# Find angle such that beam hits a certain point

• Niles
In summary, Niles is trying to find the angle β such that the X-rays hit the point A. He is not sure where to start, and needs help from his classmates.
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.

#### Attachments

• pic_A.png
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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.

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.

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?

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

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?

tiny-tim said:
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.

tiny-tim said:
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

## 1. "What is the formula for finding the angle at which a beam will hit a certain point?"

The formula for finding the angle at which a beam will hit a certain point is: tanθ = opposite/adjacent, where θ represents the angle, opposite is the length of the side opposite to the angle, and adjacent is the length of the side adjacent to the angle.

## 2. "How do you determine the position of the beam in relation to the point of intersection?"

To determine the position of the beam in relation to the point of intersection, you can use the trigonometric functions sine, cosine, and tangent to calculate the sides of the triangle formed by the beam and the point of intersection. Then, you can use the inverse functions to find the angle at which the beam hits the point.

## 3. "What factors can affect the angle at which a beam will hit a certain point?"

Some factors that can affect the angle at which a beam will hit a certain point include the distance from the beam source to the point, the height of the beam source, and any obstructions or obstacles in the path of the beam.

## 4. "Can the angle of the beam be adjusted to hit a different point?"

Yes, the angle of the beam can be adjusted by changing the position or angle of the beam source. You can also use mirrors or lenses to manipulate the path of the beam and hit a different point.

## 5. "Are there any practical applications for finding the angle at which a beam will hit a certain point?"

Yes, there are many practical applications for finding the angle at which a beam will hit a certain point. For example, this concept is used in laser technology, surveying, and astronomy to accurately direct beams of light or radiation to specific targets or points of interest.

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