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 $12.5 \,cm$ is measured by a microscope to be $9.4\, cm$. 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. $1.73\,cm$
• B. $2.13\,cm$
• C. $1.5\,cm$
• D. $2.9\,cm$

Answer 1

Answer: (A)

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