When we talk about Snell's law, and total internal reflection in particular, we usually will draw diagrams as if light is coming off a point in a single, straight line (that bends at an interface, of course).
My question is, though, how does this light behave when it's coming off an extended object? For example, if I stand at the side of a pool and there is a person, say, under the surface, then how do I know whether or not I will see him? If the light that hits my eyes comes from beyond the critical angle, then I shouldn't be able to see anything from under the water there. But isn't it possible that some of the light he emits (well, reflects but it's as if he emits it) will come from above the critical angle while some will come below it?
As in, shouldn't the diagram we draw of light coming from this person really include lines going at all angles up to surface, some from every angle, and then once they hit the interface they will bend according to Snell's law, but rays from seemingly many different points will reach my eyes, not just from one as we usually draw in diagrams?
This is also what often confused me about deriving Snell's law from Fermat's principle-- how can we single out an individual line of light and ignore all the others? Not all light reaching my eyes goes through a single point on the interface, does it?
My question is, though, how does this light behave when it's coming off an extended object? For example, if I stand at the side of a pool and there is a person, say, under the surface, then how do I know whether or not I will see him? If the light that hits my eyes comes from beyond the critical angle, then I shouldn't be able to see anything from under the water there. But isn't it possible that some of the light he emits (well, reflects but it's as if he emits it) will come from above the critical angle while some will come below it?
As in, shouldn't the diagram we draw of light coming from this person really include lines going at all angles up to surface, some from every angle, and then once they hit the interface they will bend according to Snell's law, but rays from seemingly many different points will reach my eyes, not just from one as we usually draw in diagrams?
This is also what often confused me about deriving Snell's law from Fermat's principle-- how can we single out an individual line of light and ignore all the others? Not all light reaching my eyes goes through a single point on the interface, does it?