Find angle such that beam hits a certain point

[Niles]

Homework Statement

Hi guys

The setup is the following: I have a parallel beam of X-rays that impart of a mirror. The idea is that the X-rays are refracted to hit a point A. I think pictures of the setup will help greatly, and will minimize the chance of confusion. In picture A we are looking at the setup from above: The mirror is tilted in two ways: First with respect to the axis perpendicular to the picture (the circle with a dot inside - we call this angle α), and then with respect to an axis horizontal to the plane (we call this angle β).

My problem is that I cannot find the angle β, such that the X-rays hit the point A. I know that α has to be 2 times the scattering angle.

Do you have any suggestions on how to find β? Needless to say, we need to find β as a function of the X-ray wavelength, but I am not quite sure where to start.Niles.

 

[tiny-tim]

Hi Niles!

Is the point A off the plane?

If so, β needs to be half the angle between the plane and the perpendicular from A to the second axis.

 

[Niles]

I am not quite sure what you mean by "off the plane", but the point A is in the same plane as the incoming rays.

 

[tiny-tim]

ah, then I'm misunderstanding your question …

if the rays are reflected off a line in the plane, won't they be reflected out of the plane?

 

[Niles]

But the line the rays are reflected off is only in the plane when β = 0.

 

[tiny-tim]

Sorry, I got confused, I meant to write: if the rays are reflected off the mirror after it's been rotated about a line in the plane, won't they be reflected out of the plane?

Aren't you saying that the mirror is first rotated in the plane, then rotated (about a line in it) out of it?

 

[Niles]

Sorry, I got confused, I meant to write: if the rays are reflected off the mirror after it's been rotated about a line in the plane, won't they be reflected out of the plane?

That is correct. I have misunderstood the problem: The point A is not in the same plane as the incoming rays.

Aren't you saying that the mirror is first rotated in the plane, then rotated (about a line in it) out of it?

That is also correct. Ok, we were both confused there