A travelling microscope is focussed on to a scratch on the bottom of a beaker. Water of refractive index `(4)/(3)` is poured in it. Then the microscope is to be lifted through 2 cm focus it again. Find the depth of water in the beaker.

Explanation

To bring the same point in focus again we need to raise apparent location of bottom by a distance of 2 cm. In other words we need to fill water up to a height which is sufficient to provide upward shift of 2 cm. Let h be the height of water to be poured then we can write the following equation:
`Deltax=h-(h)/(mu)`
`rArr" "2=h(1-(1)/(mu))`
`rArr" "2=h(1-(1)/(4//3))`
`rArr" "2=h(1-(3)/(4))`
`rArr" "2=(h)/(4)`
`rArr" "h=8cm.`