Satellite dish or parabolic antenna for dummies

Why are parabolic the satellite dishes? Why are they not flat, or spherical, or square? What is so special about a parabola? To answer this question, we must know what a parable is.

A parabola is a curve of the conical families. Conical curves are those obtained by cutting a cone in different ways. You can get 4 different curves:

The circle: if we cut the cone by a plane perpendicular to its axis.
The ellipse: if we cut the cone by an inclined plane that is greater than its side.
The parabola: if we cut the cone by a plane inclined parallel to its side.
The hyperbola: if we cut the cone by a plane less inclined than its side.

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A parabola is formed by an axis that separates it into two symmetrical parts, has a line, the directrix and a point, the focus. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus.

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The parabola is a very important curve because it explains the behavior of a projectile thrown into the air. In the following image, you can see the parabolas forming a ball thrown into the air, bouncing until it stops.

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What makes the parabola a special curve is that any ray parallel to the axis that impinges on the parabola is reflected in the direction of the focus. This feature only happens with the parabola.

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Then, with all this in mind, we can already know why parabolic antennas are parabolic. By having the antennas parabolic form, any signal or wave that reaches the antenna, is reflected towards its focus. If in that focus, we put a receiver, we have a satellite dish.

This same characteristic can be applied in the opposite direction, throwing a ray from the focus to the antenna or parabolic surface. This will cause the beams to reflect all parallel to each other, in a straight line and perpendicular to the axis. This is known as a directional headlamp and is what the headlights of cars or lanterns use, for example.