position of image of flaw

Question

A clear plastic ball with a diameter of 8 cm has a flaw, which is actually 2 cm under the surface. The index of refraction of plastic is 1.4. Find the position of the image of the flaw when it is viewed along a diameter passing through the flaw from (a) the near side, (b) the far side.

Answer 1

use

RI = Real Depth / Apparent depth

this is valid for vertical viewing

In one case

real depth is 2cm

RI = 2cm / Apparent depth

1.4 = 2/ x

x = 2/1.4 cm This is distance of image from surface

In case two

RI = 6cm / y

y= 6/ 1.4

This is distance of image from far side

Remember we have used approximation in solving this problem