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.

 

[astrokreng]

Sure, I'd be happy to help explain why the Fresnel diffraction pattern of a single slit can have zero intensity at its center.

First, let's define Fresnel diffraction. This is a type of diffraction that occurs when a wavefront passes through an aperture (in this case, a single slit) and the diffracted wave is observed in the near field (close to the aperture). This is in contrast to Fraunhofer diffraction, which occurs when the diffracted wave is observed in the far field (far away from the aperture).

Now, let's consider the diffraction pattern of a single slit in the Fresnel regime. As the wavefront passes through the slit, it is diffracted and spreads out in all directions. The diffracted waves interfere with each other, creating a pattern of bright and dark fringes on a screen placed in the near field. The central maximum of this pattern is typically the brightest point, but in the case of a single slit, it can have zero intensity.

This is due to the fact that the diffraction pattern is created by the interference of waves that are diffracted at different points along the slit. At the center of the pattern, the waves are diffracted at the same point on the slit, resulting in destructive interference. This means that the peaks of one wave cancel out the troughs of another, resulting in zero intensity at the center.

In contrast, in the Fraunhofer regime, the diffracted waves are observed in the far field and the interference pattern is created by waves that are diffracted at different angles. This results in a central maximum that is not zero, as the waves are not diffracted at the same point on the slit.

I hope this explanation helps clarify why the Fresnel diffraction pattern of a single slit can have zero intensity at its center. Good luck on your exam!