Q. A tank is filled with water to a height of 12.5cm.The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4cm.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?

Answer

Actual depth of the needle in water, h₁=12.5cm

Apparent depth of the needle in water, h₂=9.4cm

Refractive index of water=6

The value of6 can be obtained as follows:

Therefore the refractive index of water is about 1.33.

Water is restore by a liquid of refractive index,

The authentic depth of the needle remains the same however its apparent depth changes.

Permit y be the new apparent depth of the needle. Thus we can write the relation:

Therefore the new apparent depth of the needle is7.67cm it is less than h₂.

Thus to focus the needle again the microscope must be moved up.

*Distance by which the microscope must be moved up = 9.4-7.67 = 1.73cm