Question

When light of two colours A and B are passed through a plane boundary, A is bent more than B. Which colour travels more slowly in the second medium?

Answer 1

We know that light undergoes refraction when it travels from one medium to another. Using Snell’s law we also know that the angle of the refracted light also depends on the medium i.e. the refractive index of the medium and in turn also on the nature of the light.

Formula used:
$\mu_{1} sin( i)=\mu_{2} sin( r)$

Complete step-by-step answer:
We know that the ability for light to bend or bounce back when it interacts with a medium is given as the reflection and refraction of light.
Here since the light rays travel from one medium to another, they undergo refraction. Then we can talk about the refractive index of water and air, which describes how fast or slow the light travels in the given medium.
From Snell’s law, we can say that $\mu_{1} sin( i)=\mu_{2} sin( r)$
$\implies \dfrac{sin (i)}{sin (r)}=\dfrac{\mu_1}{\mu_2}=\dfrac{v_2}{v_1}$
where $i$ is the angle of incidence of the light ray from the medium one whose refractive index is given as $\mu_{1}$ and velocity $v_1$, while $r$ is the angle of refraction of the light ray at the second medium whose refractive index is given as $\mu_{2}$ and velocity $v_2$.
Clearly,
$\sin \theta\propto \dfrac{1}{v}$
Which means more the angle made by the light, less the speed.
Here, since the medium is the same, we can say that since A bends more than B, clearly the angle made by A is greater, hence it will move slowly in the new medium as compared to B.

Note: Snell’s law gives the relationship between the angle made by the light, speed of the light and the refractive indices of the medium. Using the above relationship, we can compare and understand various parameters of the light and its properties.