First slide

Prism

Question

For a prism of refractive index 1.732, the angle of minimum deviation is equal to the angle of the prism. The angle of the prism is

Moderate

A

80°
B

70°
C

60°
D

50°

Solution

$μ = \frac{\sin \frac{A + δ_{m}}{2}}{\sin \frac{A}{2}} = \frac{\sin \frac{A + A}{2}}{\sin \frac{A}{2}} = \frac{\sin A}{\sin \frac{A}{2}} = \frac{2 \sin \frac{A}{2} \cos \frac{A}{2}}{\sin \frac{A}{2}} = 2 \cos \frac{A}{2} So, \sqrt{3} = 2 \cos \frac{A}{2} \Rightarrow \frac{\sqrt{3}}{2} = \cos \frac{A}{2} \Rightarrow A = 60^{\circ}$

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