Two identical glass `(mu_(g)=3//2)` equiconvex lenses of focal length `f` are kept ini 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. `(4)/(3)f`
D. `(3)/(4)f`

Answer

D

Explanation

If R is radius of curvature of each surface of convex lens. Then `(1)/(f_(1))=(1)/(f_(2))=(mu_(g)-1)((1)/(R_(1))-(1)/(R_(2)))`
`=((3)/(2)-1)((1)/(R)+(1)/(R))=(1)/(R)`
`f_(1)=f_(2)=R=f`
For water in between lens
`(1)/(f_(3))=((4)/(3)-1)((-1)/(R)-(1)/(R))=(1)/(3)((-2)/(f))=(-2)/(3f)`
Using, `(1)/(F)=(1)/(f_(1))+(1)/(f_(2))+(1)/(f_(3))`
We get, `(1)/(F)=(1)/(f)+(1)/(f)-(2)/(3f)impliesF=(3)/(4)f`