In the Auckland Uni lectures, Professor Feynman explains refraction and reflection from a quantum superposition point of view. Ie, a photon of light can take any possible path, and the chances of seeing it at any measurement point is the superposition of all the various paths that it could have taken to get there.
He uses phase arrows quite cleverly to show the effect of summing phase differences with the different path lengths. Eg, that two paths that have the photon arriving precisely 180deg out of phase will cancel out.
This shows that most measurement points will see nothing, because for them, the many different paths will all cancel out. But for that particular measurement point where the time taken by many possible paths changes the least, the paths don’t cancel out, so we measure the photon arriving at that point.
He explains that the path where the time taken changes the least is also ('almost always') the shortest path.
Which explains why angle of reflection = angle of incidence.
And also, if you apply the same principle to refraction, why Snell’s law explains the changing path of light through a medium (say, glass) where it moves slower. Light will take the shortest path, so will change direction to minimise how much glass it must move through.
(Just like the famous lifesaver running fast across the sand and swimming more slowly through the water to save ‘the pretty girl’. Ah well, it was the 70s…)
So here’s my question (finally): Can you ‘trick’ light by shaping a piece of glass such that what would ‘appear’ to be the shortest path isn’t shorter at all.
On hitting the slower medium, the light will refract towards the normal. But I could in theory shape my piece of glass so that the path taken by the refracted ray was significantly longer than a direct path would be, right?.
I’m assuming quantum physics is far, far cleverer than my trick piece of glass, but I’m interested in how this works.
If my question makes no sense, please let me know and I’ll rephrase and/or add a diagram showing an example 'trick' piece of glass.
Incidentally, since we had Snell's law long before QED came along, why did anyone poreviously think light would behave in a way that got it to the drowning lassie the fastest?
PS: The 2nd vid from the one I linked has magnificent application of this theory to "build" a convex lens. A wonderful magic trick.