A mark of the surface of sphere `(mu=(3)/(2))` is viewed from a diametrically opposite position. It appears to be at a distance 15 cm from its actual position.Find the radius of sphere.

Explanation

To solve the problem of finding the radius of the sphere when a mark on its surface appears to be at a distance of 15 cm from its actual position, we will follow these steps:

### Step 1: Understand the Setup
We have a sphere with a refractive index \( \mu = \frac{3}{2} \). A mark on the surface of the sphere is viewed from a diametrically opposite position, and it appears to be 15 cm away from its actual position.

### Step 2: Define the Variables
- Let \( r \) be the radius of the sphere.
- The object (mark on the surface) is at a distance \( u \) from the center of the sphere, which is \( -2r \) (negative because it is on the left side of the reference point).
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