Figure(a) shows two plano-convex lenses in contact as shown. The combination has focal length 24cm. Figure (b) shows the same with a liquid introduced between them. If refractive index of glass of the lenses is 1.50 and that of the liquid is 1.60, the focal length of system in figure (b) will be

Options

A. `-120cm`
B. 120cm
C. `-24cm`
D. `24cm`

Answer

a.

Explanation

Since the refractive index of the liquid is grater than the refractive index of glass, therefore the focal length of the system has to be negative. So, options (b) and (d) are excluded.
Now, `(1)/(24)=(1.5-1)(2)/(R)`
or `R=24cm`
Again, for liquid concave lens,
`(1)/(f)=-(1.6-1)((2)/(24))`
`(1)/(f)=-(3)/(5)xx(1)/(12)`
or `(1)/(f)=-(1)/(12)` or `f=-20cm`
Now,`(1)/(F)=(1)/(24)-(1)/(20)=(5-6)/(120)`
or `F=-120cm`