The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respec

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Solution

Q.
The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are [2016]

1 45°; $\sqrt{2}$

2 30°; $\frac{1}{\sqrt{2}}$

3 45°; $\frac{1}{\sqrt{2}}$

4 30°; $\sqrt{2}$

Ans.
(4)

Given, $i = 45 °,$ $A = 60 °$

Since the ray undergoes minimum deviation, therefore, angle of emergence from second face, $e = i = 45 °$

$∴$ $δ_{m} = i + e - A = 45 ° + 45 ° - 60 ° = 30 °$

$μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})} = \frac{\sin (\frac{60 ° + 30 °}{2})}{\sin (\frac{60 °}{2})} = \frac{\sin 45 °}{\sin 30 °} = \frac{1}{\sqrt{2}} \times \frac{2}{1} = \sqrt{2}$

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