The effective focal length of the lens combination shown in Fig. is `-60 cm`. The radii of curvature of the curved surfaces of the plano-convex lenses are `12 cm` each and refractive index of the material of the lens is `1.5`. The refractive index of the liquid is :
.

Options

A. `1.33`
B. `1.42`
C. `1.53`
D. `1.60`

Answer

D

Explanation

The system shown in Fig. is equivalent to combination of there lenses of focal lengths, `f_(1), f_(2), f_(3)` in contact.

`(1)/(f_(1)) = (1.5 - 1)((1)/(-oo) - (1)/(-12)) = (1)/(24)`
`(1)/(f_(2)) = (mu - 1)((1)/(-12) - (1)/(12)) = -(mu - 1)/(6)`
`(1)/(f_(3)) = (1.5 - 1)((1)/(12) - (1)/(oo)) = (1)/(24)`
As `(1)/(F) = (1)/(f_(1)) + (1)/(f_(2)) + (1)/(f_(3))`
`:. (1)/(-60) = (1)/(24) - (mu - 1)/(6) + (1)/(24)`
`(mu - 1)/(6) = (1)/(60) + (1)/(12) = (6)/(60) = 0.1`
`mu - 1 = 0.6`
or `mu = 1.6`