Question

The apparent vertical shift of the image of a coin placed at the bottom of a water tank having constant depth of water is proportional to (given refractive index of water =$\mu$).

• A. $\mu$
• B. $\frac{1}{\mu }$
• C. $\mu -1$
• D. $\mu +1$

Answer 1

The correct option is B $\frac{1}{\mu }$

Answer is B.
The apparent vertical shift is given by the equation $AD=\frac{RD}{\mu },thatis,\mu =\frac{RD}{AD}$, where AD is the apparent vertical shift, RD is the real depth of the tank and n is the refractive index of the denser medium, that is, water.
As real depth and refractive index is going to be constant always, the apparent shift or depth will be independent of viewing angle.
From the above equation, we can see that the apparent vertical shift is inversely proportional to the refractive index. That is, $\frac{1}{\mu }$.