# How to calculate reflection profile of a beam shining onto a moving mirror?

I want to build a projector, where a beam of light is shining on to mirrors, placed at different angles, which are spinning fast enough to draw lines. The question is, how to calculate the needed angles/distances/sizes to get the desired image output? Can anyone point in the right direction?

The goal is to get a line as shown in the top view. It needs to be N wide. In order to do that, I need to figure out how high the moving mirrors should be placed and at what angle. The same goes for the laser pointer. Also how big the mirrors should be.

-
How can one suggest something if you don't give some hint about the image you wish to create? Can you give more details? –  Sofia Mar 4 at 22:33
Your diagram still isn't particularly clear, what way is the mirror oriented/spinning? –  Chris2807 Mar 4 at 22:52
They are facing the beam and they are spinning along the circle, (each mirror should be at an angle to create more lines on the table). –  Yan Mar 4 at 22:59

## 2 Answers

Simple geometry tells you that the size of the image $s$, for a given distance from mirror to screen $d$, is a function of angle according to

$$\tan\frac{\theta}{2} = \frac{s}{2d}$$

For example, an image of 1 meter at a distance of 10 meters needs the mirror to sweep through an angle of $2 \cdot \tan^{-1}(0.05)\approx5.7°$

-

The response time of the human eye is something like 60 Hz. This means that you need to draw the full line in 1/60th of a second. Based on your drawing (which isn't particularly clear) you are trying to draw a line using roughly 90° of mirror rotation. Put this all together and you need the mirror to be rotating at an angular speed of 900 rotations per minute.

-
I'm interested in knowing, what should be the height of the mirror (dimension of the mirror)/laser and their angle in order to produce N width line on a table. –  Yan Mar 5 at 16:29