Some water is filled in a container of height | vedclass

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Question

(C) Let the height of the water filled in the container be $x$. The apparent depth of the bottom of the container as seen from the top is given by $d'

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) Let the height of the water filled in the container be $x$. The apparent depth of the bottom of the container as seen from the top is given by $d' = \frac{x}{n}$, where $n$ is the refractive index of water. Given $n = \frac{4}{3}$, the apparent depth is $d' = \frac{x}{4/3} = \frac{3x}{4}$. The container appears half-filled, which means the apparent depth of the bottom from the top surface of the water is equal to the height of the empty part of the container. The height of the empty part is $30 - x$. Therefore, we set $d' = 30 - x$. $\frac{3x}{4} = 30 - x$ $3x = 120 - 4x$ $7x = 120$ $x = \frac{120}{7} \approx 17.14 \, cm$. Wait, re-evaluating the condition "appears half-filled": If the total height is $30 \, cm$, half-filled means the apparent position of the bottom is at $15 \, cm$ from the top. So, $(30 - x) + d' = 15$ is not correct. The condition "appears half-filled" means the apparent depth of the bottom is $15 \, cm$. $d' = 15 \, cm$. Since $d' = \frac{x}{n}$, we have $15 = \frac{x}{4/3}$. $x = 15 	imes \frac{4}{3} = 20 \, cm$. Thus, the height of the water should be $20 \, cm$.

Some water is filled in a container of height $30 \, cm$. If it is to appear half-filled to the observer when viewed from the top of the container, the height up to which water should be filled in it is [Refractive index of water $= \frac{4}{3}$] (in $cm$)

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