Another analogy is with a ball rolling on two surfaces crossing the boundary. The first very little friction, then second a bit more.
From AI:
“The direction in which the ball veers when moving from a smooth to a rough surface depends on several factors, especially the initial direction of motion and the orientation of the boundary between the two surfaces. Here’s a general outline of how it might behave:
If Moving at an Angle to the Boundary:
Suppose the ball moves diagonally across the boundary between the smooth and rough surfaces (i.e., it doesn’t cross perpendicularly).
When it hits the rough surface, frictional resistance increases more on the component of motion along the boundary line than on the perpendicular component.
This causes the ball to veer slightly toward the rougher surface, meaning it will change direction in a way that aligns more closely with the boundary.
This is similar to a light ray entering water. So is the physics the same? (on second reading, its not so clear, if you put a golf ball from a smooth surface to a rough one, what happens to the angle at the boundary?)
Well in this case, the momentum of the ball clearly won’t increase, instead it will be constantly losing momentum and if the second surface was floating it would be pushed so as to conserve momentum. Unlike for light however if it then re-enters the smooth surface it will be going slower. It seems the ball would lose momentum at both transition boundary. (however if the rough surface was perfectly floating, then perhaps it would regain it)
Anyway for a rough surface that is perfectly floating, it seems the ball gives some momentum to the rough surface when it enters it, (making it have velocity) then recovers it and returns the rough surface to zero velocity when it exits it. In that case the momentum of the ball decreases while travelling over the rough surface.
Not trying to give answers here, just add to the confusion lol.
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
Another analogy is with a ball rolling on two surfaces crossing the boundary. The first very little friction, then second a bit more.
From AI:
This is similar to a light ray entering water. So is the physics the same? (on second reading, its not so clear, if you put a golf ball from a smooth surface to a rough one, what happens to the angle at the boundary?)
Well in this case, the momentum of the ball clearly won’t increase, instead it will be constantly losing momentum and if the second surface was floating it would be pushed so as to conserve momentum. Unlike for light however if it then re-enters the smooth surface it will be going slower. It seems the ball would lose momentum at both transition boundary. (however if the rough surface was perfectly floating, then perhaps it would regain it)
Anyway for a rough surface that is perfectly floating, it seems the ball gives some momentum to the rough surface when it enters it, (making it have velocity) then recovers it and returns the rough surface to zero velocity when it exits it. In that case the momentum of the ball decreases while travelling over the rough surface.
Not trying to give answers here, just add to the confusion lol.
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