Futurama Physics: The Secrets of Fresnelling

Last week's episode of Futurama showed Fry becoming a cop and dispensing justice Tron-style. During a high-speed motorcycle pursuit, he and his partner chase a suspect to a place called Fresnel Circle. Suddenly, the man splits into many different versions of himself, all going in expanded, concentric rings around the circle. What's going on? Only physics can explain.

Lenses are generally smooth things, with bulging middles tapering gently to thin sides. Contact lenses, telescope lenses, and the lenses in the eye are all smoothed out. The shape of lenses is determined by their intended function, which is generally to focus parallel streams of light to a point. The light is bent inwards by refraction when it enters the lens, and inwards again when it leaves the other side. The streams of light converge to a single point, which is where a person should position their eye (or their film) to get a single focused image.

The Fresnel Lens doesn't look or work like that. It's flat on one side, and chopped up into little shelf-like stairs on the other. The stairs are concenctric rings, slim towards the center and buidling up towards the edges. So a Fresnel lens looks a bit like a perfectly circular amphitheater standing on its side. The difference is the tops of each of the 'stairs' are cut at a slight angle. This angle bends the lights leaving the lens, forcing it to a focal point. It's at this focal point that someone would put their eye if they wanted a clear picture.

Although they wouldn't get nearly as clear a picture as they would if they had a smooth lens. Because of the spaces between the stairs, Fresnel lenses produce a wide beam of concentric rings instead of a focused single beam. They were first used because they cut out the bulk of a regular lens without giving up much of the transmission of light. They were used a great deal in early lighthouses, and in cheap magnifying glasses. The rotating lens in Fresnel Circle looks like many of the early lighthouse lenses, with many Fresnel lenses stuck back-to-back.

Futurama Physics: The Secrets of Fresnelling

There is also what's known as a Fresnel zone. When an electromagnetic wave leaves an aperture, it spreads out in a roughly circular way in every direction, much the way that waves in water spread out in a roughly circular way when they leave a tunnel and move into a pool. Unlike water waves, electromagnetic waves, when made by humans, are generally meant to be received at the other end of their journey. (Radio waves will be picked up by a radio receiver, for example.) If the transmitter and the receiver are the only things that the radio waves touch, the signal will be clear no matter what.

Usually, though, there is some obstacle, if not directly between the transmitter and the receiver, then off slightly to the side. The electromagnetic waves that have traveled out to the side sometimes bounce off that obstacle and get directed back towards the receiver. When wave crests meet, they build up even higher. When troughs meet, they sink even lower. And when a crest and a trough meet, they cancel each other out. If the receiver is placed at the spot where the crest of the wave that was directly transmitted and the trough of the wave that was bounced off the obstacle meet, there will be no signal. If it is moved slightly to where the crest of the deflected wave meets the crest of the transmitted wave, it will receive a very strong signal.

Futurama Physics: The Secrets of Fresnelling

Fresnel zones are ellipsoid 'shells' that mark out exactly how a deflected wave will interact with the transmitted wave. For example, if an object is in Fresnel Zone 1, the wave that bounces off it may be between 0 and 90 degrees out of phase with the transmitted wave. The deflected wave will meet the transmitted wave anywhere between the neutral beginning of the wave and the first crest. If an object is in Fresnel Zone 2, the wave will be between 90 and 270 degrees out of phase, and so on. In this way, researchers can get an idea of where and how the signal will blink out of existence and where it will be extra strong.

Via How Stuff Works, Wisconsin Edu, and Zytrax.