The refractive indices of the material of a lens for yellow and red lights are 1.54 and 1.51, respectively. If the focal length of the lens for red light is 36.0 cm, the focal length of the lens for yellow light will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 34.0 cm
By the lens maker's formula, the radii of curvature are the same for both colours, so only (n − 1) changes.
\( \displaystyle \frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
\( \displaystyle \frac{f_y}{f_r} = \frac{n_r - 1}{n_y - 1} \)
\( \displaystyle f_y = 36.0\,\mathrm{cm} \times \frac{0.51}{0.54} = 34.0\,\mathrm{cm} \)
Yellow light is bent more (larger n), so its focal length is shorter than that for red light.