JEE Main 2025 Jan 22 Shift 1, Physics Q20: Thin Lens and Mirrors

JEE Main2025Jan 22, Shift 1Physics

Given is a thin convex lens of glass (refractive index $μ$ ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself.

A
R/ $μ$
B
R/( $2 μ - 3$ )
C
$μ$ R
D
R/( $2 μ - 1$ )

Solution

A silvered lens acts as an equivalent mirror with power $P_{e q} = 2 P_{ℓ} + P_{m}$ , where $P_{ℓ}$ is the lens power and $P_{m}$ is the mirror power of the silvered back surface.

$P_{ℓ} = (μ - 1) (\frac{1}{R} - \frac{1}{- R}) = \frac{2 ( μ - 1 )}{R}$ .

$P_{m} = \frac{2}{R}$ (concave mirror formed by silvering the back surface of radius $R$ ).

$P_{e q} = 2 \cdot \frac{2 ( μ - 1 )}{R} + \frac{2}{R} = \frac{4 μ - 4 + 2}{R} = \frac{4 μ - 2}{R}$ .

So $f_{e q} = \frac{R}{4 μ - 2} = \frac{R}{2 ( 2 μ - 1 )}$ . For the image to form on the object itself in a mirror, the object must be at the centre of curvature, i.e. at distance $2 f_{e q}$ :

$d = 2 f_{e q} = \frac{R}{2 μ - 1}$ .

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JEE Main 2025 Jan 22 Shift 1, Physics Q20: Thin Lens and Mirrors

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