First slide

Ray optics

Question

Coming from vacuum, a ray of light in incident on a slab of glass of refractive index $\sqrt{3}$ such that the angle of incidence is twice the angle of deviation. Refraction is at only one surface. Then the angle of deviation is

Moderate

A

60^o
B

15^o
C

30^o
D

37^o

Solution

$i = 2 δ = 2 (i - r) \Rightarrow i = 2 r$
By snell's law, $\sin i = μ \sin r \Rightarrow \sin 2 r = μ \sin r \Rightarrow 2 \sin r \cos r = μ \sin r$
$∴ r = \cos^{- 1} (\frac{μ}{2}) = \cos^{- 1} (\frac{\sqrt{3}}{2}) = 30^{o}$
$∴ i = 2 x 30^{o} = 60^{o} and δ = \frac{60^{o}}{2} = 30^{o}$

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