A biconvex lens has radii of curvature of 10 cm each. If the refractive index of the material of the lens is 1.5, what will be its focal length in air?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 cm
The focal length follows from the lens maker's formula. With the Cartesian sign convention (light from left to right), the first surface of a biconvex lens has \( R_1 = +10\,\mathrm{cm} \) and the second has \( R_2 = -10\,\mathrm{cm} \).
\( \displaystyle \frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
\( \displaystyle \frac{1}{f} = (1.5 - 1)\left(\frac{1}{10} + \frac{1}{10}\right)\,\mathrm{cm^{-1}} = 0.5 \times \frac{2}{10}\,\mathrm{cm^{-1}} = \frac{1}{10}\,\mathrm{cm^{-1}} \)
\( \displaystyle f = 10\,\mathrm{cm} \)