Question

A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 upto the same height, by what distance would be microscope have to be moved to focus on the needle again?

Answer 1

We know that $\eta =\frac{realdistance}{apparentdistance}$

$\eta =\frac{12.5}{9.4}=1.329$

When the water is replaced by liquid of 1.63

$\eta =\frac{12.5}{apparentdepth}$

$1.63=\frac{12.5}{x}$

$x=7.67$

So Distance by which microscope have to be moved is $9.4-7.67=1.73cm$