Question

The radius of curvature of the curved surface of a plano-convex lens is \(20\,\text{cm}\). If the refractive index of the material of the lens is \(1.5\), it will

• A. Act as a convex lens only for the objects that lie on its curved side.
• B. Act as a concave lens for the objects that lie on its curved side.
• C. Act as a convex lens irrespective of the side on which the object lies.
• D. Act as a concave lens irrespective of the side on which the object lies.

Hint:

The nature of a lens depends on the sign of its focal length, not on the side from which light enters. A plano-convex lens always behaves as a converging lens in air.

Answer 1

The Correct Option is C

Concept: The nature of a lens is determined by its focal length. According to the lens maker's formula, \[ \frac{1}{f} = (\mu-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] For a plano-convex lens, \[ R_1=20\,\text{cm}, \qquad R_2=\infty \] and \[ \mu=1.5 \]

Step 1:Calculate the focal length. \[ \frac{1}{f} = (1.5-1) \left( \frac{1}{20} -\frac{1}{\infty} \right) \] \[ \frac{1}{f} = 0.5\times\frac{1}{20} \] \[ \frac{1}{f} = \frac{1}{40} \] \[ f=40\,\text{cm} \]

Step 2: Interpret the result. Since \[ f>0 \] the lens is a converging (convex) lens. Changing the side from which light enters does not change the nature of the lens. Therefore, it behaves as a convex lens for objects placed on either side.

Step 3: State the answer. \[ { \begin{array}{c} \text{A plano-convex lens acts as a convex lens} \text{irrespective of the side on which the object lies.} \end{array} } \] Hence, the correct option is \[ {(C)} \]