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

Options

A. `f//3`
B. f
C. `4f//3`
D. `3f//4`

Answer

D

Explanation

Here, `mu_(g)=(3)/(2),mu_(w)=(4)/(3)`
Focal length (f) of glass convex lens is given by
`(1)/(f)=(mu_(g)-1)((2)/(R))`
or `(1)/(f)=((3)/(2)-1)(2)/(R)=(1)/(R) "or" f=R` …(i)
Focal length (f.) of water filled concave lens is given by
`(1)/(f.)=(mu_(w)-1)(-(2)/(R))`
or `(1)/(f.)=((4)/(3)-1)(-(2)/(R))`
`=-(2)/(3R)=-(2)/(3f)` [Using eqn. (i)]
Equivalent focal length `(f_(eq))` of lens system
`(1)/(f_(eq))=(1)/(f)-(2)/(3f)+(1)/(f)=(3-2+3)/(3f)=(4)/(3f)`
`:.f_(eq)=(3f)/(4)`