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 be 1.5, then focal length of lens will be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 40\,\mathrm{cm} \)
The focal length of a thin lens follows from the lens maker's formula. For a plano-convex lens the plane surface has \( R_2 = \infty \), and with light falling on the curved surface \( R_1 = +20\,\mathrm{cm} \).
\( \displaystyle \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
\( \displaystyle \frac{1}{f} = (1.5 - 1)\left(\frac{1}{20} - \frac{1}{\infty}\right) = \frac{0.5}{20} = \frac{1}{40} \)
\( \displaystyle f = +40\,\mathrm{cm} \)
The result is the same if the lens is turned round. A convex lens is converging, so its focal length is positive.