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Splitting light into colors, mathematical expression (fourier transforms)

I am trying to solve a problem that includes a function of the light hitting a certain area. My question is, how would I change a function $G(x)$ of photons hitting a certain area to include just ...
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Do the other properties of a particle also have a phase?

Particles have a phase that oscillates in space-time. We know this because particles have a phase frequency (De Broglie wavelength) and this is why they interfere in space, like in the double slit ...