How much water should be filled in a container of height 21 cm, so that it appears half filled to the observer when viewed from the top of the container? ( μ = 4/3 )

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Let the total height of the container be $H = 21$ cm and the height of the water filled be $h$ .

The height of the empty part of the container is $H - h$ .

The apparent depth of the water when viewed from the top is $h_{a pp} = \frac{h}{μ}$ .

For the container to appear half filled, the apparent depth of the water must be equal to the height of the empty part.

$h_{a pp} = H - h$

$\frac{h}{μ} = 21 - h$

Given $μ = \frac{4}{3}$ ,

$\frac{3 h}{4} = 21 - h$

$\frac{3 h}{4} + h = 21$

$\frac{7 h}{4} = 21$

$h = 12$ cm.

Answer: $12$ cm

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