Lens-maker's formula: A double-convex thin lens is made of glass with an index of refraction of 1.52. The radii of curvature of the faces of the lens are 60 cm and 72 cm. What is the focal length of the lens?

Question

Quizplus · Accepted Answer

The lens-maker's formula is given by $\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$, where $f$ is the focal length of the lens, $n$ is the index of refraction of the material, $R_1$ and $R_2$ are the radii of curvature of the two surfaces of the lens. For a double-convex lens, if we consider the light coming from left to right, $R_1$ is positive and $R_2$ is negative because the center of curvature for the second surface is to the left of the lens. Plugging in the given values, $n = 1.52$, $R_1 = 60$ cm, and $R_2 = -72$ cm, we get $\frac{1}{f} = (1.52 - 1) \left( \frac{1}{60} - \frac{1}{-72} \right) = 0.52 \left( \frac{1}{60} + \frac{1}{72} \right)$. Solving this gives $f \approx 63$ cm.

Lens-Maker's Formula: a Double-Convex Thin Lens Is Made of Glass