Simple Ray Optics Problem-Check my answer?

[bcjochim07]

Simple Ray Optics Problem--Check my answer?

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

I just wanted to make sure I was visualizing this setup right. So I drew a right triangle with legs 5 m and .002 m. Then I took the arctan(.002/5) and got .023 degrees. Is this correct?

 

[rl.bhat]

In reflection, when the mirror rotates through theta, the reflected beam rotates through 2 theta.

 

[bcjochim07]

Oh ok... I see an error in my drawing. So the answer is 0.0115 degrees

 

[dorkenstine00]

Okay, so I know I'm missing some really simple geometry here...but I don't understand why the angle created is equal to 2theta and not just theta. Any help would be appreciated! :D

 

[rl.bhat]

Here the indecent beam is at rest making zero angle with the normal to the cylinder. When the cylinder rotates through a small angle theta, angle of indecent is theta and angle of reflection is theta. Hence the angle between the indecent beam and the reflected beam becomes 2(theta).

 

[dorkenstine00]

okay. Thanks a lot! :D