Posted by: **Dave Richeson** | June 4, 2009

## 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?

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 WordPress.com blogs?)

### Like this:

Like Loading...

*Related*

[…] and focal points II Yesterday I wrote about parabolic mirrors. I pointed out that parallel rays hitting a parabola typically do not reflect back to a focal […]

By:

Parabolas and focal points II « Division by Zeroon June 5, 2009at 11:14 am

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

By:

Sime S.on June 6, 2009at 4:00 pm

Sorry, it’s WordPress, not WordPress.com. Sime S.

By:

munshi2on June 7, 2009at 4:29 am

Thanks, that’s what I was afraid of.

By:

Dave Richesonon June 7, 2009at 7:10 am