Question

The velocity of light in a medium is $1.5\times {{10}^{8}}m{{s}^{-1}}$. What is the refractive index of the medium with respect to air, if the velocity in air is $3\times {{10}^{8}}m{{s}^{-1}}$?
A. 4
B. 3
C. 2
D. 1

Answer 1

Hint: Refractive index ($\mu $) of a medium is that characteristic which decides the speed of light. It is defined as the ratio of the speed of light in vacuum (c) to the speed of light (v) in the given medium i.e. $\mu =\dfrac{c}{v}$. The speed of light in air is almost equal to the speed of light in vacuum.

Formula used:
$\mu =\dfrac{c}{v}$

Complete step-by-step answer:
Speed of light is different in different mediums. If a ray of light passes from one medium to another, the speed of light changes. The medium in which the speed of light is faster is called the rarer medium and the medium in which the speed of light is slower is called denser medium. When the speed of light changes, it also changes its direction and the light appears to be bending at the interface of the mediums. This bending of light is called refraction.
To understand the speed of light in a medium, we have something known as a refractive index. Refractive index ($\mu $) of a medium is that characteristic which decides the speed of light. It is defined as the ratio of the speed of light in vacuum (c) to the speed of light (v) in the given medium i.e. $\mu =\dfrac{c}{v}$.
The speed of light in air is almost equal to the speed of light in vacuum. Therefore, the refractive index of air is one.
Therefore, the refractive index of the given medium is:
$\mu =\dfrac{c}{v}=\dfrac{3\times {{10}^{8}}m{{s}^{-1}}}{1.5\times {{10}^{8}}m{{s}^{-1}}}=2$

Additional Information:
To compare the refractive indices of different mediums we have relative refractive index. When light travels from medium (1) to medium (2) then refractive index of medium (2) with respect to medium (1) is called its relative refractive index and is written as ${}_{1}{{\mu }_{2}}$.
${}_{1}{{\mu }_{2}}=\dfrac{{{\mu }_{2}}}{{{\mu }_{1}}}=\dfrac{\dfrac{c}{{{v}_{2}}}}{\dfrac{c}{{{v}_{1}}}}=\dfrac{{{v}_{1}}}{{{v}_{2}}}$
If ${}_{1}{{\mu }_{2}}$ is the relative refractive index of medium (2) w.r.t medium (1). Then ${}_{2}{{\mu }_{1}}$ is the relative refractive index of medium (1) w.r.t medium (2).

Note: As you can see, the refractive index is the ratio of the speed of the light in vacuum to the speed of light in other mediums. Since, the speed of light in vacuum is the fastest, the ratio will always be greater than one. Therefore, the value of the refractive index ($\mu $) is always greater than one. This fact can help in some questions.