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JEE Main 2026 · 8 Apr · Shift 2, Physics question 30

A thin biconvex lens is prepared from the glass (μ=1.5\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.

Choose one option
Answer and worked solution

Official answer: A

Lens. 1f=0.5⋅220\dfrac1f=0.5\cdot\dfrac2{20}, so f=20f=20 cm.

Silvered surface. A concave mirror with fm=10f_m=10 cm.

Equivalent mirror. 1F=220+110=15\dfrac1F=\dfrac2{20}+\dfrac1{10}=\dfrac15, so F=5F=5 cm. The image coincides with the object at 2F=102F=10 cm.

(A)