A convex lens having a power of one dioptre is made of glass having refractive index 1.48. What will be the power of convex lens made of material with refractive index 1.6 and same dimension?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.25 D
By the lens maker's formula, the power of a lens in air is \( P = \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \). The two lenses have the same dimensions, so the bracket is the same and \( P\propto(\mu - 1) \).
\( \displaystyle \frac{P_2}{P_1} = \frac{\mu_2 - 1}{\mu_1 - 1} = \frac{1.6 - 1}{1.48 - 1} = \frac{0.6}{0.48} = 1.25 \)
\( P_2 = 1.25\times1\,\mathrm{D} = 1.25\,\mathrm{D} \)