# Determine the focal length of a Fresnel Zone Plate

1. Nov 4, 2012

### Ratpigeon

1. The problem statement, all variables and given/known data
Derive an expression for the Fresnel Zone Plate's focal length

2. Relevant equations
The fresnel zone plate has a transmittance function
1/2 (1+cos (ar^2)circ(r/2l)

3. The attempt at a solution
Using Eulers formula. this splits into e^(iar^2)+e^(-iar^2) Since the transmittance funciton of a lens is e^(i$\pi$r^2/$\lambda$f) The fresnel zone transmittance function is pretty much equivalent to a lens which satisfies
a=$\pi$/$\lambda$f
Hence; the focal length is f= $\pi/$/$\lambda$a
Is this right?