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JEE Main 202523 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
23 January
Shift
Evening Shift
Subject
Physics
Chapter
Ray Optics

JEE Main 2025 · 23 January · Evening Shift · Physics · Ray Optics

The refractive index of the material of a glass prism is 3 . The...

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?

Options

  1. A60∘60^{\circ}
  2. B58∘58^{\circ}
  3. C48∘48^{\circ}
  4. D50∘50^{\circ}

Correct answer

A. 60∘60^{\circ}

Step-by-step solution

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}3=sin⁡Asin⁡A2=2sin⁡A2cos⁡A2sin⁡A2cos⁡A2=32A=60∘\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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