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:
- (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.
$\mu=\frac{\sin (\frac{A+\delta_m}{2})}{\sin (A / 2)}$
$=\frac{\sin 45^{\circ}}{\sin 30^{\circ}}=\frac{1}{\sqrt{2}} \cdot(\frac{2}{1})=\sqrt{2}$
