First slide

Ray optics

Question

The angle of incidence for a ray of light at a refracting surface of a prism is $45^{0}$ . The angle of prism is $60^{0}$ . 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

Moderate

A

$45 °; \sqrt{2}$
B

$30 °; \frac{1}{\sqrt{2}}$
C

$45 °; \frac{1}{\sqrt{2}}$
D

$30 °; \sqrt{2}$

Solution

$Given, i = 45 °, A = 60 °$
$Since the ray undergoes minimum deviation, therefore, angle$
$of emergence from second face, e = i = 45 °$
$∴ δ_{m} = i + e - A = 45 ° + 45 ° - 60 ° = 30 °$
$μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})} = \sqrt{2}$

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