A cross mark at the bottom of an empty vessel is focussed with the help of a vertical microscope. Now water `("refractive index" = (4)/(3))` is poured in the vessel. The height of water in the vessel is 4cm. Another lighter liquid which does not mix with water and whose refractive index is `(3)/(2)`, is poured on water. The height of the liquid is 2 cm. How much should the microscope be raised vertically to focus the mark again?

Explanation

The real depth of the combination of water and the liquid = 4 + 2 = 6cm
The apparent depth of cross mark
`= (4)/((4)/(3) ) + (2)/((3)/(2)) = 3 + (4)/(3) = 4.33 cm`
So, to focus the cross mark, the microscope is to be raised vertically through a height (6 - 4.33) = 1.67cm .