Fractional Distillation and Reflux Ratios

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The following definition for reflux ratio is from http://www.solvent--recycling.com/reflux%20ratio.html
"The Reflux ratio is the ratio between the boil up rate and the take-off rate. Or in other words, it is the ratio between the amount of reflux that goes back down the distillation column and the amount of reflux that is collected in the receiver (distillate).
If 5 parts of the reflux go back down the distillation column and 1 part is collected as distillate then the reflux ratio is 5:1. In the case where all the reflux is collected as distillate the reflux ratio would be 0:1. If no distillate is collected then a reflux ratio is not assigned. Instead we call this "total reflux" or equilibration.
The higher the reflux ratio, the more vapor/liquid contact can occur in the distillation column. So higher reflux ratios usually mean higher purity of the distillate. It also means that the collection rate for the distillate will be slower."

As for the formula...here is what I understand.

If we divide the two...

Now we also know that:
Pa = Na Poa (where Na is the mole fraction of a and Poa is the vapor pressure of pure a)
Pb = Nb Pob (where Nb is the mole fraction of b and Pob is the vapor pressure of pure b)

So they all equal each other.

As applied to fractional distillation, we are looking at the relative ratio of a and b in the distillation column. The higher the ratio of Pa:Pb, the more pure the distillate containing a will be.

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