Lens-maker's formula: A lens is made with a focal length of -40 cm using a material with index of refraction 1.50. A second lens is made with the SAME GEOMETRY as the first lens, but using a material having refractive index of 2.00. What is the focal length of the second lens?

Question

Quizplus · Accepted Answer

The lens-maker's formula is $ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) $. Since the geometry is the same, $ \frac{1}{R_1} - \frac{1}{R_2} $ is constant. For the second lens, $ \frac{1}{f_2} = (2.00 - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) $. Solving for $ f_2 $ gives $ f_2 = \frac{-40 \times 1.5}{2.00 - 1} = -20 $ cm.

Lens-Maker's Formula: a Lens Is Made with a Focal Length