JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Geometrical Optics

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Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at ______ cm from the object.

Answer: 200

Solution

For refraction at a single spherical surface,

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

With the object in air,

μ_{1} = 1

μ_{2} = 1.5

u = - 100

cm, and

R = + 20

cm (convex surface, centre of curvature on the outgoing side):

\frac{1.5}{v} - \frac{1}{- 100} = \frac{1.5 - 1}{20} = 0.025

\frac{1.5}{v} = 0.025 - 0.01 = 0.015

v = 100 cm

The image forms 100 cm beyond the surface, and the surface is itself 100 cm from the object, so the image lies

100 + 100 = 200

cm from the object.

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Integer answer

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