Two plano-concave lenses of glass of refractive 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 yhem is filled with a liquid of refractive index 2/3. Find the focal length of the system.

Explanation

Lens 1

`1/(f_(1))=(3/2-1)(1/(oo)-1/20)=-1/40`
Lens 2

`1/(f_(2))=(2/3-1)(1/20-1/30)=(1/3)(5/60)=1/36`
Lens 3

`1/(f_(3))=(3/2-1)(1/(-30)-1/(oo))=(-1)/60`
`1/F=1/(f_(1))+1/(f_(2))+1/(f_(3))`
`=(-1)/40+1/36-1/60=(-9+10-6)/360=(-5)/360`
F=- 72 cm