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1. The problem statement, all variables and given/known data

At a particular point, a Guassian beam of wavelength λ has a radius of curvature of R1 and spot radius w1. Determine distance (z) of this point from the beam waist in these terms.

2. Relevant equations

R= z + (z0^2/z)

z0 = (pi*w0^2) / λ

w1 = w0 * sqrt(1 + (z/z0)^2)

(may be more that I'm unaware of)

3. The attempt at a solution

I have basically tried solving for all the variables and substituting them in the other equations but it all falls apart at the end and I get something like

z^2*R - (pi*w1^2)/λ = z^3-z^2

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# Optics-radius of curvature

Can you offer guidance or do you also need help?

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