Two equi-convex lenses of focal length `30cm` and `70cm,` made of material of refractive index`=1.5,` are held in contact coaxially by a rubber band round their edges.A liquidof refractive index `1.3` is introduced in the space between the lenses filling it completely. Find the position of the image of a luminous point object placed on teh axis of the combination lens at a distance of `90cm` from it.

Explanation

We have `abs(R_(1))=abs(R_(2))=f_(1)=30 cm`
Similarly, `abs(R_(3))=abs(R_(4))=f_(2)=70 cm`
The focal length of the liquid lens (in air).
`1/(f_(3))=(mu-1)(1/R_(2)-1/R_(3))=(1.3-1)(1/(-30)-1/(+70))=-1/70`
Further, equivalent focal length of the combination,
`1/F=1/(f_(1))+1/(f_(2))+1/(f_(3))=1/30+1/70-1/70=1/30`
Using the lens formula`1/v-1/u=1/F,` we have
`1/v-1/(-90)=1/30rArrv=+45 cm`
This image will be formed at a distance of 45 cm from the combination.