A classical mechanics problem by Nazmus sakib

Classical Mechanics Level 3

While filling up a swimming pool, John notices that the base of the pool appears to shift upwards. If the height of the pool is h h , to what height does the pool needs to be filled with water so that it appears half filled when seen from the top?

Refractive index of water is 4 3 \dfrac{4}{3} .

2 h 3 \dfrac{2h}{3} 3 h 4 \dfrac{3h}{4} 3 h 5 \dfrac{3h}{5} 5 h 7 \dfrac{5h}{7} 4 h 7 \dfrac{4h}{7}

Nazmus Sakib by Nazmus sakib , 24, Bangladesh

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1 solution

Md Zuhair
Sep 14, 2017

We know

R e a l D e p t h A p p a r e n t D e p t h = μ w a t e r \dfrac{Real \space Depth}{Apparent \space Depth}= \mu_{water}

R h 2 = 4 3 \dfrac{R}{\dfrac{h}{2}} = \dfrac{4}{3}

⟹ R = 2 h 3 \implies \boxed{ R= \dfrac{2h}{3}}

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Moderator note:

This problem is a specific application of Snell's Law; more details at the wiki here .

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