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  4. 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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Q. 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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Solution:

$\mu=\frac{\sin \left(\frac{ A +\delta_{ m }}{2}\right)}{\sin \frac{ A }{2}}$
$\mu=\cot \frac{ A }{2}$
$\Rightarrow \sin \left(\frac{ A +\delta_{ m }}{2}\right)=\cos \frac{ A }{2}$
$\delta_{ m }=180-2 A$