Question 426: 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?
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1mh7gb1du/87481a44-9dde-4b24-858e-87d93fc1644e/569f4a20-b246-11f0-99cb-7b77b0f41524/file-jaoe38c1mh7gb1dv.png?format=png)

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.
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1mh7gf4zr/dd84cc0b-e3b1-464b-9956-766f3565499b/c8a58170-b246-11f0-99cb-7b77b0f41524/file-jaoe38c1mh7gf4zs.png?format=png)

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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