JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Geometrical Optics

A transparent block A having refractive index

μ = 1.25

is surrounded by another medium of refractive index

μ = 1.0

as shown in figure. A light ray is incident on the flat face of the block with incident angle

θ

as shown in figure. What is the maximum value of

θ

for which light suffers total internal reflection at the top surface of the block?

Answer: (C)

Solution

Let

r

be the refraction angle at the vertical entry face and

θ_{C}

the angle at the horizontal top face. Because the two faces are perpendicular,

r + θ_{C} = 9 0^{\circ}

. Total internal reflection just sets in when the top-face angle equals the critical angle, with

sin θ_{C} = \frac{1.0}{1.25} = \frac{4}{5}

, so

cos θ_{C} = \frac{3}{5}

. Snell's law at the entry face gives

sin θ = 1.25 sin r = 1.25 cos θ_{C} = 1.25 \times \frac{3}{5} = \frac{3}{4}

. The largest incidence angle is

sin^{- 1} (3/4)

JEE Main · 2025 · 07 Apr 2025 · Shift 2 · Single correct option