Bragg's Law Experiment: Questions and Answers

[chimay]

Hi,

I read the quite common introduction to the Bragg's Law, but there are some points I have not clear at all; I hope you can help me.

1) The book says that, for the diffraction to be evident, the wave length of the incident wave must be comparable with the order of magnitude of the characteristic lenght of the system that is used for the experiment. Why is this so evident? I have no background in optics but just in EM fields, so if the answer is there, could you please explain it to me in few words?

2) Actually the problem it's far more complicated, since each atom absorbs radiation and then emits it isotropically; anyway, the experiment can be summarized by the well know formula, which models the phenomenon like the reflection of a plane wave that incides on all the planes that can be identified inside the lattice of the crystal. Does this conclusion come from experimental fact, right?

3) With reference to point 2: the formula refers two just a couple of plans, and says $$n \lambda = 2d\sin(\alpha)$$
Since the rays reflected by the cristal are parallel ( so they don't meet ), how can they give rise to constructice interference?

Thank you for any suggestion

 

[Pierce610]

I try to explain it. In the case of x-rays the crystal lattice works as a diffraction grating.
If you want to observe constructive interference, the difference of path 2dsin(α) between two wave which are reflected by two parallele plains must be a multiple of their wavelenght; so the two waves are in phase and the intensity on a radiographic screen increases. The word evident means that the phenomenon is observable.
Therefore the rule is that the two waves keep this difference of path after the reflection and so the same phase.

I'm not an expert but I hope to give you a right suggestion; however let's wait for other answers with sharp terms.

 

[chimay]

Thank you for your answer.
Actually I know where the Bragg's formula comes from; my doubts are explained in those 3 very specific point.
Anyway thank you!

 

[Kingkill33]

Hi,

I read the quite common introduction to the Bragg's Law, but there are some points I have not clear at all; I hope you can help me.

1) The book says that, for the diffraction to be evident, the wave length of the incident wave must be comparable with the order of magnitude of the characteristic lenght of the system that is used for the experiment. Why is this so evident? I have no background in optics but just in EM fields, so if the answer is there, could you please explain it to me in few words?

2) Actually the problem it's far more complicated, since each atom absorbs radiation and then emits it isotropically; anyway, the experiment can be summarized by the well know formula, which models the phenomenon like the reflection of a plane wave that incides on all the planes that can be identified inside the lattice of the crystal. Does this conclusion come from experimental fact, right?

3) With reference to point 2: the formula refers two just a couple of plans, and says $$n \lambda = 2d\sin(\alpha)$$
Since the rays reflected by the cristal are parallel ( so they don't meet ), how can they give rise to constructice interference?

Thank you for any suggestion

I am not sure if I understand your questions well, but I'll try.
1). You may refer to this question: why does wavelength affect diffraction
http://physics.stackexchange.com/questions/125903/why-does-wavelength-affect-diffraction

2). Can't understand the question well. However the lights diffracted are not emitted by the atoms, but reflected. Absorption of lights by atoms need meet wavelength condition to happen.

3). I think you can't consider the light as a single fine line here but it's a probability case.

Sorry for my English.

 

[chimay]

1) Thank you for the link; I have read almost all the answers, but the point was different from mine. People have tried to explain why the diffraction pattern depends on the wave length by intuitive arguments. Actually, my question is the last one you can find, that is:
"The question "why does the wavelength affect diffraction", I think, could be best answered by looking at the two extreme cases. Assuming a narrow opening is illuminated..."
What I want to know is why in the first picture we don't see diffraction, while in the second we do. (please refers to the photos of the guy I have quoted )
2) I try to be more clear: Does the fact that we can study reflection by means of parallel planes of the lattice come from experimental evidence or theoretical calculations?
3) Here I don't get you answer; if we study the phenomenon by means of reflection of a plane wave with the planes of the lattice, Why can't I consider each beam like a fine line?

Thank you very very much