The radius of curvature of the curved surface of a plano – convex lens is 20 cm. If the refractive index of the material of the lens is 1.5, it will
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → act as a convex lens irrespective of the side on which the object lies
By the lens maker’s formula, with the curved face first, \( R_1 = +20 \) cm and \( R_2 = \infty \).
\( \displaystyle \frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) = (1.5 - 1)\left(\frac{1}{20} - 0\right) \)
\( \displaystyle f = +40\,\mathrm{cm} \)
Turned round, \( R_1 = \infty \) and \( R_2 = -20 \) cm give the same f = +40 cm. A thin lens has the same focal length from both sides, so it converges whichever side the object is on.
Why the other options are incorrect
Option (1) act as a convex lens only for the objects that lie on its curved side. — Incorrect. Converging does not depend on the side.
Option (2) act as a concave lens for the objects that lie on its curved side. — Incorrect. In air it converges from either side; it would diverge only in a medium denser than 1.5.
Option (4) act as a concave lens irrespective of side on which the object lies — Incorrect. Its focal length is positive.
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