Question

A tank 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?

Answer 1

Given: height of the water level in the tank is 12.5 cm, and the apparent depth of a needle at the bottom of the tank is 9.4 cm.

The refractive index of a medium is given as,

μ= h 1 h 2

where, actual depth of the needle is h 1 and apparent depth of the needle is h 2 .

By substituting the given values in the above equation, we get,

μ= 12.5 9.4 =1.33

Therefore, the refractive index of water is 1.33.

Now, water is replaced by a liquid of refractive index 1.63.

The new apparent height of the needle can be given as,

h= h 1 μ'

where, the actual depth of the needle is h 1 , apparent depth of the needle is h, and refractive index of the liquid is μ'.

By substituting the given values in the above equation, we get,

h= 12.5 1.63 =7.67 cm

The new apparent height of the needle is 7.67 cm.

The distance by which the microscope should move to focus the needle again is given as,

a= h 2 −h =9.4−7.67 =1.73 cm

Thus, the distance by which microscope should move up is 1.73 cm.