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Calculate the Speed of Light in a Medium Whose Critical Angle is 45° - Physics

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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.

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Solution

 
(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 s1.
(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.
 
Concept: Snell’s Law
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