Given is a thin convex lens of glass (refractive index μ) and each… | JEE Main 2025 (22 Jan, Shift 1)

Q16JEE Main 2025 · 22 JAN · SHIFT 1Medium

Combination of Lenses

Given is a thin convex lens of glass (refractive index $\mu$ ) 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?

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Answer: (b)

Lens: $\frac{1}{f_L} = \frac{2(\mu-1)}{R}$ ; silvered surface: concave mirror, $\frac{1}{f_m} = \frac{2}{R}$ .
$\frac{1}{F} = \frac{2}{f_L} + \frac{1}{f_m} = \frac{4(\mu-1)+2}{R} = \frac{2(2\mu-1)}{R}$
Image on the object itself when the object is at $2F = \frac{R}{2\mu-1}$ .
So the answer is (b) $\frac{R}{2\mu-1}$ .

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