Thus the equation for l is: l = C / f
Likewise the equation for f is: f = C / l .
The l of the first subharmonic of the Upper Sideband of the mixture is
lm
= C / (f1 + f2 ) / 2
lm
= C / (C / lR + C / lG ) / 2
by substitution of the frequency equations for Red and Green light.
Where f1 is the first frequency of the mixture, and
f2 is the second frequency of the mixture.
lm
= 2C / (C / lR + C / lG )
by simplification.
lm
= 2C / C (1 / lR + 1 / lG )
by factoring C out of the bracketed term.
lm
= 2 / (1 / lR + 1 / lG )
by cancelling out the C's in the numerator and denominator.
lm = 2 / ( 1 / 680e-9 + 1 / 515e-9 ) =
2 / (1,470,588.235 + 1,941,747.573)
lm = 2 / 3,412,332.808 = 586.109e-9 meters or 586nm. A nice bright Yellow.