Question

A ray of light traveling in the air has wavelength \[\lambda \] frequency n, velocity v, and intensity I. If this ray enters the water, then these parameters are \[{\lambda ^1}\],\[{{\rm{n}}^{\rm{'}}}\],\[{v^1}\] and \[I^1\] respectively. Which relation is correct?
A. \[\lambda = \lambda \]
B. \[n = {n^1}\]
C. \[v = v\]
D. \[I = I\]

Answer 1

Hint: Before we start addressing the problem, we need to know about what data has been provided and what we need to solve. Here they have given the wavelength, frequency, velocity, and intensity of a light ray traveling in the air. Then when it enters water these parameters will change, then we need to find the correct relation between them. Refraction is defined as the bending of light rays when it travels from one medium to another.

Formula used:
Expression of frequency is,
\[n = \dfrac{{{v_m}}}{{{\lambda _m}}}\]
Where, $v_m$ is the velocity in medium and $\lambda _m$ is the wavelength in medium.

Complete step by step solution:
We know that when the light travels from one medium to another medium the frequency will not change; it remains the same which means that frequency does not depend on the medium. By the equation of frequency we have,
\[n = \dfrac{\text{velocity in medium}}{\text{wavelength in medium}}\]
\[\Rightarrow n = \dfrac{{{v_m}}}{{{\lambda _m}}}\]

For air we have,
\[n = \dfrac{v}{\lambda }\] …… (1)
For water we have
\[{n^1} = \dfrac{{{v^1}}}{{{\lambda ^1}}}\] …... (2)
If we equate the equation (1) and (2) we get,
\[n = {n^1} = \dfrac{v}{\lambda } = \dfrac{{{v^1}}}{{{\lambda ^1}}}\]
\[ \therefore n = {n^1}\]
From this we can say that the frequency doesn’t change when it travels from one medium to another. Therefore, the frequency remains the same.

Hence, option C is the correct answer.

Note:When light enters from one medium to another medium there is a change in speed of light, this is the cause of refraction. When the light goes from air into water, it starts bending towards the normal because there is a reduction in its speed, that is, for a given frequency of light, the wavelength is proportional to the speed of a wave.