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