Question

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? (\(\mu =4/3\))

• A. \(8\) cm
• B. \(10.5\) cm
• C. \(12\) cm
• D. \(14\) cm

Hint:

Find the apparent position of the container bottom using apparent depth in water, then require the water surface to lie at its midpoint.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Water of depth \(d\) appears shallower: its bottom is seen at an apparent depth \(\dfrac{d}{\mu}\) below the water surface.
The container looks half filled when the water surface is seen at the middle of the apparent depth of the container.

Step 2: Set up the apparent depths
Height of the container is \(H=21\) cm. The water surface is \((21-d)\) cm below the top.
The apparent depth of the bottom from the top is \((21-d)+\dfrac{d}{\mu}=(21-d)+\dfrac{3d}{4}=21-\dfrac{d}{4}\).

Step 3: Calculation
Half filled means the surface depth equals half of the apparent total depth:
\(21-d=\dfrac{1}{2}\left(21-\dfrac{d}{4}\right)\)
\(42-2d=21-\dfrac{d}{4}\)
\(21=\dfrac{7d}{4}\), so \(d=12\) cm

Step 4: Compare the options
12 cm matches option (C).

Final Answer:
The container should be filled with 12 cm of water. \[ \boxed{\text{(C) }12\text{ cm}} \]