JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Geometrical Optics

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A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm . Refractive index of glass is 1.5 . The rays converge to a point at a distance x cm from the centre of the curvature of the spherical surface. The value of x is ____ cm .

Answer: 100

Solution

Refraction at a single spherical surface obeys

\frac{μ _{2}}{v} - \frac{μ _{1}}{u} = \frac{μ _{2} - μ _{1}}{R}

. For a parallel incident beam

u \to \infty

, so

\frac{1.5}{v} = \frac{1.5 - 1.0}{50} = \frac{0.5}{50}

, giving

v = 150 cm

measured from the surface. The centre of curvature lies

R = 50 cm

from the surface, so the rays converge at a distance

x = 150 - 50 = 100 cm

from the centre of curvature.

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Integer answer

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