A swimming pool is 1.4 m deep and 12 m long. Is it possible for you to dive to t

Question

A swimming pool is 1.4 m deep and 12 m long. Is it possible for you to dive to the very bottom of the pool so people standing on the deck at the end of the pool do not see you?

Part A: Assume you dive to the very bottom of the pool so people standing on the deck at the end of the pool can see you. Find the minimum height of the person's eyes at the far side of the pool, so you would be observable by this person. Take an angle 48.5 for a ray that is incident at the water-air interface (nwater = 1.33).

The answer is not: 1.82 m, 1.597 m, 2.054 m, 1.01 m

Explanation / Answer

let height of the person's eye level is h.

let horizontal distance from the person where the ray hits the air-water interface is dd.

given that incident ray is 48.5 degrees,

then tan(48.5)=d/h

==>d=h*tan(48.5)=1.1303*h

let angle of refraction be theta.

using snell's law:

1*sin(48.5)=1.33*sin(theta)

==>theta=34.272 degrees

then your horizontal distance from the point where incident ray hits the water-air interface is

=1.4*tan(34.272)=0.954 m

so to be barely visible, you should be at the other end of the pool

that means total horizontal distance=length of the pool=12 m

then 1.1303*h+0.954=12

==>h=(12-0.954)/1.1303=9.7726 m

which is impossible.

hence if you dive to the end surface of the pool, people wont be able to see you.

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