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A beam of light is incident at a polarizing angle on a piece of transparent material of refractive index 6.2. What is the angle of refraction for the transmitted beam?

physical optics - polarization of light
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A beam of light is incident at a polarizing angle on a piece of transparent material of refractive index 6.2. What is the angle of refraction for the transmitted beam?


1 Answer


Solution:

Given,

Refractive index (μ) = 1.62,
The angle of refraction (r) =?
If θp be the polarizing angle, then

\(\tan\left(\theta_p\right)=\mu\)
Or, \(\theta_p=\tan^{-1}\left(\mu\right)\)
Or, \(\theta_p=\tan^{-1}\left(1.62\right)\)
Or, \(\theta_p=58.3^\circ\)

Again, 

\(\theta_p+r=90^\circ\)
Or, \(r=90^\circ-\theta_p\)
Or, \(r=90^\circ-58.3^\circ\)
∴ r = 31.7°

Hence the required angle of refraction for the transmitted beam is r = 31.7°

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