A plano-convex lens has focal length 0.5 m and the refractive index of the material of the lens is 1.5. The radius of curvature of the convex surface of the lens is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.25 m
By the lens maker's formula, with the flat face having an infinite radius of curvature (\( R_2 = \infty \)):
\( \displaystyle \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) = \frac{\mu - 1}{R} \)
\( \displaystyle R = (\mu - 1)\,f = (1.5 - 1) \times 0.5\,\mathrm{m} = 0.25\,\mathrm{m} \)
For \( \mu = 1.5 \), a plano-convex lens has \( f = 2R \).