The power of a biconvex lens is 12 D and the radius of curvature of each surface is 10 cm. The refractive index of the material of the lens is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.6
The power of a lens is \( P = 1/f \) with \( f \) in metres, and the lens maker's formula gives
\( \displaystyle \frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
For a biconvex lens \( R_1 = +R \) and \( R_2 = -R \), so
\( \displaystyle P = \frac{1}{f} = (n-1)\,\frac{2}{R} \)
\( P = 12\,\mathrm{D} \)
\( R = 10\,\mathrm{cm} = 0.10\,\mathrm{m} \)
\( \displaystyle 12 = (n-1)\,\frac{2}{0.10} = 20\,(n-1) \)
\( \displaystyle n - 1 = \frac{12}{20} = 0.6 \;\Rightarrow\; n = 1.6 \)