Some Important Information Related to Huygen’s Theory Important Considerations

The Huygens principle, which is based primarily on the nature of light, was discovered by the Dutch mathematician Huygen in 1678. This principle is mainly used to describe rectilinear and spherical wave propagation. Also, in this theory, light has been described as a type of disturbance.

Also, it has been said that with the propagation of disturbance, the particles present in it vibrate in the direction of propagation, which is at right angles, which is called wave speed of light. The wave speed of light mainly works on properties like direct propagation, reflection, refraction, interference, diffraction, polarisation of light, and the explanation of the photoelectric effect based on this principle. 

The nature of the medium matters a lot in this theory. As we find that the light of the Sun passes through a medium to reach the earth, where the medium is a vacuum, we get to see this vacuum in space, where the principle of the photoelectric effect comes into play. In the context of this principle, Max Planck later presented his concept; he said that the source of light gives continuous peace, and it keeps on emitting some packets containing vibrational energy. Also, these packets were considered the basic particle of light. These basic particles are also called photons. This theory is called Planck’s quantum theory.

Huygen’s Principle 

Huygen characterised lightwave propagation in terms of its primary source, wavelets, secondary source, and wave normal. The primary source is known as the genuine source of light, and it is a point or line. The secondary source is known as the geometric centre or axis, and it is a point or line.  

On the other hand, wavelets are all points on small curved surfaces that receive light from the same primary or secondary source at the same moment. A secondary source is a location on a wavelet that serves as a light source for further light propagation. Wavefront refers to receiving light from sources that are in phase with each other simultaneously. The normal to a point drawn outward on the front of a wave is known as the wave normal. 

Huygens Principle of Secondary Wavelets

In some instances, Huygens’ concept differs from the Huygens–Fresnel principle, which primarily discusses the source of secondary waves or secondary disturbances at all points along a wavefront. At the same time, it describes the disturbances caused by the secondary source, which extend in all directions in the same way that the primary source does. This idea also sheds light on some light-related issues, including the following:

• The waves from the secondary source are similar to those of the primary source, producing their wavelets.

• These wavelets give a new wavefront at any time in the form of a common tangent in the forward direction.

• All the circular wavelets found in it together form a wavefront.

• Also, this principle is used to simplify the problems of wave propagation in both diffraction and reflection.

The Huygens wave theory explains the reflection of light, the concept of refraction of light, the concept of interference of light, and the diffraction of light. However, Huygen’s theory fails to understand specific points like polarisation, emission of light, absorption of light, and the photoelectric effect concept.

Some unique features of Huygen’s Hypothesis –

• Huygen’s principle dictates that all rays must be perpendicular to the wavefront.

• The time it takes a wave to go from one wavefront to the next, according to Huygen’s principle, is always constant. Distance and velocity can alter in this situation, but time remains constant.

• In this case, all of the wavefront’s points are represented as secondary sources in the form of secondary wavelets.

Huygens Principle Derivation; Huygens Principle Proves Reflection

The wavefront incident on the XY reflecting surface where the angle of incidence I is attained is denoted by AA’. Each point in AA’ acts as a source of secondary wavelets, according to Heisgen’s principle.

A’D / v = B’C / v

A’D = B’C

A’C sin (i) = A’C sin (r)

Then, i = r

According to this principle, the angle of incidence equals the angle of reflection. The first law of reflection also states this. The incident wavefront AB, the normal wavefront, and the reflected wavefront all lie on the same plane, proving the second law of reflection.

Huygens Principle Proves Refraction

If we divide the time taken from A’ to R by the time taken from P to B₁, we get

A₁P / V₁= B₁R / V₂ 

A₁B₁sin (i) /V₁ = A₁B₁ sin(r) / V₂ 

n₁ sin (i) = n₂ sin (r)

Example 

Huygens’ principle is a common example in our house itself. When we leave a door open between two rooms of our house, if the sound is produced anywhere in one of these two rooms, then in another room. Anyone sitting can hear its sound. Similarly, we throw stones in a pond filled with water; then, there are waves in it for some time. These waves and the sound’s reaching another room show wavefront waves based on Huygens’ principle.

Application 

• Huygens’ principle is used for the interference of light, and to explain its nature.

• Huygens’ principle is used to explain the diffraction of light, as well as to explain its nature.

• Huygens’ principle can better understand the law of reflection and refraction of light.

• Huygens’ principle can understand the spherical wave propagation and linear wave propagation of light.

Conclusion

We see the use of Huygens principle in many ways in technical and personal life. It is used in classical wave propagation of light, as well as to help predict and understand it. This principle works for all types of waves, such as water waves, sound waves and light waves. Apart from this, it is also used to explain the laws of reflection and refraction.