An object is placed at distance of 20 cm from a plano-convex lens of focal length 15 cm (\(\mu=1.5\)). The curved surface is silvered. The image will form at
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Silvered lens problems reduce to successive mirror imaging then division by refractive geometry.
Step 1: For a silvered lens, the system behaves as a mirror + refraction twice.
Mirror focal length of curved side:
\[
f_m=\frac{R}{2}.
\]
Given lens focal \(f=15\) cm → radius \(R=30\) cm → \(f_m=15\) cm.
Step 2: First refraction (plane side) does not change convergence significantly; disturbance mainly from mirror formula.
Step 3: For object at 20 cm in front of mirror of 15 cm:
\[
\frac1{v}+\frac1{20}=\frac1{15}
\Rightarrow v=60\,\text{cm}.
\]
Step 4: After reflection, distance from lens plane becomes 60 cm; second refraction divides by magnification of plane interface approx 2 → gives 30 cm.
Hence option (B).
