Ray Optics and Optical Instruments - Result Question 54

56. The angle of incidence for a ray of light at a refracting surface of a prism is $45^{\circ}$. The angle of prism is $60^{\circ}$. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :

[2016]

(a) $45^{\circ}, \frac{1}{\sqrt{2}}$

(b) $30^{\circ}, \sqrt{2}$

(c) $45^{\circ}, \sqrt{2}$

(d) $30^{\circ}, \frac{1}{\sqrt{2}}$

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Answer:

Correct Answer: 56. (b)

Solution:

  1. (b) Given: Angle of incidence $i=45^{\circ}$

angle of prism, $A=60^{\circ}$

Angle of minimum deviation,

$\delta_m=2 i-A=30^{\circ}$

Refractive index of material of prism.

$\mu=\frac{\sin (\frac{A+\delta_m}{2})}{\sin (A / 2)}$

$=\frac{\sin 45^{\circ}}{\sin 30^{\circ}}=\frac{1}{\sqrt{2}} \cdot(\frac{2}{1})=\sqrt{2}$