SATHEE: Optics 4 Question 19

Optics 4 Question 19

20. A ray of light is incident on a prism $A B C$ of refractive index $\sqrt{3}$ as shown in figure.

$(2005, 4$ M)

(a) Find the angle of incidence for which the deviation of light ray by the prism $A B C$ is minimum.

(b) By what angle the second identical prism must be rotated, so that the final ray suffers net minimum deviation.

Show Answer

Solution:

(a) At minimum deviation, $r_{1} = r_{2} = 30^{\circ}$

$∴$ From Snell’s law

$\begin{aligned} μ = \frac{\sin i_{1}}{\sin r_{1}} or \sqrt{3} = \frac{\sin i_{1}}{\sin 30^{\circ}} \\ ∴ & \sin i_{1} = \frac{\sqrt{3}}{2} or i_{1} = 60^{\circ} \end{aligned}$

(b) In the position shown net deviation suffered by the ray of light should be minimum. Therefore, the second prism should be rotated by $60^{\circ}$ (anti-clockwise).

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Optics 4 Question 19

20. A ray of light is incident on a prism ABC of refractive index 3 as shown in figure.

Solution:

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20. A ray of light is incident on a prism $A B C$ of refractive index $\sqrt{3}$ as shown in figure.