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?
Actual depth of the pin, d = 15 cm
Apparent dept of the pin = d'
Refractive index of glass, `mu= 1.5`
Ratio of actual depth to the apparent depth is equal to the refractive index of glass, i.e.
`mu = d/d'`
`:. d' = d/mu`
`= 15/1.5 = 10 cm`
The distance at which the pin appears to be raised = d' - d
= 15 - 10 = 5 cm
For a small angle of incidence, this distance does not depend upon the location of the slab.