Two plano-concave lenses of glass of refractive index 1.5 have radii of curvature of 20 and 30 cm. They are placed in contact with curved surface towards each other and the space between them is filled with a liquid of refractive index `(4)/(3)`, find the focal length of the system.

Explanation

As shown in figure the system is equivalent to combination of three thin lenses in contact
ie `1/F=1/(f_(1)) + 1/(f_(2)) + 1/(f_(3))`
But by lens-maker’s formula
`1/(f_(1))=[3/2-1][1/oo - 1/20]=- 1/40`
`1/(f_(2))=[4/3 -1][1/20 + 1/30]=5/180`
`1/(f_(3))=[3/2-1][1/(-30) - 1/(-oo)]=- 1/60`
so `1/F =-1/40 + 5/180 - 1/60`
i.e., the system will behave as a divergent lens focal length 72cm.