by Beta » Wed Jun 09, 2010 4:20 am
I guess I should amend my statement that light always takes the shortest path. Light always takes the extremal path, which in practice means that it won't take a path if there's a slightly different path that's shorter. So for example if a candle is next to a mirror, you'll see light coming to you along two paths, one direct and one visiting the mirror. Obviously the direct path is shorter, but the light takes both because each of those two paths has the property that any slight variation (such as being slightly curved or crooked, or reflecting off a slightly different spot of the mirror) will make it longer. The same applies to gravitational lenses; there can be more than one path that is shorter than all of its immediate neighbors.
To be more precise, "longer" means more wavelengths, so if you consider things like propagation through matter (air, water, glass) which changes the wavelength, this actually explains (or at least predicts) the way lenses and mirages work.
I guess I should amend my statement that light always takes the shortest path. Light always takes the [i]extremal[/i] path, which in practice means that it won't take a path if there's a slightly different path that's shorter. So for example if a candle is next to a mirror, you'll see light coming to you along two paths, one direct and one visiting the mirror. Obviously the direct path is shorter, but the light takes both because each of those two paths has the property that any slight variation (such as being slightly curved or crooked, or reflecting off a slightly different spot of the mirror) will make it longer. The same applies to gravitational lenses; there can be more than one path that is shorter than all of its immediate neighbors.
To be more precise, "longer" means more wavelengths, so if you consider things like propagation through matter (air, water, glass) which changes the wavelength, this actually explains (or at least predicts) the way lenses and mirages work.