Question

A small pin fixed on a tabletop is viewed from above from a distance of 50cm. By what distance would the pin appear to be raised if it is viewed from the same point through a 15cm thick glass slab held parallel to the table? The 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
The apparent depth of the pin=d'
The refractive index of glass,\(\mu\)=1.5
The ratio of actual depth to apparent depth is equal to the refractive index of glass,i.e.,\(\mu\)=\(\frac{d}{d'}\)
∴d'=\(\frac{d}{\mu}\)=\(\frac{15}{1.5}\)=10cm
The distance at which the pin appears to be raised=d'-d=15-10=5cm
For a small angle of incidence, this distance does not depend upon the location of the slab.