Chapter 44: Problem 12

Question: A double convex lens is to be made of glass with an index of efraction of n=1.5. One surface is to have twice the radius of curvature of the other and the focal length is to be $6~{\rm cm}$. Find the radii.

Solution:

$${1\over f}~=~(n-1)\left( {1\over R_1}-{1\over R_2}\right)$$

which in this case becomes

$${1\over f}~=~(n-1)\left( {1\over R}+{1\over 2 R}\right)~=~(n-1)\left( {3\over 2R}\right)$$

which leads to

$$R~=~{3\over 4} f~=~4.5~{\rm cm}$$