Question

Calculate the speed of light in a medium whose critical angle is 45°. Does critical angle for a given pair of media depend on the wavelength of incident light ? Give reason.

Answer 1

 

(i) According to Snell's Law, we have

`μ=1/sinC                  .....(i)`

where

 C = Critical angle of medium
  μ = Refractive index of the medium

Also,

`μ=c/ν                   .....(ii)`

 

where c=Speed of light in vacuum

  

ν=Speed of light in medium

From (i) and (ii), we have

`c/ν=1/sinC`

⇒v=sinC×c

⇒v=sin45^∘×3×10⁸

⇒v=2.12×10⁸

Therefore, speed of light in the medium is 2.12×10⁸ m s⁻¹.

(ii) We know that the critical angle of the medium depends on its refractive index which is given by

`C=sin−1(1/μ)`

The refractive index μ of a medium is inversely proportional to the wavelength of incident light. So, the critical angle of the medium also depends upon the wavelength of incident light.