Question

Find the value of θ in the given figure.

Options

• `sin^-1(2/sqrt3)`

• `sin^-1(1/sqrt3)`

• `sin^-1(1/2)`

• `sin^-1(1/sqrt2)`

Answer 1

`bb(sin^-1(1/sqrt3))`

Explanation:

For total internal reflection, μ = `1/sin"c"`​

where, C = critical angle

Condition for TIR, the angle of incidence must be greater than critical angle C,

(90 - θ₁) > C

sin (90 - θ₁) > sinC

cosθ₁ = `1/mu`

cosθ₁ > `1/(2//sqrt3)`

cosθ₁ > `sqrt3/2`

θ₁ > 30°

According to Snell’s law,

μ₁sinθ = μ₂sinθ₁

1sinθ = `2/sqrt3`sinθ₁

sinθ = `2/sqrt3`sin30°

sinθ = `1/sqrt3`

So, θ = `sin^-1(1/sqrt3)`