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

Answer

D

Explanation

For equiconvex lens
`(1)/(A)=((3)/(2)-1)((1)/(R)-(1)/(-R))`
`(1)/(f)=(1)/(2)*(2)/(R)`
`R=f`
For 2nd lens `(1)/(f_(2))=((4)/(3)-1)((1)/(-f)-(1)/(-f))`
`(1)/(f_(2))=(1)/(3)xx(2)/(-f)`
`f_(2)=(-3f)/(2)`
For combination
`(1)/(f')=(1)/(f_(1))+(1)/(f_(2))+(1)/(f_(3))`
`=(1)/(f)+(2)/(-3f)+(1)/(f)`
`(1)/(f')=(3-2+3)/(3f)=(4)/(3f)`
`f'=(3f)/(4)`