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Huygens Principle

# Huygens’s Principle

## Christiaan Huygens

Christiaan Huygens (1629-1695) is a Dutch physicist, mathematician and astronomer. The meaning of Huygens is “son of Hugo”. He has made many contributions in field of science. The wave theory of light is one of his major discovery in physics. He also discovered the pendulum clock, the shape of rings of Saturn and Titan which is the largest moon of Saturn etc.

## Background

Christiaan Huygens stated that light travels in the form of waves. Huygens mentioned that light is made up of waves which vibrates up and down and is perpendicular to the direction of light. He said that wavelength of the wave is very less when comparing with the dimensions of the object we measure. With the introduction of this concept, Huygens proved the laws of reflection and laws of refraction. He said that wavelength of the wave is very less when comparing with the dimensions of the object we measure.

However, these statements were against the Corpuscular theory of light proposed by Sir Isaac Newton. Newton described that light is made up of tiny particles. The theory again states that the speed of light increases from rarer to denser medium. But Huygens found that the speed of light in denser medium is less compared to the speed of light in rarer medium. Initially the wave theory of light was not approved.

Later, another scientist named Thomas Young performed the famous Interference experiment, which is called the Young’s Double Slit Experiment (YDSE). This experiment proved the wave nature of light. After this, many other experiments were carried out which included the interference, diffraction and polarization patterns. These experiments were only explained by considering the wave nature of light. Finally, the wave theory of light came into existence.

Huygens’s wave theory

## Light Wave Theory

Huygens proposed that light waves are longitudinal waves, but later it was found out that light waves are transverse in nature which means particles move perpendicular to the direction of wave. Light wave possesses a sinusoidal wave form. Wavelength and frequency are the two characteristics of light wave. Wavelength is defined as the distance between two peaks of waves. Frequency is the number of peaks that travels beyond a point in one second. The wave theory could explain the various optical phenomena of light like interference, diffraction, polarization and dispersion compared to the particle theory of light. But it could not explain the photo electric effect of light.

Light waves

Light waves are also considered as electromagnetic waves. This concept was introduced by James Clark Maxwell. Light waves are linked with changing electric and magnetic fields. Light waves also have those properties like reflection, refraction, interference, diffraction, polarization etc. Later it was found out that light does not need any medium to travel. It can travel through empty space.

## Huygens’s Principle

### Wavefront

Wavefront is a surface (which is either real or imaginary) for which an optical wave comprises a constant phase. It can be the crest or the trough of the same wave. For Example, drop a stone or pebble into a calm and still pond. We can see the formations of circular rings in the pond. Circular waves are formed on the surface of the pond. Here all particles inside the waves oscillate in same phase. They oscillate in synchronization with each other. These waves of constant phase is called as wavefront. The speed of the wave is defined as the speed with which the wavefront moves outwards from the source. The energy of the wave travels in the direction which is perpendicular to the wavefront. How does a plane wavefront and spherical wavefront moves is shown here.

Wavefronts

In plane wavefront, the rays are parallel to each other with constant amplitude. Spherical waves are produced from a single spherical point source.

### Huygens’s Principle

Huygens Principle mentions how a wavefront moves in space with the help of geometrical constructions. Huygens principle states that every point on a wavefront behaves as a secondary source of light and emits secondary spherical wavelets of light. These emitted waves are semicircular in nature. The new wavefront will be the line tangent to all these secondary wave lets. These secondary wavelets propagates with the velocity of light in the same medium. Huygens principle could determine the shape of the wavefront at a later time t = ԏ, if we know the shape of wavefront at time t = 0.

Formation of Spherical wavelets based on Huygens’s Principle

Huygens could also derive the laws of reflection and laws of refraction by this principle. It can also explain the interference phenomenon of light. The principle clearly mentions that diffusion of waves do not take place while propagating. For Example let’s consider a light bulb which is turned on for a second. Later the person who views the bulb from quite a distance away actually sees the bulb as turned on. Similarly we are able to see the clear images of stars from such a long distance. These are all due to the concept of Huygens’s principle.

Huygens’s Principle illustration

### Modification on the Principle

The Huygens principle is applicable for not only for light waves but also for all types of waves, especially sound waves. However this principle could not explain the diffraction effects. It was also difficult to explain the phenomenon of polarization of light. Later Augustin Jean Fresnel provided a much more detailed clarification on the principle which could explain the diffraction phenomena. He described the rectilinear propagation of light on the basis of wave theory. It was Fresnel who mentioned that light waves are transverse waves.

Fresnel expanded on the principle and referred that the amplitude of the light wave at a point is identical the superposition of the amplitudes of those secondary wavelets at that point. It is because the secondary wavelets are having the same frequency as that of the original wave. Later Gustav Kirchoff arrived at Huygens-Fresnel Principle from Maxwell’s equation. The above figure explains the Huygens – Fresnel principle of diffraction.The equation is S = vt, where is the distance, v is the speed of propagation and t is the time taken. The emitted waves are semicircular in nature. Huygens – Fresnel principle states that every unobstructed point on the wavefront behaves as a source for secondary wavelets. The resultant amplitude of all wavelets will be the sum of all individual waves.

## Summary

• The wave theory of light was proposed by Christiaan Huygens.
• Wave front is a real or imaginary surface where the phase of oscillation is the same.
• Huygens Principle defines that each point on a wavefront act as a secondary source of light and emits secondary spherical wavelets of light. These secondary wavelets travels same as that of the velocity of light in vacuum.
• The principle can explain the laws of reflection and refraction.
• Augustin Jean Fresnel elaborated on the principle and by Huygens-Fresnel principle it was able to explain the diffraction effects.

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