Question

A Liquid is filled in a vessel of height $\frac{2H}{3}.$ At the bottom of the vessel there is a spot $\text{P}$ and a hole from which liquid is coming out. Let $d$ be the distance of image of $\text{P}$ from an eye at height $H$ from bottom at an instant when level of liquid in the vessel is $x$. Which of the following represents the correct graph between $d$ and $x$,

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let $d$ be the distance between image of $\text{P}$ and observer eye at a particular instant.

So, by using the concept of apparent depth, $d$ will be

$d=(H-x)+\frac{x}{\mu }$

where, $(H-x)\to$ distance travelled by lightray in air.

and,

$\frac{x}{\mu }\to$ distance travelled by light ray in liquid.

$\Rightarrow d=H+x(\frac{1}{\mu }-1)$

$\Rightarrow d=-(1-\frac{1}{\mu })x+H$

comparing above equation with $[y=mx+c]$ we get,

$c=H;m=-(1-\frac{1}{\mu })$


Hence, option (c) is the correct answer.