Workout: Curved mirror equations

Read

Curved mirrors and Curved mirror equations.

Launch

the github Optical Bench simulation or the Optics Bench Interactive from The Physics Classroom. You may have to authorize or update Java on your computer to get the github sim to run, but it does a lot more than the one from The Physics Classroom. If you can't get GitHub to work, use the Physics Classroom one and try to infer the answers to the questions  from creative variations.

Set up

The GitHub sim comes up with a blank black screen with a control panel above it. The control panel looks like this:

Select Mirror/Line Segment and draw a straight line vertical mirror. Then choose Point Source and click somewhere on the screen to drop a point source. Light rays leave the point source in all directions. Your result should look something like the image at the right. (The rays reflected from the mirror look curved. This is an optical illusion. They are actually straight. Check it out!)

Then turn on "Extended rays" to show the path a brain observing the reflected rays would assume the rays come from. (To turn "Extended rays" off again, select "Rays".)

Answer these questions

  1. Where do the reflected rays appear to converge? Move the point source around and describe what happens to the convergence point of the extended rays.
  2. Now press "Reset" (on the toolbar at the upper right) to clear the screen. Select "Mirror/Circular Arc" and pull a straight line on the screen with your mouse. Play with moving the three red dots on the mirror to change its shape. Make an arc curving toward the right and put a point source near it so that it looks something like the figure shown at the right.   

    This is pretty complicated. What's happening? What is the convergence point of the light? Why is it farther away from the mirror than the source? Play with the position of the source and describe one interesting thing that happens.

Joe Redish 4/22/18

Article 727
Last Modified: July 1, 2019