Question

A microscope is focused on a coin lying at the bottom of a beaker. The microscope is now raised up by $1 cm$. To what depth should the water be poured into the beaker so that coin is again in focus? (Refractive index of water is $\frac{4}{3}$ )

• A. $15\,cm$
• B. $12\,cm$
• C. $10\,cm$
• D. $4\,cm$

Answer 1

Answer: (D)

$4\,cm$

Answer 2

Suppose initial height of the water level was $H$. Initial position of the observer was $L$ and final position is $L'$

Now for the image to be formed at the same place.
From adjacent figure
$x + \frac{H}{\mu_w} = y + \frac{h'}{\mu_w}$
(Object distance should be same)
$\Rightarrow y -x = \frac{H - h'}{\mu_w}$
$\Rightarrow -3 = \frac{H - h'}{\mu_w}$
$\Rightarrow h' - H = \mu_w(3)$
$= \frac{4}{6} \times 3$
$= 4\,cm$
Water level increased by $4 \,cm$.