Ray Optics

JEE Main level, single correct, medium

245 of 295

Question 245 of 295

The refractive index of the material of a glass prism is 3\sqrt{3}. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

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Answer: (A) 60∘60^{\circ}

μ=sin⁡(A+δmin⁡2)sin⁡A2\mu=\frac{\sin \left(\frac{A+\delta_{\min }}{2}\right)}{\sin \frac{A}{2}}

Given δmin⁡=A\delta_{\min }=\mathrm{A}
$\begin{aligned}
& \sqrt{3}=\frac{\sin A}{\sin \frac{A}{2}}=\frac{2 \sin \frac{A}{2} \cos \frac{A}{2}}{\sin \frac{A}{2}} \\
& \cos \frac{A}{2}=\frac{\sqrt{3}}{2} \\
& A=60^{\circ}
\end{aligned}$

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