Satellite dishes and death rays
Most of us have a vague idea that satellite dishes catch TV signals from the sky and beam them into our living rooms. But how they actually do this is all down to mathematics.
The curved surface of a satellite dish is the shape made by rotating a mathematical curve, called a parabola. Parabolas were discovered over two millennia ago when the Greeks were investigating conic sections — the shapes made by slicing a cone — which generate many of the fundamental curves known to mathematics. You might remember from school that the equation for a parabola is y = x2.
In fact we are all very familiar with the shape of a parabola: it is the shape a ball traces out when you throw it through the air. It is important in many areas of physics and its mathematical properties have been invaluable in engineering and technology over the centuries.
A parabola (shown in red) focusses incoming parallel lines
The most important property of a parabola is the ability to focus incoming parallel lines — if we shine a light into a parabola they are all sent to the same spot, called the focus. And parabolic dishes do the same thing with the electromagnetic waves containing satellite TV signals. The dish reflects all of these waves to the antenna sitting at the focus of the parabola, increasing the signal strength and sending the data, including your favourite programmes, to your TV set.
But what about the other way around, if we put a light at the focus of a parabolic mirror? In a similar way the light gets sent down to the mirror which then reflects all the light as parallel rays outward. This is exactly what happens in car headlights, creating a far brighter and more direct light than the light bulb could produce on its own.
These properties have been known for a long time. Archimedes decided to harness these properties to build a death ray in order to attack incoming ships. He set up huge mirrors in the side of a cliff and angled them so that they lay along a large parabola. These mirrors focussed the sun's light and it is believed that they were able to ignite the enemies’ wooden ships.
Throughout the centuries, whether beating your enemy at sea or seeing your favourite team beating the enemy on the football pitch, parabolas have been essential in meeting our technological challenges.
- Written by Kit Yates
- Image of satellite dishes by/ Wayne Marshall / CC BY-NC-SA 2.0
- Image of parabola found at http://en.wikipedia.org/wiki/File:Parabola_with_focus_and_arbitrary_line.svg / CC BY-SA 3.0