Fresnel Number

1. Dec 3, 2011

khanley

Hi guys,

I can't find my notes on Fresnel diffraction and I have my Optics exam on Monday...

Does anyone know how to derive F=a2/λL where L=1/z+1/z'

I've googled it to death, checked here and tried in Optics 4th edition by Hecht with no luck...

I'd really appreciate any help.

Thank you so much!

2. Dec 3, 2011

Niles

I'll give it a try, but its only an approximate derivation. Maybe it will point you in the correct direction: So we are looking at a slit of width 2a, and a point source S placed some distance behind it. The distance from S to the upper/lower part of the slit we denote R.

The distance between the opening and R we denote Δ, and is the difference between the plane wavefront to the curved wavefront. We find

$$\Delta = R-\sqrt{R^2-a^2} = R-R\sqrt{1-\frac{a^2}{R^2}}\approx \frac{a^2}{2R}$$

If the wavefront is plane we must have Δ<<λ so R >> a2/λ. This is the Fraunhofer regime, so the Fresnel regime is R ~ a2/λ.

I hope it helps.