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JEE Main 2021 (1 Sep, Shift 2) · Refraction, Glass Slab & Apparent Depth

Refraction, Glass Slab & Apparent Depth question from JEE Main 2021 (1 Sep, Shift 2)

Q59JEE Main 2021 · 1 SEP · SHIFT 2Medium

Refraction, Glass Slab & Apparent Depth

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water ( $\mu$ = 4/3) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

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Answer: (b)

Let the actual water height be $h$ . Water looks $\dfrac{h}{\mu}$ deep, while the empty part above is seen as its real length $17.5 - h$ .
He feels it half filled when these look equal: $\dfrac{3h}{4} = 17.5 - h$ .
$\dfrac{7h}{4} = 17.5 \Rightarrow h = 10$ cm.
So the answer is (b) 10 cm.

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