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?

Explanation

`rArr` Real depth =Height upto which water is filled
h= 12.5 cm
A pparrent deth h. = 9.4 cm
`rArr` Refractive index of water
`""^(a)mu_(w) = h/h. = (12.5)/(9.4) = 1.33`
`rArr` Refractive index of liquid,
`""^(a)mu_(w)=(h)/(h.)=(12.5)/(9,4) ~~1.33`
`rArr` refreative index of liquid ,
`a_(mu_l) = (h)/(h..)`
`therefore 1.63 = (12.5)/(h..)`
`therefore h.. = (12.5)/(1.63) = 7.669 ~~ 7.7 cm`
`therefore` Apparent dept in liquid h.. = 7.7 cm
`rArr` Distance by which microscope is displaced,
`= h. - h..`
= 9.4 - 7.7
`= 1.7 cm `