Chapter 24, Problem 58GP

A lensmaker wants to make a magnifying glass from glass with n = 1.55 and with a focal length of 20.0 cm. If the two surfaces of the lens are to have equal radii, what should that radius be?

*24.58. SetUp: We apply the thin-lens equation: $\frac{1}{f}=\left(n-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$, when n = 1.55 and f = 20.0 cm.

Solve: Since f > 0 we choose R₁ =R and R₂ = −R, where R is the magnitude of the radius of curvature. Thus we have $\frac{1}{f}=\left(n-1\right)\left(\frac{1}{R}-\frac{1}{-R}\right)=\frac{2(n-1)}{R}$. Solving for R we obtain R = 2(n − 1)f = 2(1.55 − 1)(20.0 cm) = 22 cm.

Reflect: For identical convex surfaces, the relation between f and R is $f=\frac{1}{n-1}\cdot \frac{R}{2}$. This is reminiscent of the relation for spherical mirrors, which is $f=\frac{R}{2}$.