Question

A coin is placed at the bottom of a container of depth d filled with a liquid of index of refraction n .show that rays issued from a point on the coin close to the normal appear to come from a point o distance d/n from the surface

Answer 1

An object placed in a denser medium, when viewed from rarer medium appears to be at lesser depth than its real depth due to refraction of light .

When a ray of light passes from denser to rarer medium , it bends away from normal . Thus, a lateral shift occurs between incident ray and the emergent ray .

Here, the apparent shift of object = real depth - apparent depth

From Snell's Law

=>  index of refraction = sin(i)/sin(r)

=> n = real depth/apparent depth

=> n = d/apparent depth

Thus, apparent depth = d/n

Thus, rays issued from a point on the coin close to the normal appear to come from a point o distance d/n from the surface .