/sci/ - Science & Math

The trick is that if you change things slightly about the beam, there's a huge amount of destructive interference by all the lower layers. Typically the diagrams only show the first layer f constructive interference, but if for example the x-rays were slightly longer or shorter wavelength, they'd destructively interfere.

But the destructive interference of the x-rays reflecting off the hundreds of consecutive crystal planes will basically cancel it all out, for some particular angle. That's how I understand it to work.

>>9454948
I'm having trouble with my connection at the moment, so my apologies if things get posted multiple times.

I forgot to add, these xrays are produced many at a time and over an extended region of space. The two interfering outgoing rays didn't scatter off one atoms and one directly below it, but rather maybe one or two off to the side. The perfect periodicity of the crystals is the only reason any of this works at all.

>>9454937
aint that shit the same as with the diffraction grating ?

>>9454984
Sorry, i meant the Fabry Perrot interferometer
The only thing that changes is that there's a cos instead of a sin

>>9454992
>>9454984
I'm not very familiar with that. But in the case of a diffraction grating, something similar happens as the grating density increases. With low density grating, the light gets split in a way that looks like the double slit, with envelopes of brightness surrounding a much higher frequency pattern.

With the super high density though, light basically gets split like a prism and multiple copies of the visible spectrum come out with different angles.

It's hard for me to describe this, I'm not that kind of physicist.

>>9455006
Yeah I know interferences with n waves problems are often the same, it's usually a problem of geometry
Three questions you gotta ask yourself:
- Is the interference thingy well set? (here it's an exercise so ok)
- How am I lighting it? / Where is the light coming from?
- Where do I look for the interferences?
Start with the third question and consider only two rays, it should help you start writing some equations

>>9455006
First you should consider the problem when the beam comes in orthogonal to the surface. This is comparable to thin-film interference. Then as the angle changes, and dependent on which angle you choose to describe the problem with, you end up with the equation in your slides.
Of course if the first two layers interfere constructively, the other layers will do the same if the spacing is constant.
A useful derivation can be found at:
https://en.wikipedia.org/wiki/Thin-film_interference
Look at the Theory part.

>>9455027
>>9455036
I'm not OP, and definitely not looking to prove things about diffraction gratings.

>>9454937
>But why?
Because they're in phase.

>https://en.wikipedia.org/wiki/X-ray_crystallography

The X-ray source is on one side of the crystal and a florescent screen is on the other side.
Procedure in the above link or look for "X-ray diffraction through a crystal" for more articles and images.
What you see on the screen is an approximately radial pattern of spots. I'm trying to attach a sample image, but 4Chan is fighting me. Maybe it's for the best.
>https://www.slideshare.net/bharathpharmacist/81347482-xraydiffractiontechnique-39635806
gives a better explanation of Bragg's Law

OP here. Had some problems with CloudFlare and couldn't post.

Anyway, I still don't really understand. Maybe it's not even the Bragg's Law, but rather just generally how can two separate light beams that are a certain distance apart ever interfere (constructively or not)? Shouldn't they just go on their way indefinitely without ever interfering?

Maybe it's like the double slit experiment, only instead of the slits we have the crystal atoms? And where the x ray detector is positioned is where the double slit experiment's film shows brightest?

File upload still doesn't work, I wanted to post this: https://thiscondensedlife.files.wordpress.com/2016/05/double_slit_diffraction_1-624x567.jpg

The X-ray detector is positioned where the X-rays go AFTER passing through the crystal.
Look at the diagrams in
>https://www.slideshare.net/bharathpharmacist/81347482-xraydiffractiontechnique-39635806
The crystal scatters photons like a diffraction grating. At some angles the waves reinforce and at other angles they cancel. X-rays have very short wavelengths and we can't rule a grating that fine. The lattice spacing in crystals though is just right.
You get a geometric pattern of light and dark spots rather than the simple banding of the two slit experiment, so the computations are harder, but the basic principle's the same.

>>9455136
Two light rays pass right through each other and go their separate ways. But at the intersection, the electric field is the sum of the electric fields of the individual rays. The photons die and their energy is absorbed when they hit a surface. If the intersection point occurs AT the point of contact, the electric field may be stronger or weaker than the field of an individual photon. So you get brighter and dimmer areas,
Note that a localized cancellation does not mean that energy has been destroyed. It just shows up at one of the extra-bright areas. Interference does not change the total energy.

Seems to be something wrong with 4Chan today. Can't upload images.

>>9454937
Do you understand how young's interference experiment works, and the math that describes it? It's basically just that.

>>9454937
Does this help? Won't let me upload pictures
https://chem.libretexts.org/@api/deki/files/12295/Bragg'sLaw.jpg?revision=1&size=bestfit&width=444&height=236

>>9455210
>You get a geometric pattern of light and dark spots
But the X ray detector is positioned where the brightest spot is then, right?

>>9455242
Yeah, I guess it is. It's still kinda weird that nowhere did I read that it's similar to the double slit experiment or diffraction grating.

So in essence, what we really get is pic related (sort of), but we are only interested in the angle that corresponds to the "central bright fringe"?

>>9455254
They look at the entire pattern to determine the angles. Of course, that's when they used film. Maybe they scan the detector and measure one pixel at a time these days. But you need the whole thing.
Damn, I wish I could upload an image.
Think of the two-slit experiment. The spot directly between the 2 slits is bright. Because it's an equal distance from slit A and slit B. The waves travel the same distance, so they arrive in synch and reinforce. A little to one side they're out of phase and the screen is dark. A little further and the path difference is exactly one wavelength, so they reinforce again. Dark. Bright when the path lengths differ by two wavelengths, and so on.
From the wavelength of the light and the spacing of the dark lines on the screen you can calculate the distance between the slits. Follow?
Each successive peak corresponds to the next angle at which the difference in path-lengths between slit A and slit B is an integer multiple of the wavelength.
In Bragg diffraction you are calculating the equivalent of spacing between slits -- the spacing between atoms in the crystal. .

>>9454937
How the fuck do you even study solid state without actually understanding optics first.

>>9455266
>In Bragg diffraction you are calculating the equivalent of spacing between slits -- the spacing between atoms in the crystal.
Yeah, I get it now, thank you. It's weird to me that nowhere do you find this sort of comparison in any textbook or even online article. Or maybe it's obvious and I'm just dumb. But I'm not the only one since I've found forum threads on Quora and other websites asking the same thing: how does interference actually occur in the textbook diagrams for Bragg's Law.