Splitting light into colors, mathematical expression (fourier transforms)

[FordDJ22]

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 photons of a certain wavelength, say red light. I feel like this could be accomplished using a Fourier transform and de broglie's law, but I'm not sure. Can someone please help, just for a general gaussian function G(x)?

 

[Jano L.]

What does this function represent? It may help if you post more detailed specification of your problem.

 

[FordDJ22]

Basically, given a function that gives the number of photons hitting a certain area, I want a mathematical way to determine how many of those photons are of a specific frequency (such as red light).

 

[cattlecattle]

Basically, given a function that gives the number of photons hitting a certain area, I want a mathematical way to determine how many of those photons are of a specific frequency (such as red light).

I don't think you can get that distribution simply from the number of photons hitting the area. One thing does not lead to another. You can perfectly have N photons with all kinds of different frequency distribution.
You mentioned Fourier Transform, yes, it does transform between time domain to frequency domain, but here the "frequency" has a different meaning than what you might have in mind (it means the spatial periodicity of the underlying time-domain function, not the frequency of the EM wave)

 

[FordDJ22]

I don't think you can get that distribution simply from the number of photons hitting the area. One thing does not lead to another. You can perfectly have N photons with all kinds of different frequency distribution.
You mentioned Fourier Transform, yes, it does transform between time domain to frequency domain, but here the "frequency" has a different meaning than what you might have in mind (it means the spatial periodicity of the underlying time-domain function, not the frequency of the EM wave)

Ok, then how would this look specifically for a Gaussian slit experiment? Does that give the frequency distribution you were looking for?