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 } ) $
Show Answer
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 } ) $
