# Ratio of atoms in different laser levels

1. Nov 3, 2015

### Jon.G

1. The problem statement, all variables and given/known data
For large intensities, what is the maximum ratio of atoms in N1 compared with N3?
I suppose this is just a bit of maths I'm struggling with, seems simple I just can't get it for whatever reason D:

Working through previous question, I got to:
N3= (Ip/Is) / ((Ip/Is) +1 ) N1
(Ip is the 'pump' intensity, Is is the saturation intensity)
2. Relevant equations

3. The attempt at a solution
My first thought was with the large intensities, they would be >> 1, so I could just ignore that and get N3 = N1. But then because it's the same fraction in the numerator and the denominator, and the +1 comes after the Ip/Is, I thought this to be wrong.
My only other thought is that if the fraction reaches the point where it becomes 1, then N3 = 0.5 N1.
But I'm not sure where my reasoning of this would come from. I don't think it would be ∞/∞ as, if I am correct, that is not defined, not 1.

Any hints?