A ball is kept at a height h above the surface of a heavy transparent sphere made of a material of refractive index The radius of the sphere is R. At t = 0, the ball is dropped to fall normally on the sphere. Find the speed of the image formed as a function of time for `tlt sqrt((2h)/g)`. Consider only the image by a single refraction.

Explanation

To solve the problem of finding the speed of the image formed by a ball dropped from a height \( h \) above a transparent sphere of radius \( R \) and refractive index \( \mu \), we can follow these steps:

### Step 1: Determine the height of the ball above the sphere as a function of time
The ball is dropped from a height \( h \) and falls under the influence of gravity. The distance fallen after time \( t \) is given by:
\[ h' = \frac{1}{2} g t^2 \]
Thus, the remaining height of the ball above the surface of the sphere at time \( t \) is:
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