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Now how do we get to that angle?
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So this blue line here is called the scattering vector,
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and that's how different the arrow coming out is from the arrow going in.
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That's just a funny mathematical or geometric thing that people have defined;
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they call it the scattering vector.
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Now this length is exactly the same as that length.
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This length is exactly the same as that length,
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and when you turn at a given angle,
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the vector between those will be perpendicular to the direction they're going
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and they'll be in-phase again.
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And if you draw the line that connects the two points,
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notice the scattering vector is perpendicular to that line.