# Diffraction of a extensive source

1. Aug 8, 2010

### viko

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

There is an extensive source (since it isn't important it can be monochromatic). The waves goes through a condenser lens that makes them converge. So, what we have is the "image" reproduced at the other side of the lens, at the focal plane.
So now: I understand that each dot of that image works again as a point source. Is that correct? (I assume that's correct.)

Now supose we have a single slit at the focal plane.
---->How can I solve the diffraction?<---- (I'll use, for example, the kirchhoff integral in the Fraunhofer aproximation).

2. Relevant equations

Kirchhoff integral in fraunhoffer aproximation:

$$E= \frac{-1}{2 \pi \lambda}$$ $$\frac{e^{i(wt-kr)}}{r}$$ $$\frac{1+ \cos( \Theta )}{2}$$ $$\int_{ }^{ } \int_{S}^{ } E_{incident}(r')$$$$e^{ik\frac{x}{r}x'}$$ $$e^{ik\frac{y}{r}y'} dx' dy'$$

$$E_{incident}(r') =$$ $$\frac{A}{z'}$$ $$e^{i(wt-kz') + ik$$ $$\frac{(x'^2+y'^2)}{z'}$$

3. The attempt at a solution

Considering that I have a single source at each point of the slit,
trying to solve the integral, I found that I cannot evaluate the waves in the slit, because the waves cannot be evaluated at the convergence point.

So, what to do?

I dont know why, but I think in consider the waves at the focal plane as a plane wave. Does that make any sense?

Last edited: Aug 8, 2010