A planoconvex lens has the radius of curvature of its curved surface 50 cm and the refractive index of its material is 1.5. Its focal length will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 m
Use the lens maker's formula. For a plano-convex lens the plane surface has an infinite radius, so its term \( 1/R_2 \) is zero.
\( \displaystyle \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) = (\mu - 1)\,\frac{1}{R} \)
\( \displaystyle \frac{1}{f} = (1.5 - 1) \times \frac{1}{50\,\mathrm{cm}} = \frac{1}{100\,\mathrm{cm}} \)
\( \displaystyle f = 100\,\mathrm{cm} = 1\,\mathrm{m} \)
Shortcut: For \( \mu = 1.5 \), a plano-convex lens has \( f = 2R \) and an equiconvex lens has \( f = R \). Here \( f = 2 \times 50\,\mathrm{cm} = 1\,\mathrm{m} \) at once.