An equiconvex lens, with redii of curvature of magnitude `10 cm` each, is put over a liquid layer poured on top of a plane mirror. `A` small needle, with its tip on the principal axis of the lens, is moved along the axis until its inverted real image coincides with the needle itself. The distance of the needle, from the lens, is measured to be `15 cm` .
On removing the liquid layer, and repeating the experiment the distance is measured to be `10 cm` . Given that the two values of the distance measured represent the force length values in the two cases, calculate the refractive index of the liqiud.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understanding the Setup
We have an equiconvex lens placed over a liquid layer on a plane mirror. A small needle is placed on the principal axis of the lens. The distances measured when the liquid is present and when it is removed are given as 15 cm and 10 cm, respectively.

### Step 2: Identifying Focal Lengths
1. **With Liquid Layer**:
- The distance measured (15 cm) corresponds to the focal length of the combination of the lens and the liquid. Let's denote this focal length as \( F_L \).
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