases
(B) Increases
(C) Remains unchanged
(D) Becomes infinity

Answer 1

Hint : To solve this question, we need to use the formula for the refractive index of a medium in terms of the speed of light in that medium. Then substituting the speed of light in terms of its wavelength and frequency, we will get the final answer.

Formula used: The formulae for used to solve this question are given
 $ \mu = \dfrac{c}{v} $ , here $ \mu $ is the refractive index of a medium in which the speed of light is $ v $ , and $ c $ is the speed of light.
 $ v = \lambda \nu $ , here $ v $ is the speed of a wave of $ \lambda $ wavelength and $ \nu $ is the frequency of the wave.

Complete step by step answer
We know that the refractive index of a medium is given by
 $ \mu = \dfrac{c}{v} $ .................................(1)
Now, we know that light is an electromagnetic wave. So the velocity is given by
 $ v = \lambda \nu $ .................................(2)
Substituting (2) in (1) we have
 $ \mu = \dfrac{c}{{\lambda \nu }} $
Or
 $ \lambda = \dfrac{c}{{\mu \nu }} $
The velocity of light in vacuum is constant. Also the frequency of the light does not change with medium. So we can write
 $ \lambda \propto \dfrac{1}{\mu } $ .................................(3)
Now, according to the question the ray of light is entering from air to water. We know that the refractive index of water is more than that of the air. So from (3) the wavelength of light in water must be less than that in the air.
So the wavelength of light will decrease when it enters from air to water.
Hence, the correct answer is option A.

Note
We might think as to why the frequency of light remains constant in every medium. This is due to the fact that the frequency of the light depends on the energy with which the light is being emitted. Since the energy does not change with the medium so the frequency is constant.