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The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -

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$180 - 2 A$

$90 - 2 A$

$180 + 2 A$

$180 - 3 A$

answer is A.

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Detailed Solution

$\begin{array}{l} μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin \frac{A}{2}} \\ μ = \cot \frac{A}{2} \\ \Rightarrow \sin (\frac{A + δ_{m}}{2}) = \cos \frac{A}{2} \\ δ_{m} = 180 - 2 A \end{array}$

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