Q 9.3 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 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?
Given:
Actual height of the tank,h = 12.5 cm
The apparent height of the tank, h' = 9.4 cm
let the refractive index of the water be
so the refractive index of water is approximately 1.33.
Now, when water is replaced with a liquid having
Hence the new apparent height of the needle is 7.67 cm.
Total distance we have to move in a microscope = 9.4 - 7.67 = 1.73 cm.
Since the new apparent height is lesser than the previous apparent height we have to move UP the microscope in order to focus the needle.