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The refracting angle of a prism is $A$ and the refractive index of the material of the prism is $\cot (A / 2)$. The angle of minimum deviation of the prism is
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$\pi-2 A$
$\begin{array}{rlrl} & \mu=\cot \frac{A}{2}=\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin A / 2} \\ & \text { or } \frac{\cos \frac{A}{2}}{\sin \frac{A}{2}} =\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin \frac{A}{2}} \\ & \text { or } \sin \left(90^{\circ}-\frac{A}{2}\right) =\sin \left(\frac{A+\delta m}{2}\right) \\ & \text { or } 90^{\circ}-\frac{A}{2} =\frac{A+\delta m}{2} \\ & \text { or } 180^{\circ}-A =A+\delta m \\ & \therefore \delta m =180^{\circ}-2 A=\pi=2 A\end{array}$
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