Understanding Braggs x-ray diffraction and why light is treated as a single "ray/line"

Question

I'm not familiar with optics. So my knowledge of treating light as single lines is almost completely foreign to me. Although I do know something about EM waves and Maxwells equations, so you can answer in that language.

In the image, are both lines meant to be parts of a same beam of light, and these lines correspond to the edges of such beam?

If yes, why is it correct to only understand the behaviour of the edges of the beam?

Supposedly the path difference can yield constructive interference, but I don't see how this can be correct if both lines do not land on the same point on the detector! -- This is a major confusion for me.

Finally, beams of light are not of such small diameters. They are way bigger. How does this view of the braggs x-ray spectrometer scale up? Is this event (the one in the image) happening on a big scale, and so we tell the same story for each of those events?

Isn't it important that ray(2) can crash with a plane that is not immediately below the first plane? Does this sort of thing introduce error?

Thanks.

Answer 1

are both lines meant to be parts of a same beam of light, and these lines correspond to the edges of such beam?

No, both lines are meant to be representative of different possible paths for light, which really extend through a large area, and are separated for the purpose of illustration.

Supposedly the path difference can yield constructive interference, but I don't see how this can be correct if both lines do not land on the same point on the detector!

Imagine that the "Ray 1" in the figure was moved over a little bit. Then you could see the outgoing light vectors from Ray 1 and Ray 2 would indeed be headed for the same point on the detector and could interfere. What actually happens is that effectively many rays strike all over the surface, which correspond similarly to scattering events off of the next plane of atoms (also occurring mostly continuously).

Is this event (the one in the image) happening on a big scale, and so we tell the same story for each of those events?

Right. Imagine dragging the whole picture across, making many copies of those events.

Isn't it important that ray(2) can crash with a plane that is not immediately below the first plane? Does this sort of thing introduce error?

If Ray 2 has a half-wavelength difference, then a hypothetical Ray 3 would have a full-wavelength difference and not interfere, and a hypothetical Ray 4 would have a half-wavelength again, etc. It is important that much scattering can occur, because it allows you to probe the crystal structure in further ways--most real materials are not so simple, after all.

Answer 2

First two reflections of unknown sample are absent due to mounting error of the sample. The ratio between third and forth reflections is 68 % , what is crystal structure of the sample ? If the diffraction angle (2 theta) of third reflection is 54 degree( A-1.79 Å) then calculate the lattice parameter of the sample.