Two identical glass `(mu_g=3/2)` equiconvex lenses of focal length f each 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. `(4f)/(3)`
B. `(3f)/(4)`
C. `f/3`
D. f

Answer

A, C, D

Explanation

From lensmaker.s formula
In `1/f=(mu_g-1)((1)/(R_1)-(1)/(R_2)),R_1=R,R_2=-R`
`1/f=(mu_g-1)(2/R)`
`=(3/2-1)(2/R)`
`therefore 1/f=1/R`
`therefore 1/f=1/R`
`therefore f=R` … (1)

Focal length of concave lens of water,
In `(1)/(f.)=(mu_w-1)((1)/(R_1)-(1)/(R_2)),R_1=-R,R_2=R`
`(1)/(f.)=(4/3-1)(-2/R)`
`therefore (1)/(f.)=-(2)/(3R)`
`therefore f.=-(3f)/(2) [becauseR=f` given]
Now for lenses in contact equivalent focal length be f.
`1/F=1/f+(1)/(f.)+1/f`
`=2/f+(1)/(f.)`
`=2/f+(1)/(f.)`
`=(6-2)/(3f)`
`=(4)/(3f)`