A convex lens of focal legnth `0.2 m` and made of glass `(mu = 1.50)` is immersed in water `(mu = 1.33)`. Find the change in the focal length of the lens.

Answer

`0.58 m`

Explanation

For glass lens in air,`.^a mu_g = 1.5 and f_a = 0.2 m`
`(1)/(f_a) = (.^a mu_g) ((1)/(R_1) - (1)/(R_2))`
`(1)/(0.2) = (1.5 - 1) ((1)/(R_1) - (1)/(R_2))`
`:. (1)/(R_1) - (1)/(R_2) = 10`
For the same lens in water,
`(1)/(f_w) = ((.^a mu_g)/(.^a mu_w) -1 ) ((1)/(R_1) - (1)/(R_2)) = ((1.5)/(1.33) - 1) xx 10`
`f_w = (1.33)/(1.71) = 0.78 m`
Change in focal length `= f_w - f_a = 0.78 - 0.20`
=`0.58 m`.