A ray of light travels from a medium of refractive index μ to air . Its angle of incidence in the medium is θ , measured from the normal to the boundary and its angle of deviation is δ with the angle of refraction ϕ. A graph is plotted between δ and θ which is shown in the figure. Choose the correct relation from the following
A
δ1δ2=μ
B
δ1δ2=2
C
sinϕ=21
D
f=2π−sin−1(π1)
Hard
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Solution
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Correct option is B)
Given: refractive index of medium u,
angle of incidence ,θ.
angle of deviation, δ
angle of refraction,ϕ . For θ < c, δ = ϕ - θ with sinϕ / sinθ = μ or ϕ = sin-1 (μsin θ).
∴ δ = sin-1 (μsin θ) - θ This is a nonlinear relation.
The maximum value of δ is δ1 = π/2 - c for θ = c and ϕ = π/2.
For θ > c, δ = π - 2θ δ decreases linearly with θ.