A tank is filled with water to a height of 12.5 cm . . .

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 the microscope have to be moved to focus on the needle again?

Doubt by Sonali 

Solution :

Case I

Real Depth (h) = 12.5 cm
Apparent Depth (h') = 9.4 cm 

We know, 
Refractive index (µ) = h/h'
µ = 12.5/9.4
µ = 1.329
µ = 1.33

Case II

µ = 1.63

h = 12.5 cm
h' = ?

µ=h/h'
1.63=12.5/h'
h' = 12.5/1.63
h' = 7.668
h' = 7.67 cm

Distance moved by the microscope

= 9.4-7.67

= 1.73