Fresnel Diffraction: Explaining Zero Intensity at Center

[bartieshaw]

Hey people...

This isn't really a homewrok question, I am asking it to try and improve my understanding, but if i still have posted it in the wrong place i sincerely apologise if i upset anyone.

I am going over some notes before my exam in 4 days and have encountered a problem...

the synopsis says i need to be able to "explain why the Fresnel diffraction pattern of a single slit can have zero intensity at its centre."

its not in my notes, and I've looked it up in Giancoli, but it doesn't distinguish between Fresnel diffraction and Fraunhofer diffraction so it was no help...

Just a brief description would be all i need...can anyone help?

cheers,
bart

 

[caffeine]

Knowing what light will do when it approaches an obstacle is a very difficult problem. It's actually an E&M problem in disguise. An exact solution is almost always impossible, so we develop techniques to simplify the calculation in order to get the answer.

When we care about what happens far from the obstacle, we can make certain simplifying approximations, and call it "far field diffraction". This is called Fraunhofer diffraction. It's mathematically more simple than Fresnel diffraction.

When we care about what happens close to the obststacle, we can make other simplifying approximations, and call it "near field diffraction". This is called Fresnel diffraction. It's mathematically more complex than Fraunhofer diffraction.

I happen to be extremely weak in optics. My only real experience with optics is teaching geometric optics and reading the chapter on Kirchhoff's diffraction theorem in Max Born's book on optics (mainly because I have a keen interest in E&M).

I believe all the pretty pictures you see of diffraction, like the archtypical "single slit diffraction pattern" are all Fraunhofer images, but I could be mistaken about that.

As for why Fresnel diffraction can have a minima at the center... I have no idea. I assume your teacher meant light going through a slit and impinging on a flat screen. No clue. Diffraction theory is a really difficult subject.