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

To solve the problem step by step, we will follow the outlined approach based on the information provided in the question.

### Step 1: Understand the System
We have two equi-convex lenses with focal lengths \( f_1 = 30 \, \text{cm} \) and \( f_2 = 70 \, \text{cm} \). The lenses are made of a material with a refractive index of \( 1.5 \), and they are in contact with each other. A liquid with a refractive index of \( 1.3 \) is introduced between the lenses.

### Step 2: Calculate the Focal Length of the Liquid Layer
Using the Lensmaker's formula for the concave lens formed by the liquid layer:
\[
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