If the refractive index of the material of a prism is $\cot \left(\frac{A}{2}\right)$, where $A$ is the angle of prism then the angle of minimum deviation will be
Solution
<p>$$\begin{aligned}
& \cot \frac{\mathrm{A}}{2}=\frac{\sin \left(\frac{\mathrm{A}+\delta_{\min }}{2}\right)}{\sin \frac{\mathrm{A}}{2}} \\
& \Rightarrow \cos \frac{\mathrm{A}}{2}=\sin \left(\frac{\mathrm{A}+\delta_{\min }}{2}\right) \\
& \frac{\mathrm{A}+\delta_{\min }}{2}=\frac{\pi}{2}-\frac{\mathrm{A}}{2} \\
& \delta_{\min }=\pi-2 \mathrm{~A}
\end{aligned}%$$</p>
About this question
Subject: Physics · Chapter: Optics · Topic: Refraction and Snell's Law
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