Question

A vessel is filled with water to a height of $13cm$. The apparent depth of a screw lying at the bottom of the vessel is measured by a microscope to be $8.5cm$. If water is replaced by a liquid of refractive index $1.70$ upto the same height. Find the distance at which microscope have to be moved to focus on the screw again?

• A. $0.85cm$
• B. $0.52cm$
• C. $0.65cm$
• D. $1.02cm$

Answer 1

Answer: (A)

Actual depth of the screw in water $h_1=13cm$
and apparent depth is $h_2=8.5cm$
${\mu }_{\text{water }}=\frac{h_1}{h_2}=\frac{13}{8.5}=1.53$
When water replaced by a liquid of refractive index ${\mu }^{\prime }=1.70$
then the actual depth remains same, but its apparent depth changes.
Let $h_3$ be the new apparent depth of the needle
${\mu }^{\prime }=\frac{h_1}{h_3}$
or $h_3=\frac{h_1}{{\mu }^{\prime }}=\frac{13}{1.7}=7.65$
here, $h_3$ is less than $h_2$. Thus for focus the microscope should be moved up.
Distance by which microscope should be moved up
$=8.5-7.65=0.85cm$