Question

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

• A. $1cm$
• B. $4/3cm$
• C. $3cm$
• D. $4cm$

Answer 1

Answer: (D)

$4cm$

Refractive index of water $\left(\mu \right)$= $\frac{4}{3}$

Separation = 1 cm

From the formulas

$\text{Apparent depth (}{\text{d}}^1\text{) =}\frac{\text{Real depth (d)}}{\text{mu}}$

$\Rightarrow {\text{d}}^{\text{1}}\text{=}\frac{\text{d}}{\mu }$

Also, Separation = Real depth – Apparent depth

$\Rightarrow \text{1 = d -}\frac{\text{d}}{\mu }$

$\Rightarrow \text{d}\left(\text{1 -}\frac{\text{1}}{\mu }\right)\text{= 1}$

$\Rightarrow \text{d}\left(\text{1 -}\frac{3}{4}\right)\text{= 1}$

$\Rightarrow \text{d}\left(\frac{1}{4}\right)\text{= 1}$

$\Rightarrow \text{d = 4 cm}$

Water should be poured up to the depth of 4 cm.