Question

A ray of light travels from a medium of refractive index to air . Its angle of incidence in the medium is , measured  from the normal to the boundary and its angle of deviation is with the angle of refraction . A graph is plotted between   and   which is shown in the figure. Choose the correct relation from the following

1759982
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A

B

C

D

Hard
Solution
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Correct option is B)

Given: refractive index of medium u,
angle of incidence ,θ.
angle of deviation, 
angle of refraction,ϕ .
For θ < c, = ϕ - θ with sinϕ / sinθ = μ or ϕ = sin-1 (μsin θ). 
∴  = sin-1 (μsin θ) - θ This is a nonlinear relation. 
The maximum value of  is 1 = π/2 - c for θ = c and ϕ = π/2.
 For θ > c,  = π - 2θ  decreases linearly with θ. 
max = π - 2c = 2 = 21.
therefore, 21=2.

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