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A planoconvex lens of focal length 20 cm has its plane side silvered This question has multiple correct options

1. The radius of curvature of curved surface of given plano-convex lens is equal to half of radius of curvature of a surface of equiconvex lens of focal length \( 20 \mathrm{cm} \)
2. An object placed at \( 15 \mathrm{cm} \) on the axis on the convex side of silvered plano-convex lens gives rise to an image at a distance of \( 30 \mathrm{cm} \) from it
3. An object placed at a distance of \( 20 \mathrm{cm} \) on the axis on the convex side of silvered plano-convex lens gives rise to an image at \( 40 \mathrm{cm} \) from it
4. silvered plano-convex lens acts as a concave mirror of focal length \( 10 \mathrm{cm} \)

Correct answer: silvered plano-convex lens acts as a concave mirror of focal length \( 10 \mathrm{cm} \)

Solution

For a plano-convex lens, the curved surface gives the full power; when the plane side is silvered, light refracts through the lens, reflects, and refracts again, doubling the lens effect. This makes the combination behave like a concave mirror with focal length half the lens focal length, i.e. 10 cm.

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