I read about better analogy long time ago: use two wheels on an axle instead of single ball, then refraction come out naturally. Also I think instead of difference in friction it is better to use difference in elevation, so things slow down when they go to an area of higher elevation and speed back up going down.
I tried to derive it, turned out to be easy: BC is wheel pair, CD is surface, slow medium above. AC/Vfast=AB/Vslow and for critical angle D touches small circle (inner wheel is on the verge of getting out of medium) so ACD is right triangle, so AC*sin (ACD)= AD (and AD same as AB) so sin(ACD) = AB/AC= Vslow/Vfast. Checking wiki it is the same angle (BC here is wavefront so velocity vector is normal to it). Honestly I am a bit surprised this analogy works so well.
Cool, that was my intuition. GPT was absolutely sure in the golf ball analogy however that it couldn’t happen. That is the ball wouldn’t “reflect” off the low friction surface. Tempted to try and test somehow
I read about better analogy long time ago: use two wheels on an axle instead of single ball, then refraction come out naturally. Also I think instead of difference in friction it is better to use difference in elevation, so things slow down when they go to an area of higher elevation and speed back up going down.
Yes that does sound better, and is there an equivalent to total internal refraction where the wheels are pushed back up the slope?
I tried to derive it, turned out to be easy: BC is wheel pair, CD is surface, slow medium above. AC/Vfast=AB/Vslow and for critical angle D touches small circle (inner wheel is on the verge of getting out of medium) so ACD is right triangle, so AC*sin (ACD)= AD (and AD same as AB) so sin(ACD) = AB/AC= Vslow/Vfast. Checking wiki it is the same angle (BC here is wavefront so velocity vector is normal to it). Honestly I am a bit surprised this analogy works so well.
Cool, that was my intuition. GPT was absolutely sure in the golf ball analogy however that it couldn’t happen. That is the ball wouldn’t “reflect” off the low friction surface. Tempted to try and test somehow