Q 9.3   A 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?

Answers (1)


Actual height of the tank,h = 12.5 cm 

Apparent height of tank,h' =  9.4 cm 

let refrective index of the water be \mu

 \mu = \frac{h}{h'} =\frac{12.5}{9.4} = 1.33 (approx)

so the refractive index of water is approximately 1.33.

Now, when water is replaced with a liquid having  \mu = 1.63

\mu = \frac{h}{h'} =\frac{12.5}{h'_{new}} = 1.63

h'_{new}= \frac{12.5}{1.63}= 7.67 cm

Hence the new apparent height of the needle is 7.67 cm.

Total distance we have to move in a microscope = 9.4 - 7.67  = 1.73 cm.

Since new apparent height is lesser than the previous apparent height we have to move UP the microscope in order to focus the needle.