Question

A biconvex lens of glass (n=3/2) is shifted from air (n=1) to water (n = 4/3). Determine the factor by which the focal length of the lens changes.

Answer 1

\(As,\ \frac{1}{f} = \left(\frac{n_2}{n_1 } - 1\right)\left[\frac{1}{R_1} + \frac{1}{R_2}\right] =\left (\frac{n_2}{n_1} - 1\right)K\) 

\(\frac{1}{f_A} = \left(\frac{3/2}{1} - 1\right)K = \frac{1}{2}K\) 

\(\frac{1}{f_W} = \left(\frac{3/2}{4/3} - 1\right)K = \left(\frac{1}{8}\right)K\) 

\(\frac{1/f_A}{1/f_W} = \frac{1/2}{1/8}\) 

f_W/f_A = 4 

Focal length of the lens increases by a factor of 4 as it is shifted from air into water.