Atank is filled with water to a height of 12.5 cm. The apparentdepth of a needle lying at the bottom of the tank is measured by amicroscope to be 9.4 cm. What is the refractive index of water? Ifwater is replaced by a liquid of refractive index 1.63 up to the sameheight, by what distance would the microscope have to be moved tofocus on the needle again?
Atank is filled with water to a height of 12.5 cm. The apparentdepth of a needle lying at the bottom of the tank is measured by amicroscope to be 9.4 cm. What is the refractive index of water? Ifwater is replaced by a liquid of refractive index 1.63 up to the sameheight, by what distance would the microscope have to be moved tofocus on the needle again?
Actualdepth of the needle in water, h1= 12.5 cm
Apparentdepth of the needle in water, h2= 9.4 cm
Refractiveindex of water = μ
Thevalue of μcan be obtained as follows:
Hence,the refractive index of water is about1.33.
Wateris replaced by a liquid of refractive index, 
Theactual depth of the needle remains thesame, but its apparent depth changes. Let ybe the new apparent depth of the needle. Hence, we can write therelation:
Hence,the new apparent depth of the needle is7.67 cm. It is less than h2.Therefore, to focus the needle again, the microscope should be movedup.
∴Distanceby which the microscope should be moved up = 9.4 − 7.67
= 1.73 cm
Actualdepth of the needle in water, h1= 12.5 cm
Apparentdepth of the needle in water, h2= 9.4 cm
Refractiveindex of water = μ
Thevalue of μcan be obtained as follows:
Hence,the refractive index of water is about1.33.
Wateris replaced by a liquid of refractive index,
Theactual depth of the needle remains thesame, but its apparent depth changes. Let ybe the new apparent depth of the needle. Hence, we can write therelation:
Hence,the new apparent depth of the needle is7.67 cm. It is less than h2.Therefore, to focus the needle again, the microscope should be movedup.
∴Distanceby which the microscope should be moved up = 9.4 − 7.67
= 1.73 cm
