Ratio of atoms in different laser levels

AI Thread Summary
The discussion centers on determining the maximum ratio of atoms in laser levels N1 and N3 under high intensity conditions. The user derives a formula relating N3 and N1 based on pump intensity (Ip) and saturation intensity (Is). They initially consider that at large intensities, N3 could equal N1, but express confusion about the implications of the formula. Another participant suggests that while the 1 can be ignored when Ip/Is is large, the problem does not specify this condition. The conversation highlights the complexities of interpreting ratios in laser physics under varying intensity scenarios.
Jon.G
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Homework Statement


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)

Homework Equations

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?
Thank in advance :)
 
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Jon.G said:
with the large intensities, they would be >> 1, so I could just ignore that
You could ignore the 1 if the ratio Ip/Is is large, but you don't seem to be told that.
 
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