A thin convex lens made from crown glass `(mu=(3)/(2))` has focal length f. When it is measured in two different liquids having refractive indices `(4)/(3)` and `(5)/(3)`, it has the focal lengths `f_1` and `f_2` respectively . The correct relation between the focal lengths is ,

Options

A. `f_2 gt f , f_1` becomes negative
B. `f_1 and f_2` both become negative
C. `f_1 = f_2 lt f`
D. `f_1 gt f and f_2` becomes negative.

Answer

D

Explanation

From lens maker's formula
`(1)/(f)=((mu_g)/(mu_a) - )((1)/(R_1) - (1)/(R_1))`
=`((3)/(2) -1)((1)/(R_1) -(1)/(R_2)) = (1)/(2) ((1)/(R_1) -(1)/(R_2))`
`(1)/(f) = ((3//2)/(4//3) - 1)((1)/(R_1) - (1)/(R_2)) = (1)/(8) ((1)/(R_1) - (1)/(R_2))`
and `(1)/(f_1) = ((3//2)/(5//3) - 1) ((1)/(R_1) - (1)/(R_2))`
=`-(1)/(10) ((1)/(R_1) -(1)/(R_2))`
Clearly, `(1)/(f_1) lt (1)/(f)` or `f_1 gt f`
and `f_2` is negative.
Choice (d) is correct.