Why is every individual like a small mirror?
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It turns out that you can predict where light ought to go with very simple spinning arrows. Imagine that light particles have with them an arrow that spins around and around, at the frequency of the light. When we want to figure out how likely it is for light to get from some point S to another point P, we look at all the possible trips that could be taken (even weird ones you think light cannot possibly take. It turns out, maybe later you'll figure out, that we only need to think about the straight-line paths), and how much this arrow will have spun at the end of the trip. For instance here is one diagram, for reflection off a mirror.
These arrows have a length and a direction. What is important you trace out all the paths light could take, and assign each paths arrows that spin constantly (at the frequency of the light). Then the total arrow rotation that occurs is proportional to the distance traveled. Now add the arrows up (like in the diagram). The more the arrows align with eachother, the more likely light will travel along those paths. We see the paths with the greatest alignment are also the paths of minimum total trip time. The answer: Light will probably bounce off of the region F,G,H, if it ends up at P. That is what you are seeing going from top to down in this diagram. In general, light is likely to go wherever time is a local minimum. Make a time diagram now for your broken glass situation. In your broken glass example, the time diagram (the middle one) would look like a more jagged version of this graph (Ignore the "error" on the left, its somebody else's graph).
These arrows have a length and a direction. What is important you trace out all the paths light could take, and assign each paths arrows that spin constantly (at the frequency of the light). Then the total arrow rotation that occurs is proportional to the distance traveled. Now add the arrows up (like in the diagram). The more the arrows align with eachother, the more likely light will travel along those paths. We see the paths with the greatest alignment are also the paths of minimum total trip time. The answer: Light will probably bounce off of the region F,G,H, if it ends up at P. That is what you are seeing going from top to down in this diagram. In general, light is likely to go wherever time is a local minimum. Make a time diagram now for your broken glass situation. In your broken glass example, the time diagram (the middle one) would look like a more jagged version of this graph (Ignore the "error" on the left, its somebody else's graph).
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