A parabolic mirror is a form of curved mirror that has a parabolic shape. To appreciate the properties of this shape we firstly need to understand what a parabola is.

## What is a Parabola?

A parabola is a curve defined and described in mathematics by a specific equation. The standard form of a parabola is given by this equation: **y=ax ^{2}+bx+c**

Some readers will recognise this as a quadratic equation. The variables are x and y and a,b and c are constants.

To really get to grips with parabolas in mathematics it’s useful to see the graphical plot created by this formula. Luckily there is an excellent and totally free online tool that makes this very simple. You can pop over to https://www.desmos.com/calculator where parabolas are demonstrated.

If you click on the ‘Standard Form’ option you will see the parabola formula and these settings:

You can see our basic quadratic parabola equation along with the three constants a,b and c. The graph created with these settings is shown here.

As you can see, this is a very neat symmetrical curve. Play with the sliders to adjust the a, b and c constants to see how they change the plot.

## Creating a 3D Parabola

A parabolic mirror is a 3D shape which has a parabolic curve that conforms to this mathematical rule. The most common form of parabolic mirror is concave with the reflective surface on the inside surface of the curve. The key property of concave parabolic mirrors is that they focus incoming parallel light rays to a single focal point. It is this property that makes concave parabolic mirrors particularly useful in optical applications. Placing a light source at the focal point concentrates the light reflected from the parabolic surface into a narrow beam. Convex parabolic mirrors, wherein the reflective surface is on the outside of the curve, are less common.

These useful properties of 3D parabolic shapes are used in a wide variety of reflector applications to collect or project energy in various forms including light, radio waves and sound. Take a look at the satellite dishes mounted on buildings everywhere. These are all parabolic antennae that effectively focus incoming radio waves thereby increasing the strength of the signal at the focal point. Similarly, parabolic microphones collect and concentrate sound waves onto a focal point where the microphone is located, enabling quiet sounds to be collected and recorded.

As noted, if a light source is situated at the focal point of a concave parabolic mirror the surface acts as a reflector, concentrating the reflected light into a narrow projected beam. This is the basic principle used in search lights, spot lights and torches or flash lights.

## How Parabolic Mirrors are Used

Parabolic reflectors are used in a wide range of applications. We’ve already mentioned satellite dishes that effectively use the reflective properties of the parabolic dish to focus incoming radio waves onto a focal point.

Many reflecting telescopes such as Newtonian telescopes and Cassegrain telescopes, use parabolic mirrors to gather and focus light.

Torches and automobile headlights also exploit the properties of parabolic mirrors to concentrate and reflect light in the desired direction.

Search lights and spotlights are another well known application for parabolic mirrors. Stage spotlights, for example, enable a narrow beam of light to be focused on a performer and search lights use parabolic reflectors to project concentrated light beams over long distances.

Parabolic mirrors are also used to focus and concentrate sunlight and sun rays onto a focal point to generate electricity or create heat making parabolic mirrors incredibly useful in solar energy technologies.