How do waves interfere in Bragg's Law?

[mattg443]

I am aware that when an X ray is 'reflected' from the sheets of a crystal lattice, some radiation passes through whilst remaining radiation penetrates different layers or is scattered.

And that if the path difference of the wave traveled is an integral value of wavelengths, constructive interference occurs

However, my problem is, that in all the diagrams, I don't see how interference could occur, because the waves are in two distinct locations, therefore, not interfering at all.

E.g in the attachment, the wave that is reflected of the second layer cannot interfere with the wave reflected off the first layer.

Is this just an oversimplification of the diagram, or a flaw in my understanding?

Thanks!

 

[ehild]

The wave is not a straight line, those lines in the picture are normals of the extended wave-fronts. Parallel lines mean the same wave.
Imagine light waves as waves on a lake or river when a ship passes, or see waves coming to the shore.

Part of the incoming wave is reflected from the surface plane of the crystal, other part reflects from the next plane. Those reflected waves unite to a single wave with common wave-fronts when leaving the crystal. The intensity of the resultant wave depends on the path difference between the component waves.

ehild

 

[mattg443]

Ok, so the red and blue lines are wave fronts, but i still can't see how those two lines represent the same wave.

I see that it makes sense that they are the same wave, i just can't visualise how they could be the same wave, if drawn in two different spots.

 

[mattg443]

(maybe another explanation/example will help)

 

[ehild]

For simplicity, imagine a wave traveling in the x direction:

E₁(x,y,z)=A sin(wt-kx). The wavefronts are the planes where the phase wt-kx=constant. They are parallel with the y,z plane, and extend infinitely. Their normal is parallel with the x axis, and you can draw a normal anywhere. The wave is represented by the wavefronts, not with the normals.
Let be two such waves with the same frequency, polarization and direction of propagation, only the second wave has traveled a longer distance, so it has a phase shift with respect to the first wave:
E₂(x,y,z)=B sin(wt-kx+φ). The longer distance can be because of reflection. The waves interfere, their E vectors is the sum of the individual E vectors. It is easy to show that the resultant is a wave with the same frequency, polarization and direction as the individual waves, but the amplitude depends on the phase shift, and the phase constant is different form those of both original waves. So you got a single wave from both original ones.

In your problem, there is one wave inside the crystal, but two reflected waves outside. They have the same frequency, polarization and direction of propagation. They interfere and make a single wave.

ehild