The refracting angle of a prism is A, and refractive index of the material of the prism is cot (A/2). The angle of minimum deviation is [2015]

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Solution

Q.
The refracting angle of a prism is A, and refractive index of the material of the prism is cot (A/2). The angle of minimum deviation is [2015]

1 90° − A

2 180° + 2A

3 180° − 3A

4 180° − 2A

Ans.
(4)

As $μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})} or \cot \frac{A}{2} = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})}$

$\frac{\cos (\frac{A}{2})}{\sin (\frac{A}{2})} = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})} or \sin (\frac{π}{2} - \frac{A}{2}) = \sin (\frac{A}{2} + \frac{δ_{m}}{2});$

$\frac{π}{2} - \frac{A}{2} = \frac{A}{2} + \frac{δ_{m}}{2}$ $∴ δ_{m} = π - 2 A = 180 ° - 2 A$

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