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.

Answer

C, D

Explanation

`|R_1|=|R_2|=f_1=30cm (As mu=1.5)`
Similarly, `|R_3|=|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=1/30`
` :. v=+45 cm`
Thus, image will be formed at a distance of `45cm` from the combination.