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

^{∘}×3×10^{8}⇒v=2.12×10

^{8}Therefore, speed of light in the medium is 2.12×10

^{8}m s^{−1}.(ii) We know that the critical angle of the medium depends on its refractive index which is given by

The refractive index

`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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