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Question -

Atank is filled with water to a height of 12.5 cm. The apparent depth of aneedle 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 ofrefractive index 1.63 up to the same height, by what distance would themicroscope have to be moved to focus on the needle again?



Answer -

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 asfollows:

Hence, the refractiveindex of water is about 1.33.

Wateris replaced by a liquid of refractive index, 

The actual depth of the needle remains thesame, but its apparent depth changes. Let y be the newapparent depth of the needle. Hence, we can write the relation:

Hence, the new apparent depth of the needleis 7.67 cm. It is less than h2. Therefore, to focus theneedle again, the microscope should be moved up.

Distanceby which the microscope should be moved up = 9.4 − 7.67

=1.73 cm

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