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Physics Question on Refraction of Light

An isosceles prism of angle 120∘120^\circ has a refractive index 1.44. Two parallel rays of monochromatic light enter the prism parallel to each other in air as shown. The rays emerging from the opposite face

A

are parallel to each other

B

are diverging

C

make an angle 2[sin−1(0.72)−30∘]2[sin^{-1}(0.72)-30^\circ] with each other

D

with each other 2sin−1(0.72)2 sin^{-1} (0.72) with each other

Answer

make an angle 2[sin−1(0.72)−30∘]2[sin^{-1}(0.72)-30^\circ] with each other

Explanation

Solution

The diagramatic representation of the given problem is
shown in figure.
From figure it follows that ∠i=∠A=30∘\angle i=\angle A=30^\circ
From Snell's law, n1sini=n2n_1 sin i = n_2 sin r
or \hspace15mm sin r=\frac{1.44 sin 30^\circ}{1}=0.72
Now,       ∠δ=∠r−∠i=sin−1(0.72)−30∘ \, \, \, \, \, \, \angle \delta=\angle r -\angle i =sin^{-1}(0.72)-30^\circ
∴       θ=2(∠δ)=2sin−1(0.72)−30∘\therefore \, \, \, \, \, \, \, \theta =2 (\angle \delta)=2 \\{sin^{-1}(0.72)-30^\circ \\}