The refractive index of the material of glass prism is . The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism? [2025]

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Solution

Q.
The refractive index of the material of glass prism is $\sqrt{3}$ . The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism [2025]

1 50°

2 60°

3 58°

4 48°

Ans.
(2)

$μ = \frac{\sin (\frac{A + δ_{\min}}{2})}{\sin \frac{A}{2}}$

Given $δ_{\min} = A$

$\sqrt{3} = \frac{\sin A}{\sin \frac{A}{2}} = \frac{2 \sin \frac{A}{2} \cos \frac{A}{2}}{\sin \frac{A}{2}}$

$\cos \frac{A}{2} = \frac{\sqrt{3}}{2} \Rightarrow A = 60 °$

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