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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,┬аh1┬а= 12.5 cm

Apparent depth of the needle in water,┬аh2┬а= 9.4 cm

Refractive index of water =┬а╬╝

The value of┬а╬╝can be obtained asfollows:

Hence, the refractiveindex of water is about 1.33.

Wateris replaced by a liquid of refractive index,┬а

The actual depth of the needle remains thesame, but its apparent depth changes. Let┬аy┬аbe 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┬аh2. Therefore, to focus theneedle again, the microscope should be moved up.

тИ┤Distanceby which the microscope should be moved up = 9.4 тИТ 7.67

=1.73 cm

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