## Wednesday, January 28, 2015

### Different Theories of Light and Their Analysis

Light is a form of energy. It satisfies law of conservation of energy. According to this law, energy is neither created nor destroyed. It just converts from one format to another format. Hence another format of energy can be converted into light and the light also can be converted into other formats of energies.

Light exhibits a wide variety of properties. They are reflection, refraction, dispersion, interference, diffraction, polarization, photo electric effect, Compton Effect, Stark effect and Zeeman Effect. To explain all these properties of light, we have different theories of light.

If the size of the object interacting with the light is much larger than the wavelength of the light with respect to the object, light appears like a straight line and all the corresponding concepts were studied under the topic called Ray optics.

If the size of the object is comparable to the wavelength of the light, light appears like a wave and all the relevant topics are studied under the name wave optics or physical optics.

The properties of light like interference, diffraction and polarization can be explained only by assuming that light is travelling like a wave.

Right from the beginning of the human evolution, human beings are very much interested in understanding the properties of light. In this process different theories are proposed. Each theory is having its own advantages and failures and here we are going to have brief discussion of the concepts.

Newton’s corpuscular theory

Among different theories, Newton’s corpuscular theory is first one. According to this theory light is a stream of tiny particles called corpuscles
.
This tiny particle carries energy by moving along straight lines.

There are different colors of the light. According to this theory, it is due to different sizes of corpuscles.

It is assumed that this tiny particles travels with enormous velocity.

This theory is successful in explaining the concepts of reflection and refraction.

Anyway this theory is having some issues. According to this theory, velocity of the light is more in denser medium than the rarer medium. But practically it is proved that velocity of the light is actually more in the rarer medium and this theory failed to explain why.

As the light is leaving the source like particles, mass of the source shall decrease but that is not happening.

This theory failed to explain how reflection and refraction can happen simultaneously.

To address all these issues a new theory called Huygens wave theory is proposed.

Huygens wave theory

According to this theory light is not traveling like a straight line but it travels like a wave.

He assumed that light wave is mechanical in nature which demands a medium for propagation.

Hence a invisible, highly elastic low-density medium is imagined all-around and it is called ether medium.

He also proposed a principal called Huygens principle to explain the wave propagation.

This theory is successful in explaining that velocity of the light is more in the rarer medium than the denser medium and hence the problem is solved.

This theory is also successful in explaining the phenomena like interference and diffraction.

But this theory is also having some problems. It fails to explain the concept of polarization.

It also failed to explain photo electric effect and all other modern-day effects of light.

Experimentally it is proved that there is no imagined medium that is filled over the entire space and hence there is no exact way to explain how the wave is propagating from one place to another place.

To solve all these problems electromagnetic wave theory is proposed was proposed by Maxwell.

Electromagnetic wave theory

According to this theory light propagates like a electromagnetic wave and it doesn't need any medium for propagation.

A variable electric field generates a variable magnetic field around it and the propagation of the wave is perpendicular to both of them.

Because it is a non-mechanical wave we don’t need any medium for propagation itself.
The wave equations that we have written in waves and oscillations are valid in explaining the propagation of electric and magnetic fields.

Basing on the permittivity and the permeability of the vacuum we can define the velocity of the light.

It is proved that velocity of light is constant and is maximum in the vacuum. According to this theory, velocity of light in any other is less than the velocity of the light in vacuum.

This theory is successful in explaining the concepts like interference, diffraction and polarization.

At the same time this theory is unable to explain how the photoelectric effect and Compton Effect are happening.

To address this problem Plank’s quantum theory is proposed.

Plank’s quantum theory

According to Plank’s quantum theory, light is not travelling like a wave rather it is travelling like a small packets of energy called quanta.

Energy is not emitted by the source continuously but discreetly in the form of wave packets.

This theory is successful in explaining the modern-day properties of the light like photoelectric effect and Compton Effect. But simultaneously it is unable to explain the concepts like interference, diffraction and polarization.

Hence we do not have a unified theory which can explain all the properties of light. So it is assumed that light travels like a wave and exhibits certain set of properties and when it interacts with someone, it interacts like a particle and exhibits the modern-day properties. This concept is called dual nature of the light.

Huygens principle

According to this principle, every point the primary wave front behaves like a secondary source and propagates the light in the forward direction.

Wave front is the locus of all the points that are in the same phase. The wave front from a point source is spherical in nature where as the wave front from the cylindrical source is cylindrical in nature. As we move far away from the point source, the radius of the spherical wave front increases to a larger value so that it appears like a plane wave front.

Let us consider a point source at a particular position. Light starts from the source and it travels in all directions simultaneously with the same velocity. After a specified time, the distance traveled by the light is same in all directions from the source. The line joining of all the points is called a wave front. Every point on this primary wave front behaves as if like it is a source. Thus each point again propagates the light in the forward direction.

Basing on this concept reflection and refraction are explained successfully. When the light is reflecting, angle of incidence is equal to angle of reflection. When the light is refracting, it obeys a law called Snell’s law.

According to Snell’s law, the refractive index of the medium to where the light is going with respect to refractive index of the medium from where it is coming is equal to ratio of sin angle of incidence to the sin angle of refraction.

We can explain the refraction basing on this principle as shown below. As the light Ray is moving from rarer medium to denser medium, it moves towards the normal. The second light Ray travels more distance to reach the boundary that is separating the two media. Basing on some simple mathematical rules we can derive equation for the width of the refracted light beam as shown below.

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