Burning mirrors

As the generating plane becomes more and more inclined, the ellipsis becomes more and more oblong, and the second focus moves away from the first. When it is transformed into a parabola, the second focus disappears (sometimes one says it has gone to infinite) and there is only one left. And while in an elliptical mirror the rays originating from a focus ended up in the other, in a parabolic mirror the rays that start from the only remaining focus are reflected parallel to the axis, and viceversa the rays parallel to the axis concentrate in the focus.

This latter property of the parabola can be used to build a burning mirror, that is a mirror that concentrates solar rays (which we may consider parallel because of the great distance of the Sun) in the focus, where they can light up inflammable materials. We have built an indoors burning mirror, substituting solar rays with those from a halogen lamp. We have put the lamp in the focus of a second parabolic mirror, from which the light rays come out parallel after being reflected; a second reflection on the first mirror concentrate them on the focus, where in a short time they light up a match.

The same principle is at the base of the parabolic microphone: the sound waves, which can be considered parallel if they come from afar, are reflected on the parabola and concentrated on the focus, where a microphone is places. This mechanism can hear very far away and faint noises. The great radiotelescopes and the parabolic dishes of satellite TV are also built using the focal properties of the parabola.

Parabolas are often found as solutions of technical and scientific problems. A stone thrown obliquely describes a parabola, just as the cable of a suspension bridge also assumes the shape of a parabola.