## Huygens' Principle

I I you drop a stone into a pond, it produces a circular expanding ripple. Why does it expand? And how might you predict its behaviour if it then flows round an obstacle, such as a tree si in up, or reflects back from the edge of the pond? Huygens' principle is a tool for working out how waves flow by imagining ilia< every point on a wavefront is a new ripple source. Dutch physicist Christiaan Huygens devised a practical way for predicting I he progression of waves. Let's say you have cast a pebble into a lake, and rings of ripples result. If you imagine freezing a circular ripple at a moment in time, then each point on the circular wave can be thought of as a new source of circular waves whose properties match those of the frozen ripple. It is as if a ring of stones was dropped simultaneously into the water following the outline of the first wave. This next set of disturbances widens the ripple further, and the new locus marks the starting points for another set of sources of spreading wave energy. By repeating the principle many times the evolution of the wave can be tracked.

Step by Step The idea that every point on a wavefront acts like a new source of wave energy with matching frequency and phase is called Huygens' principle. The frequency of a wave is the number of wave cycles that occur in some time period and the phase of a wave identifies where you are in the cycle. For example, all wave crests have the same phase, and all troughs are half a cycle away from them. If you imagine an ocean wave, the distance between two wave peaks, known as its wavelength, is maybe

CHRISTIAAN HUYGENS

Son of a Dutch diplomat, Christiaan Huygens was an aristocratic physicist who collaborated widely with scientists and philosophers across Europe in the 17th century, including such famous names as Newton, Hooke and Descartes. Huygens' first publications were on mathematical problems, but he also studied Saturn. He was a practical scientist who patented the first pendulum clock and tried to devise a nautical clock that could be taken to sea to 100 metres. Its frequency, or the number of wavelengths that pass some point in one second, might be one wavelength of 100 metres in 60 seconds, or 1 cycle per minute. The fastest ocean waves are tsunami that can reach 800 kilometres per hour, the speed of a jet aircraft, slowing down to tens of kilometres per hour and rising up as they reach and swamp the coast.

To map the progress of a wave, Huygens' principle can be applied again and again as it encounters obstacles and crosses the paths of other waves. If you draw the position of a wavefront on a piece of paper, then the subsequent position can be described by using pairs of compasses to draw circles at many points along the wavefront, and drawing a smooth line through their outer edges to plot the next wave position. The simple approach of Huygens describes waves in many circumstances. A linear wave remains straight as it propagates because the circular wavelets it produces along its length add together to form a new linear

In 2004, a catastrophic tsunami created by a huge earthquake off Sumatra sped across the entire Indian Ocean. Its force in some places was diminished because the wave energy was spread out by diffraction as n i ravelled past and between strings of islands.

Believe your ears? Huygens' principle also explains why if you shout (o someone in another room, they hear your voice as if you are standing in (he doorway rather than elsewhere in the adjacent room. According to Huygens, when the waves arrive at the doorway, just like the harbour opening, a new set of point-like sources of wave j energy is created there. So all the listening I person knows is that these waves were generated at the doorway, the past history i of the waves in the other room is lost.

Likewise, if you watch a circular ripple as it reaches the edge of a pond, its reflection produces inverted circles. The first wave point to reach the edge acts as a new source, so the backward propagation of a new circular ripple begins. Thus wave reflections can also be described using Huygens' principle.

If ocean waves move into shallower water, such as near a beach, their speed changes and the wavefronts bend inwards towards the shallows. Huygens described this 'refraction' by altering the radius of the wavelets so that slower waves produced smaller wavelets. The slow wavelets do not travel as far as faster ones, so the new wavefront is at an angle to the original. One unrealistic prediction of Huygens' principle is that if all these new wavelets are sources of wave energy then they should generate a reverse wave as well as a forward wave. So why does a wave propagate only forwards? Huygens did not have an answer and simply assumed that wave energy propagates outwards and the backwards motion is ignored. Therefore, Huygens' principle is really only a useful tool for predicting the evolution of waves rather than a fully explanatory law.

Saturn's rings As well as wondering about ripples, Huygens also discovered Saturn's rings. He was the first to demonstrate that the planet was girdled by a flattened disk rather than flanked by extra moons or a changing equatorial bulge. He deduced that the same physics that explained the orbits of moons, Newton's gravity, would apply to many smaller bodies that would orbit in a ring. In 1655, Huygens also discovered Saturn's largest moon, Titan. Exactly 350 years later a spaceship called Cassini reached Saturn, carrying with it a small capsule, named after Huygens, which descended through the clouds of Titan's atmosphere to land on its surface of frozen methane. Titan has continents, sand dunes, lakes, and perhaps rivers, made of solid and liquid methane and ethane, rather than water. Huygens would have been amazed to think that a craft bearing his name would one day travel to that distant world, but the principle named after him can still be used to model the alien waves found there.