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. `(4f)/(3)`
D. `(3f)/(4)`

Answer

d.

Explanation

Let R be the radius of curvature of each surface. Then
`(1)/(f)=(1.5-1)((1)/(R)+(1)/(R))`
For the water lens,
`(1)/(f^('))=((4)/(3)-1)(-(1)/(R)+(1)/(R))=(1)/(3)(-(2)/(f)),`
`(1)/(f^('))=-(2)/(3f)`
Now, using `(1)/(F)-(1)/(f_(1))+(1)/(f_(2))+(1)/(f_(3))`, we have
`(1)/(F)-(1)/(f)+(1)/(f)+(1)/(f^('))=(2)/(f)-(2)/(3f)=(4)/(3f)`
`rArr F=(3f)/(4)`