JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Geometrical Optics

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water (

μ = 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?

(A)11.7 cm
(B)8.75 cm
(C)7.5 cm
(D)10 cm✓ Correct

Answer: (D)

Solution

Viewed from above, the water column of real depth

h

appears to have depth

\frac{h}{μ} = \frac{3 h}{4}

, while the empty part of height

(17.5 - h)

is seen at true size. The tumbler looks half filled when the apparent water depth equals the apparent empty depth:

\frac{3 h}{4} = 17.5 - h

. This gives

\frac{7 h}{4} = 17.5

, so

h = 10 cm

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Single correct option

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