Physics · Reflection of light, spherical mirrors, mirror formula
A planoconvex lens of focal length 20 cm has its plane side silvered This questi
A planoconvex lens of focal length 20 cm has its plane side silvered This question has multiple correct options
- A. 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 \( 20 \mathrm{cm} \)
- B. 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
- C. 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
- D. silvered plano-convex lens acts as a concave mirror of focal length \( 10 \mathrm{cm} \)
Step-by-step solution
When the plane side of a planoconvex lens of focal length 20 cm is silvered, the system behaves as a concave mirror. The effective focal length is given by 1/F = 2/f_lens + 1/f_mirror, where f_mirror is infinite for a plane mirror. Thus, 1/F = 2/20 = 1/10, so F = 10 cm. This concave mirror has a focal length of 10 cm.
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