Parabolas and focal points

A colleague from another department stopped by my office this morning with a question about parabolas and parabolic mirrors. In the simplest terms, his question was the following:

When parallel rays reflect off a parabola, do they always converge to a focal point?

As we can see in the diagram below, rays that are parallel to the axis of symmetry of the parabola reflect and converge on a focal point. What about parallel rays with a different slope?

Picture 2

The answer is “no,” and to convince him of this fact I turned to my new favorite application: GeoGebra. In a matter of minutes I whipped up an applet illustrating this fact and posted the applet online. I thought you all might like to see it too.

(By the way, does anyone know if it is possible to embed applets in blogs?)


  1. Sime S. says:

    Yes, the GeoGebra applet can be embedded in WordPress. I suggest you look at the blog colleague Jon Ingram All the best.

    1. munshi2 says:

      Sorry, it’s WordPress, not Sime S.

      1. Thanks, that’s what I was afraid of.

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