Question

 A lens, made of crown glass, has one convex surface with radius of curvature of 80.0 cm. What should be the radius of curvature of the other surface so that the focal length of the lens is 120 cm? 

Answer 1

The formula for focal length $f = 120cm$ is the following:

$$\dfrac{1}{f} = (n-1)\left( \dfrac{1}{R_1} + \dfrac{1}{R_2}\right)$$

where $n \approx 1.52$ is the refractive index of crown glass, $R_1 = 80cm, \space R_2$ are radii of the surfaces. Expressing $R_2$, obtain:

$$\dfrac{1}{R_2} = \dfrac{1}{f(n-1)} - \dfrac{1}{R_1}\\ R_2 = \dfrac{1}{\dfrac{1}{f(n-1)} - \dfrac{1}{R_1}}\\ R_2 = \dfrac{1}{\dfrac{1}{120cm\cdot (1.52-1)} - \dfrac{1}{80cm}} \approx 284cm$$

Answer. 284 cm.