Two identical glass `(mu_(g)=3//2)` equiconvex lenses of focal length f are kept in contact. The space between the two lenses is filled with water `(mu_(w)=4//3)` . The focal length of the combination is

Options

A. `f`
B. `f/2`
C. `(4f)/(3)`
D. `(3f)/(4)`

Answer

D

Explanation

Let `R` be the radius of curvature of each surface.
`(1)/(f) =(1.5 -1)((1)/(R)+(1)/(R))thereforeR=f`
For the water lens, `(1)/(f')=((4)/(3)-1)(-(1)/(R)-(1)/(R))`
`therefore (1)/(f')=-(2)/(3f)`

Using, `(1)/(F)=(1)/(f_(1))+(1)/(f_(2))+(1)/(f_(3)),`
`(1)/(F)=(1)/(f)+(1)/(f)+(1)/(f')=(2)/(f)-(2)/(3f)=(4)/(3f)thereforeF=(3f)/(4)`