Optics Question 452

Question: A prism of refractive index $ \mu $ and angle A is placed in the minimum deviation position. If the angle of minimum deviation is A, then the value of A in terms of $ \mu $ is

Options:

A) $ {{\sin }^{-1}}( \frac{\mu }{2} ) $

B) $ {{\sin }^{-1}}\sqrt{\frac{\mu -1}{2}} $

C) $ 2{{\cos }^{-1}}( \frac{\mu }{2} ) $

D) $ {{\cos }^{-1}}( \frac{\mu }{2} ) $

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Given $ {\delta _{m}}=A, $ as $ \mu =\frac{\sin ( \frac{A+{\delta _{m}}}{2} )}{\sin ( \frac{A}{2} )} $

$ \Rightarrow \mu =\frac{\sin ( \frac{A+A}{2} )}{\sin ( \frac{A}{2} )}=2\cos \frac{A}{2} $

$ \Rightarrow A=2{{\cos }^{-1}}( \frac{\mu }{2} ) $



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