Question 173: Ray Optics

Question

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?

Accepted Answer

Consider the actual height of the tumbler be H.
The refractive index of the water, $$\mu$$ = 4/3
The refractive index of the air, $$\mu$$ = 1
As we know that,
$${\mu _{water}} = {{{H_{real}}} \over {{H_{apparent}}}} \Rightarrow {4 \over 3} = {H \over {{H_{apparent}}}}$$
$$ \Rightarrow {H_{apparent}} = {{3H} \over 4}$$
Height of air observed by observer = 17.5 $$-$$ H
According to question, both height observed by observer is same.
$${{3H} \over 4}$$ = 17.5 $$-$$ H
$$\Rightarrow$$ H = 10 cm
Option (b)

Answer

11.7 cm

Answer

10 cm

Answer

7.5 cm

Answer

8.75 cm

Ray Optics

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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