Question

State the laws of refraction of light. If the speed of light in vacuum is $3\times {10}^{8}m{s}^{-1}$, find the speed of light in a medium of absolute refractive index 1.5

Answer 1

(a) There are two laws of refraction:

First law of refraction:
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This is known as Snell's law. Mathematically, it can be expressed as:
$\frac{sini}{sinr}=n_{12}$
Here, $n_{12}$ is the relative refractive index of medium 1 with respect to medium 2.

Second law of refraction:
The incident ray, the refracted ray and the normal to the interface of two media at the point of incidence lie on the same plane.
If a light ray goes from medium 1 to medium 2, then the refractive index of medium 1 with respect to medium 2 is expressed as
Here, $v_1$ and $v_2$ are the speeds of light in medium 1 and medium 2, respectively.

(B)
Given:
Speed of light in vacuum = $3\times 108m{s}^{-1}$
Refractive index of the medium:
$n_m=\frac{Speedoflightinvacuum}{Speedoflightinmedium}\Rightarrow 1.5=\frac{3\times {10}^8}{v}\Rightarrow v=\frac{3\times {10}^8}{1.5}=2\times {10}^{8}m/s$
Hence, the speed of light in the medium of refractive index 1.5 is 2 $\times$ 108 m/s.