Optics Question 96
Question: The refracting angle of prism is A and refractive index of material of prism is $ \cot \frac{A}{2} $ . The angle of minimum deviation is
[CPMT 1992]
Options:
A) 180°? 3A
B) 180° + 2A
C) 90° ?A
D) 180° ? 2A
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Answer:
Correct Answer: D
Solution:
By using $ \mu =\frac{\sin \frac{A+{\delta _{m}}}{2}}{\sin \frac{A}{2}} $
$ \Rightarrow $ $ \cot \frac{A}{2}=\frac{\sin \frac{A+{\delta _{m}}}{2}}{\sin \frac{A}{2}} $
$ \Rightarrow \frac{\cos \frac{A}{2}}{\sin \frac{A}{2}}=\frac{\sin \frac{A+{\delta _{m}}}{2}}{\sin \frac{A}{2}} $
$ \Rightarrow $ $ \sin ( 90{}^\circ -\frac{A}{2} )=\sin ( \frac{A+{\delta _{m}}}{2} ) $
$ \Rightarrow {\delta _{m}}=180-2A $
