Question

A small pin fixed on a table top is viewed from above from a distance of 50 cm. By what distance would the pin appear to be raised if it is viewed from the same point through a 15 cm thick glass slab held parallel to the table? Refractive index of glass $=$ 1.5. Does the answer depend on the location of the slab?

Answer 1

Actual depth of the pin , $d=15cm$

Apparent dept of the pin = $d^{\prime }$

Refractive index of glass is $\mu =1.5$

Ratio of actual depth to the apparent depth is equal to the refractive index of the glass i.e.

$\mu =\frac{d}{d^{\prime }}\Rightarrow d^{\prime }=10cm$

The distance at which the pin appears to be raised = $d^{\prime }-d$= $15-10=5cm$

For a small angle of incidence, this distance does not depend upon the location of the slab.