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

(d) Consider the situtation shown in figure. Let radius of curvature of the lens surfaces is R. The combination is equivalent to three lenses is contact

`therefore 1/(f_(eq))=1/(f_(1))+1/(f_(2))+1/(f_(3))=2/(f_(1))+1/(f_(2))(becausef_(1)=f_(3))`
Now, `1/(f_(1))=1/(f_(3))=(mu-1)(2/R)=1/f`
`1/(f_(2))=(u_(w)-1)(-2/R)=(4/3-1)((-2)/R)`
`=(1/3)(-2/R)=((-2)/3)(1/(2(mu-1)))1/f`
`rArr1/(f_(2))=(-1/3)(1/(3/2-1))(1/f)=-2/3xx1/f`
`therefore1/(f_(eq))=2/f-2/3xx1/f=(6-2)/(3f)=4/(3f)`
`rArr` The focal length of the combination, `f_(eq)=(3f)/4`