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 :
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Options

A. 1.33
B. 1.42
C. 1.53
D. 1.6

Answer

D

Explanation

The system shown in Fig., is equivalent to combination of three 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`.
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