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

Question

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Answer 1

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 $δ$ 1 = π/2 - c for θ = c and ϕ = π/2.
For θ > c, $δ$ = π - 2θ $δ$ decreases linearly with θ.
$δ$ max = π - 2c = $δ$ 2 = 2 $δ$ 1.
therefore, $δ$ 2 $\div$ $δ$ 1=2.

Answer 2

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

δ

1 = π/2 - c for θ = c and ϕ = π/2.

For θ > c,

δ

= π - 2θ

δ

decreases linearly with θ.

δ

max = π - 2c =

δ

2 = 2

δ

1.

therefore,

δ

2

\div

δ

1=2.