You can drag the tip of the object (red arrow) to change the object height and object distance, and you can drag the focal point (filled circle) to adjust the focal length. Also, you can drag the tip of the image (blue arrow) to re-position the image anywhere you want, to explore why an image is formed in one special location - what is special about that point?

This simulation may only appeal to me, but it is written with Richard Feynman's "explore all paths" exhortation in mind. Why is an image NOT formed at a particular point? Well, light from different parts of the mirror would arrive out of phase, and cancel. Only at the image point does light arrive in phase, constructively interfering to form the image. Ideally, the graph should always show the points lined up along the axis when the image is at the actual image point - the graph shows the difference in travel time for paths that go from the object to the image via different points on the mirror. The point at 6 is the point where the principal axis meets the mirror - time delays are measured with respect to that point.

In some cases there will not be perfect alignment, because of spherical aberration - a spherical mirror is not actually the ideal shape, so some of the outer points take a little longer or shorter than expected. Making the mirror less curved minimizes this issue.

Simulation first posted on 3-6-2018. Written by Andrew Duffy

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