A ray of light is incident from air on a glass plate having thickness √3 cm and refractive index √2. The angle of incidence is equal to the critical angle for the glass-air interface. The lateral displacement of the ray when it passes through the plate i s ___ × 10⁻² cm. (Given sin15° = 0.26)
Physics · Geometrical optics · apperant depth and shift due to slab
JEE Mains 25 January 2023 Morning Shift

Question

A ray of light is incident from air on a glass plate having thickness √3 cm and refractive index √2. The angle of incidence is equal to the critical angle for the glass-air interface. The lateral displacement of the ray when it passes through the plate i s ___ × 10⁻² cm. (Given sin15° = 0.26)

Physics · Geometrical optics · apperant depth and shift due to slab

JEE Mains 25 January 2023 Morning Shift

G1 Physics · Accepted Answer

Critical angle c satisfies sin c = 1/√2, so c = 45°. Snell's law at entry gives sin45° = √2 sin r, hence r = 30°. Lateral displacement = t sin(i-r)/cos r = √3 × sin15° × (2/√3) = 2×0.26 = 0.52 cm = 52 × 10⁻² cm.