r/Physics • u/Mysterious-Movie-283 • 1d ago
Image Billiards Refraction
I was reading Love Triangle by Matt Parker, where he tells a story about challenging a professional pool player. The only problem was he kept missing his shots despite calculating the angles. He continues on without going into too much depth about why (or he does later on, I just got distracted with this thought), but I had a hunch that it could be solved using snells law which isn’t something I’ve heard of before. After doing a few extremely ideal problems I found that it gave the same output angle as other methods. Of course this only works while the ball is rolling and slipping at the same time which in reality is very short but I still found it interesting that wave mechanics could have a larger impact on pool than just reflection. Any thoughts on this theory? How likely is it that this would be a considerable factor when playing pool?
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u/1804Sleep 1d ago
That “Snell’s Law” is basically just saying that the momentum in the y direction is conserved, right?
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u/Snoo84256 1d ago
this is an elliptical pool table where if you have a ball and a hole on the focal points of the ellipse, you can strike the ball in any direction and will always make it in the hole. If you know about optics, calculating the focal point of a concave surface stems from Snell’s law, and in a normal pool table snell’s I believe would also apply.
BUT there are sooo many more factors at play(friction of the table, ball spin, spring force of the side wall) you may as well throw it out. Might help you in iMessage 8-ball, but like learning kinematics won’t make a you a better basketball player, you cannot calculate a pool shot unless you measure everything and land a perfect shot every time.
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u/Apprehensive-Wind819 1d ago
Title issue aside, I don't think Snell's law applies here. You're assuming the ball is "slipping" while spinning. When can we assume that's true? When can we not?
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u/NicoN_1983 1d ago
AFAIK Snell's law comes from a particle view of light, you don't need the wave part to derive it (perhaps only in the consideration of index of refraction). Besides that, the law you derived is for refraction, reflection only says that the incident and reflected angles are the same (which is conservation of momentum). However, a ball is not a point, so I guess there have to be corrections for the finite size, especially on corners.
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u/HoldingTheFire 1d ago
Snell’s law has nothing to do with the (incorrect) point particle view of light. It has nothing to do with quantized energy transfer. And it predates that by hundreds of years.
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u/NicoN_1983 21h ago
Yeah I didn't explain myself well, it was late. i meant that at least the law of reflection can be explained using the wavevectors k, which of course depend on wavelength but also indicate just directions and in a modern view they are related to momentum. You don't need the electric field part to derive them. but yeah those are still wave characteristics. You also have Fermat's principle, is that what you mean by centuries older?
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u/HoldingTheFire 16h ago
Both Fermat and Snell's Law (1621) itself are centuries old. Understanding of reflection properties even predates Snell.
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u/starkeffect 8h ago
Understanding of reflection properties even predates Snell.
tbh so does Snell's law itself
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u/HoldingTheFire 7h ago
Yes, that is exactly what I said.
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u/starkeffect 7h ago
You said "reflection". I think you meant "refraction".
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u/HoldingTheFire 7h ago
Reflection was understood well before refraction. But both were understood for over a millennia.
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u/Apprehensive-Wind819 1d ago
Energy is also not fully conserved in collisions with the boundary. However, I think it's a safe enough approximation to assume energy is conserved in the collisions between the billiard balls.
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u/agaminon22 Medical and health physics 17h ago
You can prove it with electromagnetism and appropriate boundary conditions.
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u/ProfessionalConfuser 12h ago
Snell's Law is derivable from Fermat's Principle and trigonometry. It doesn't use the photon model at all.
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u/the_stanimoron 1d ago
It depends because in practicality how hard the ball hits the rail causes the rubber to compress and the ball to straighten out. Also any sidespin will also alter the reflected angle as well.