Optics Question 97

Question: A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If m is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is

[EAMCET 2003]

Options:

A) $ {{\sin }^{-1}}( \frac{1}{\mu } ) $

B) $ {{\tan }^{-1}}( \frac{1}{\mu } ) $

C) $ {{\sin }^{-1}}( \frac{\mu -1}{\mu } ) $

D) $ {{\cos }^{-1}}( \frac{1}{\mu } ) $

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Answer:

Correct Answer: D

Solution:

If $ \alpha $ = maximum value of base angle for which light is totally reflected form hypotenuse. $ (90{}^\circ -\alpha ) $ = C = minimum value of angle of incidence at hypotenuse for total internal reflection $ \sin (90{}^\circ -\alpha )=\sin C=\frac{1}{\mu } $

$ \Rightarrow \cos \alpha =\frac{1}{\mu } $

$ \Rightarrow \alpha ={{\cos }^{-1}}( \frac{1}{\mu } ) $



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