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Wave Optics

Question
CBSEENPH12039880

The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index straight mu, of the prism is, 

  • 2 sin A

  • 2 cos A

  • 1/2 cos A

  • tan A

Solution

B.

2 cos A


From the given above diagram,

angle space MON space equals space 90 space minus space straight A to the power of straight o

So comma space angle space straight r space equals space 90 space minus space left parenthesis 90 space minus space straight A right parenthesis

rightwards double arrow space angle straight r space equals straight A to the power of straight o

Using space Snell apostrophe straight s space law comma
fraction numerator sin space straight i over denominator sin space straight r end fraction space equals space straight mu

fraction numerator sin space left parenthesis 2 straight A right parenthesis over denominator sin space left parenthesis straight A right parenthesis end fraction space equals space straight mu

fraction numerator 2 space sin space straight A space cos space straight A over denominator sin space straight A end fraction space equals space space straight mu

That space is comma

straight mu space equals space 2 space cos space straight A

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