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` upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?

Explanation

Refractive index of water will be given by
`mu_(w)=("Real depth")/("Apparent depth")`
`rArr" "mu_(w)=(12.5)/(9.4)=1.33`
Again for a liquid, refractive index is given by
`mu_(1)=1.63`
`therefore" Apparent depth"=("Real Depth")/(mu_(1))=(12.5)/(1.63)`
`=7.668="7.67 cm nearly"`
Distance by which image becomes raised
`=9.4-7.67=1.73=1.7cm`
The microscope has to be moved up by 1.7 cm to focus on the needle again.