How Do You Calculate Cylinder Rotation Using Laser Reflection?

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SUMMARY

The discussion focuses on calculating the rotation angle of a vertical cylinder using an optical lever setup involving a laser and a mirror. A laser positioned 5 meters away reflects off a mirror mounted on the cylinder, which deflects the beam by 2 mm upon rotation. The angle of rotation is determined using the arctangent function, specifically arctan(0.002/5), and is divided by 2 to account for the geometry of the reflection, resulting in the formula for the angle being 2θ instead of θ.

PREREQUISITES
  • Understanding of basic trigonometry, specifically the arctangent function.
  • Familiarity with optical lever principles and laser reflection.
  • Knowledge of geometry related to angles and reflections.
  • Experience with experimental setup involving lasers and mirrors.
NEXT STEPS
  • Study the principles of optical levers in physics.
  • Learn about the geometry of laser reflections and angles.
  • Explore trigonometric functions and their applications in real-world scenarios.
  • Investigate methods for precise angle measurement in experimental setups.
USEFUL FOR

This discussion is beneficial for physics students, experimental researchers, and anyone involved in precision measurement techniques using lasers and optical devices.

dorkenstine00
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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!
 
Physics news on Phys.org
Think about the laser beam and the mirror. What do we know about the angle between the normal and the laser beam?
 

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