Homework Help: Validity of Fresnel Approximation

1. Nov 8, 2012

the_godfather

1. The problem statement, all variables and given/known data
A friend of mine asked me on the Fresnel approximations earlier, and I couldn't really remember many of the details other than it was an approximation for spherical waves based on the Taylor series. So basically I had to look it up in a text book.
One of the exercises (2.2-1) in the book fundamentals of photonics [b. saleh] was a question on the validity of the Fresnel approximation:
Determine the radius of a circle within which a spherical wave of wavelength λ = 633nm, originating a a distance 1m away, may be approximated by a paraboloidal wave. Determine the maximum angle θ and the Fresnel number N_f.

2. Relevant equations

a^4 << 4z^3λ

(N_f*θ^2) / 4 << 1

N_F = a^2 / λ

3. The attempt at a solution

I'm not really sure where to start as I don't really understand.
My initial thought was to calculate the Fresnel number using N_F = a^2 / λ. If I take the a (circle radius) as 1m. It's simple.
N_F = 1/633nm
I can then use N_F to find the maximum angle when the radius is 1m.
Now that seems way too simple.