Huygens Principle: Corpuscular Theory, Wave Theory

Huygens Principle: Thinkers and scientists have always been fascinated by light. However, scientists did not begin to understand the properties of light until the late 17th century. Sir Isaac Newton proposed that light was made up of tiny particles known as photons. In contrast, Christian Huygens proposed that light was made up of waves that propagated perpendicular to the direction of its movement. 

He also assumed that it travels in a highly elastic and very less dense medium called ether. Huygens proposed several ideas which are still in use to explain the nature of light and other types of waves, continue reading this article to understand the wave nature of light in detail.

Huygens Principle and its Applications

Corpuscular Theory of Light (Newton)

Newton, like most thinkers of his time, believed that light was a motion of particles (light corpuscles) in straight lines. This made a lot of sense—it seemed to agree with Newton’s second law (refraction being explained by forces acting on boundaries between different media) and explained image formation by lenses or pinholes.

Similarly, one could comprehend reflected light beams, mirrors, and so on. 

Wave Theory of Light (C Huygens)

Light, according to Huygens, is a wave that travels through space like ripples in water or sound in air. As a result, light spreads out like a wave in all directions from a source. A wavefront is the location of points that moved a certain distance over a fixed time interval.

Thus, the locus of points that light has traveled during a fixed time period from a point source of light is a sphere (a circle if you consider a (2D source).

Wavefronts

A wavefront is the Locus of all the points where waves starting simultaneously from a source reach at the same time, and hence the particles at these points oscillate with the same phase. It could either be a line or a surface.

Types of Wavefronts:

• Spherical Wavefronts 
• Plane Wavefronts
• Cylindrical Wavefronts

Spherical Wavefront: If a point source in an isotropic medium emits three-dimensional waves, the wavefronts are spheres centred on the source, as shown in the diagram of the wavefront below. This type of wavefront is known as a spherical wavefront.

Shape of Light Source: Point source
Shape of Wavefront:

Variation of Amplitude with Distance: \(A \propto \frac{1}{d}\)

Variation of Intensity with Distance : \(I \propto \frac{1}{{{d^2}}}\)

2. Cylindrical Wavefront: When the light source is linear, all of the points equidistant from it lie on the surface of a cylinder, as shown in the figure. This type of wavefront is known as a cylindrical wavefront.

Shape of Light Source: Linear or slit

Diagram of Shape of Wavefront:

Variation of Amplitude with Distance: \(A \propto \frac{1}{{\sqrt d }}\)

Variation of Intensity with Distance: \(I \propto \frac{1}{d}\)

3. Plane Wavefront: When the light source is linear, all of the points equidistant from it lie on the surface of a cylinder, as shown in the figure. A wavefront of this type is known as a cylindrical wavefront.

Shape of Light Source: Extended large source situated at a very large distance

Diagram of Shape of Wavefront:

Variation of Amplitude with Distance: \(A = {\rm{constant}}\)

Variation of Intensity with Distance:  \(I = {\rm{constant}}\)

Properties of Wavefronts

• The wavefront is defined as the locus of all points with the same phase at a given point in time.
• The phase difference between various particles on the wavefront is zero.
• The wavefront’s shape is determined by the shape of the source of the disturbance.
• Normal to the wavefront represents a ray of light.
• A wavefront is always perpendicular to the light rays.

• Backward propagation of a wavefront is not possible.
• The wavefront travels with the speed of light in all directions in an anisotropic medium.

Huygens Principle

According to the Huygens-Fresnel principle (widely known as Huygen’s Principle), every point on a wavefront is a source of wavelets. These wavelets spread out in the same direction as the source wave, with the speed of light.

The sum of these spherical wavelets forms the wavefront. This new wavefront is a line that is perpendicular to all of the wavelets. At any given point in time, the common tangent on the wavelets in the forward direction gives the new wavefront. Thus, it is a geometrical method to find the wavelength.

Primary and Secondary Sources

Huygens’s principle states that light is a wave that propagates through space like ripples in water. Hence, the light spread out from a source like a wave in all directions. The locus of points that traveled some distance during a fixed time interval is called a wavefront.

Thus, from a point source of light, the locus of points up to which light has traveled in a fixed time period is a sphere (a circle for a 2D source).

After the creation of the primary wavefront, a secondary wavefront is created from every primary wavefront. Secondly, every point on this wavefront acts as a secondary source of light which emits more wavefronts. The effective wavefront generated is tangential to all the secondary wavefronts generated by the secondary source.

This is how a light wave propagates through space by generating secondary sources and wavefronts. The distance between any two consecutive wavefronts gives the wavelength of the wave.

Law of Refraction Based on Huygens Principle

A plane wave \(AB\) is incident at the surface \(PP′\) separating mediums \(1\) and \(2\) at an angle \(‘i’.\) Refraction occurs in the plane wave, and \(CE\) represents the refracted wavefront. In the figure velocity in medium \(2\) i.e. \({v_2} < {v_1},\) causing the refracted waves to bend towards the normal. \(?\) is the time interval.

To determine the shape of the refracted wavefront we draw a sphere of radius \({v_2}\tau \) from point \(A\) in the second medium (the speed of the wave in the second medium is \({v_2}\)). Let \(CE\) be a tangent plane drawn from point \(C\) to the sphere.

The refracted wavefront would then be represented by \(AE = {v_2}\tau .\) When we consider the triangles \(ABC\) and \(AEC\) together, we can easily obtain

\(\sin i = \frac{{BC}}{{AC}} = \frac{{{v_1}\tau }}{{AC}}…….1\)

\(\sin r = \frac{{AE}}{{AC}} = \frac{{{v_2}\tau }}{{AC}}…….2\)

where \(i\) and \(r\) are the angles of incidence and refraction, respectively

From the equation \(1\) and \(2,\) we get

\(\frac{{\sin i}}{{\sin r}} = \frac{{{v_1}}}{{{v_2}}}……..3\)

The important result of the above equation is that if \(r < i\) (i.e. if the ray bends toward the normal), the speed of the light wave in the second medium \(\left( {{v_2}} \right)\) will be less than the speed of the light wave in the first medium \(\left( {{v_1}} \right).\)

This prediction contradicts the prediction of the corpuscular model of light, and as subsequent experiments demonstrated, the prediction of the wave theory is correct. If \(c\) denotes the speed of light in a vacuum, and \({n_1}\) and \({n_2}\) denote the refractive index of medium \(1\) and \(2,\) then,

\({n_1} = \frac{c}{{{v_1}}}……..4\)

\({n_2} = \frac{c}{{{v_2}}}………5\)

From Equations \(4\) and \(5\) we can write the Equation \(3\) as below:

\({n_1}\sin i = {n_2}\sin r\)

The above equation is called Snell’s law of reflection.

Law of Reflection Based on Huygens Principle

We can see in the above diagram that a ray of light is incident on this surface, as is another ray that is parallel to this ray. Plane \(AB\) is incident on the reflecting surface \(MN\) at an angle \(‘i’.\) Because these rays are incident from the surface, we refer to them as incident rays.

If we draw a perpendicular from point \(‘A’\) to this ray of light, we will see a line connecting point \(A\) and point \(B,\) which is known as a wavefront, and this wavefront is incident on the surface.

Because this incident wavefront carries two points, point \(A\) and point \(B,\) we can say that light travels a distance from point \(B\) to point \(C.\) If \(‘v’\) represents the speed of the wave in the medium and \(‘?’\) represents the time it takes the wavefront to travel from point \(B\) to point \(C,\) then the distance is \(BC=v?\)

To create the reflected wavefront, we draw a sphere with a radius \(v?\) from point \(A.\) Let’s say \(CE\) represents the tangent plane drawn from point \(C\) to this sphere. So, \(AE=BC=v?\)

If we consider the triangles \(EAC\) and \(BAC,\) we will see that they are congruent, and thus the angles \(‘i’\) and \(‘r’\) are equal. This is the law of reflection.

Diffraction and Huygens’ Principle

When light passes through an aperture (a hole in a barrier), each point of the light wave within the aperture creates a circular wave that propagates outward from the aperture.

As a result, the aperture is regarded as generating a new wave source that propagates in the form of a circular wavefront. The intensity of the wavefront is highest in the centre, fading as it approaches the edges.

It explains the observed diffraction and why light passing through an aperture does not produce a perfect image of the aperture on a screen. Based on this principle, the edges “spread out.”

Summary

According to Huygens’ principle, each point on a wavefront is a source of secondary waves, which add up to form the wavefront at a later time. Huygens’ construction shows that the new wavefront is the forward envelope of the secondary waves.

Secondary waves are spherical when the speed of light is independent of direction. After that, the rays are perpendicular to both the wavefronts and the time of travel has the same value when measured along any ray. This principle is the foundation for the well-known laws of reflection and refraction.

Frequently Asked Questions (FAQs)

Below are the frequently asked questions on Huygens Principle:

Q.1. What is Newton’s Model of light?
Ans: Newton proposed that light was made up of tiny particles known as photons.

Q.2. What is a wavelet?
Ans: Huygens’ principle states that every point on a wavefront may be considered as a source of secondary waves or a wavelet.

Q.3. What is a wavefront?
Ans: Wavefront is the Locus of all the points where waves starting simultaneously from a source reach at the same time, and hence the particles at these points oscillate with the same phase. It could either be a line or a surface.

Q.4. As per Huygens’ assumption, what are the qualities of the vacuum medium called ether spread in the entire universe?
Ans: Huygens considered light needs a medium to propagate called ether is highly elastic and less dense.

Q.5. What is the use of concept of secondary wave in Huygens’s Principle?
Ans: Huygens’ concept of a secondary wave is a geometrical method to find the wavelength.

We hope this article on Huygens Principle and its Applications helps you in your study. Let us know if you face any difficulty. We will get back to you at the earliest.

Stay tuned to embibe for the latest update of CBSE exams.