Question

The refractive index of glass with respect to air is $\dfrac{3}{2}$. The refractive index of air with respect to glass will be:
${\text{A}}{\text{. 1}} \\\ {\text{B}}{\text{. }}\dfrac{3}{2} \\\ {\text{C}}{\text{. 2}} \\\ {\text{D}}{\text{. }}\dfrac{2}{3} \\\$

Answer 1

The refractive index of a one medium with respect to another can be defined as the ratio of the sine of the angle of incidence in one medium to the sine of the angle of refraction in the second medium. The reverse of this expression gives the refractive index of the second medium with respect to first.

Detailed step by step solution:
The phenomenon of bending of light when it travels from one medium to another is called refraction.
Refraction is governed by two laws of refraction given below:
1. The incident and refracted light ray and the normal drawn perpendicular at the point of incidence, all lie in the same vertical plane.
2. If we take ratio of the sine of the angle of incidence to the sine of the angle of refraction, we get a quantity called the refractive index which decides the amount of refraction of light and is given as
$\mu = \dfrac{{\sin i}}{{\sin r}} = \dfrac{{{\text{Velocity of light in air or vacuum}}}}{{{\text{Velocity of light in a medium}}}}{\text{ }}...{\text{(i)}}$
where $\mu$ is called the refractive index, i is the angle of incidence and r is the angle of refraction.
Now if the refractive index of glass with respect to air is $\dfrac{3}{2}$ then it means that light ray travels from air to glass and velocity of light decreases by a factor of $\dfrac{3}{2}$.
Now if we consider light ray to be travelling from glass to air then velocity of light will increase by a factor of $\dfrac{2}{3}$ therefore, refractive index of water with respect to glass is reciprocal of the given refractive index which is $\dfrac{2}{3}$.
Hence, the correct answer is option D.

Note: The student should note that the refractive index of any medium can never be less than 1 because in equation (i), we can see that no velocity can be faster than the velocity of light which will always give us $\mu \geqslant 1$.