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
lMix
= C / (f1 + f2 ) / 2
Where f1 is the first frequency of the mixture, and
f2 is the second frequency of the mixture.
lMix
= C / (C / l1 + C / l2 ) / 2
by substitution of the frequency equations for the two frequencies.
lMix
= 2C / (C / l1 + C / l2 )
by simplification.
lMix
= 2C / C (1 / l1 + 1 / l2 )
by factoring C out of the bracketed term.
lMix
= 2 / (1 / l1 + 1 / l2 )
by cancelling out the C's in the numerator and denominator.