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

`(1)/(f) = (mu_(g-1))/(1) [(2)/(R)]`
`(1)/(f) = ((3)/(2)-1)/(1)[(2)/(R)]`
`(1)/(f) = (1)/(R)` ...(1)
Combination is a combination of three lens, where two lens each is eqviconex of focal length & and another one is equiconcave of water. Let focal length of this lens is f'
`(1)/(f') = ((4)/(3)-1)/(1)[(-2)/(R)]`
`(1)/(f') = (-2)/(3R)`
From (1) `(1)/(f') = (-2)/(3f)`
Focal length of combination is `f_(eq)`
`(1)/(f_(eq)) = (1)/(f) +(1)/(f)+(1)/(f')`
`(1)/(f_(eq)) =(2)/(f)-(2)/(3f)`
`f_(eq) = (3f)/(4)`