Question

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 ?

Answer 1

Here, real depth `=12.5 cm` , apparent depth `= 9.4 cm , mu = ?`
As `mu = ("real depth")/("apparent depth") :. mu = (12.5)/(9.4) = 1.33`
Now, in the second case, `mu = 1.63`, real depth `= 12. 5 cm` , apparent depth, `y = ?`
`:. 1.63 = (12.5)/(y)`
`y = (12.5)/(1.63) = 7.67 cm`.
`:.` Distance through which microscope has to be moved up `= 9.4 - 7.67 = 1.73 cm`.