First slide

Prism

Question

The angle of a prism is 60° and its refractive index is $\sqrt{2}$ . The angle of minimum deviation suffered by a ray of light in passing through it is

Moderate

A

$About 20^{\circ}$
B

$30^{\circ}$
C

$60^{\circ}$
D

$45^{\circ}$

Solution

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

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