Question

he apparent depth of a needle lying at the bottom of the tank, which is filled with water of refractive index $1.33$ to a height of $12.5cm$ is measured by a microscope to be $9.4cm$. If water is replaced by a liquid of refractive index $1.63$ upto the same height. What distance would the microscope have to be moved to focus on the needle again?

• A. $1.73cm$
• B. $2.13cm$
• C. $1.5cm$
• D. $2.9cm$

Answer 1

Answer: (A)

Apparent depth $=\frac{\text{Real deapth}}{{}^a{\mu }_l}$
Here, Real depth $=12.5cm$ and
${}^a{\mu }_l=1.63$
$\therefore$ Apparent depth $=\frac{12.5}{1.63}=7.67cm$
Now the microscope will have to shift from its initial position to focus $9.4cm$ depth object to focus $7.67cm$ depth object.
Shift distance $=9.4-7.67$
$=1.73cm$