A thin biconvex lens is prepared from the glass (μ = 1.5) both curved… | JEE Main 2026 (8 Apr, Shift 2)

Q8JEE Main 2026 · 8 APR · SHIFT 2Medium

Combination of Lenses

A thin biconvex lens is prepared from the glass $(\mu = 1.5)$ both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ______ cm.

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Answer: (a)

Lens: $\frac{1}{f_L} = (1.5-1)\left(\frac{1}{20}+\frac{1}{20}\right) = \frac{1}{20}$ ; silvered surface acts as a concave mirror with $f_m = \frac{R}{2} = 10\text{ cm}$ .
Light passes the lens twice and reflects once: $P = \frac{2}{f_L} + \frac{1}{f_m} = \frac{2}{20} + \frac{1}{10} = \frac{1}{5}$ , so $F = 5\text{ cm}$ (concave mirror).
Image coincides with the object when the object is at the centre of curvature: $u = 2F = 10\text{ cm}$ .
So the answer is (a) 10 cm.

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