NEET-XII-Physics
09: Ray Optics And Optical Instruments
- #3A 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?
Ans : Actual depth of the needle in water, h1 = 12.5 cm
Apparent depth of the needle in water, h2 = 9.4 cm
Refractive index of water = μ
The value of μcan be obtained as follows:
Hence, the refractive index of water is about 1.33.
Water is replaced by a liquid of refractive index,
The actual depth of the needle remains the same, but its apparent depth changes. Let y be the new apparent depth of the needle. Hence, we can write the relation:
Hence, the new apparent depth of the needle is 7.67 cm. It is less than h2. Therefore, to focus the needle again, the microscope should be moved up.
∴Distance by which the microscope should be moved up = 9.4 - 7.67
= 1.73 cm