Question 76: Ray Optics

Question

Two identical prisms of refractive index $$\sqrt{3}$$ are kept as shown in the figure. A light ray strikes the first prism at face AB. Find
(A) the angle of incidence so that the 
emergent ray from the first prism has 
minimum deviation; 
(B) through what angle, the prism DCE 
should be rotated about C so that the 
final emergent ray also has minimum 
deviation?

Accepted Answer

(A) At minimum deviation $$r_{1}=r_{2}=30^{\circ}$$
From Snell's law $$\mu=\frac{\sin i_{1}}{\sin r_{1}}$$
or $$\quad \sqrt{3}=\frac{\sin i_{1}}{\sin 30^{\circ}}=\frac{\sin i_{1}}{\frac{1}{2}}$$
$$	herefore \quad \sin i_{1}=\sqrt{3} 	imes \frac{1}{2}=\frac{\sqrt{3}}{2}=\sin 60^{\circ}$$
$$	herefore \quad i_{1}=60^{\circ}$$
(B) In the position shown below net derivation suffered by the ray of light should be minimum.
Rotate DCE about C for final emergent ray to have minimum deviation.
This is achieved when the second prism is rotated anti-clockwise by $$60^{\circ}$$ about C.

Answer

(A) = 45$$^\circ$$, (B) = 60$$^\circ$$

Answer

(A) = 60$$^\circ$$, (B) = 45$$^\circ$$

Answer

(A) = 45$$^\circ$$, (B) = 45$$^\circ$$

Answer

(A) = 60$$^\circ$$, (B) = 60$$^\circ$$

Ray Optics

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