How Do You Calculate Cylinder Rotation Using Laser Reflection?

[dorkenstine00]

Homework Statement

You're helping with an experiment in which a vertical cylinder will rotate about its axis by a very small angle. You need to devise a way to measure this angle. You decide to use what is called an optical lever. You begin by mounting a small mirror on top of the cylinder. A laser 5 m away shoots a laser beam at the mirror. Before the experiment starts, the mirror is adjusted to reflect the laser beam directly back to the laser. Later, you measure that the reflected laser beam, when it returns to the laser, has been deflected to the side 2 mm. Through how many degrees has the cylinder rotated?

Homework Equations

The Attempt at a Solution

So I understand the part about solving for arctan (0.002/5)
I know to get the solution, this needs to be divided by 2. I know its probably some simple geometry that I'm lacking, but I can't figure out why the angle here is 2theta and not just theta. Thanks in advance for the help!

 

[verty]

Think about the laser beam and the mirror. What do we know about the angle between the normal and the laser beam?