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Validity of Fresnel Approximation

  1. Nov 8, 2012 #1
    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.
     
  2. jcsd
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