A ray of light entering from air into a denser medium of refractive index 4 3 , as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle θ should be equal to:

Step-by-step solution

At maximum angle θ ray at point B goes in gazing emergence, at all less values of θ , TIR occurs. At point B 4 3 × sin θ ' ' = 1 × sin 90 ° θ ' ' = sin - 1 3 4 θ ' = π 2 - θ ' ' At point A 1 × sin θ = 4 3 × sin θ ' sin θ = 4 3 × sin π 2 - θ ' ' sin θ = 4 3 cos cos - 1 7 4 sin θ = 4 3 × 7 4 θ = sin - 1 7 3