A thin equiconvex lens of glass` ( mu = 1.5)` with radius of curvature 4m is placed on a horizontal plane mirror. When the space between the lens and mirror is filled with a liquid, an object held at a distance 6m vertically above the lens is found to coincide with its own image. What is the refractive index of the liquid.

Explanation

To solve the problem step by step, we will follow the concepts of optics, particularly focusing on lenses and their properties.

### Step-by-Step Solution:

1. **Understanding the Setup**:
We have a thin equiconvex lens made of glass with a refractive index (μ) of 1.5 and a radius of curvature (R) of 4 m. The lens is placed on a horizontal plane mirror. An object is positioned 6 m vertically above the lens.

2. **Coincidence of Object and Image**:
...