hen you mix two Radio waves, you end up with
two possible mixtures: the Upper Sideband, which is the Sum of the two Frequencies,
and the Lower Sideband, which is the difference between the two Frequencies.
Audio Engineers mix sound waves the same way by combining frequencies. Thus I
see no reason to be different when mixing Light waves. Within any Spectral, the
difference frequency will always equal the first frequency because 2x - x = x,
which is clearly not the frequency of the mixture. The Sum of the two frequencies
will give us a frequency almost twice as large as any frequency in the spectral.
However by dividing the Sum of the two frequencies by two, the resulting frequency
ends up being a frequency within the spectral. There is a special relationship
between a frequency and its double, and between a frequency and its half. Each
doubling of a frequency takes it up one harmonic, while each halving of a frequency
takes it down one subharmonic. Thus you take the first subharmonic of the
Upper Sideband of the two frequencies you wish to mix in order to get the
frequency of the mixture.
You don't need to be a great mathematician to note
that the Sum of two numbers divided by two also happens to be the average value between
the two numbers. Of course working with colors you start with wavelengths so
you need to convert these to frequencies, which involves calculations with the
speed of light. Taking the first subharmonic of the Upper Sideband of these two
frequencies will give you the average frequency which you then convert back into
a wavelength. This final conversion also involves the speed of light. I have
combined both conversions and the averaging calculations into a
single formula for the mixture:
