Wave theory of light

Discovered by Christiaan Huygens

Statement:-

Every point on a wave-front may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wave-front is the tangential surface to all of these secondary wavelets.

What is light?

Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is the visible spectrum that is visible to the human eye and is responsible for the sense of sight.  The spectrum is the collection of all waves, which include visible light, Microwaves, radio waves ( AM, FM, SW ), X-Rays, and Gamma Rays.

Sir Isaac Newton, held the theory that light was made up of tiny particles. In 1678, Dutch physicist, Christiaan Huygens, believed that light was made up of waves vibrating up and down perpendicular to the direction of  the light travels, and therefore formulated a way of visualizing wave propagation. This became known as 'Huygens' Principle'.  Huygens theory was the successful theory of light wave motion in three dimensions. Huygen suggested that light wave peaks form surfaces like the layers of an onion. In a vacuum, or other uniform mediums, the light waves are spherical, and these wave surfaces advance or spread out as they travel at the speed of light. This theory explains why light shining through a pin hole or slit will spread out rather than going in a straight line (see diffraction). Newton's theory came first, but the theory of Huygens, better described early experiments. Huygens' principle lets you predict where a given wavefront will be in the future if you have the knowledge of where the given wavefront is in the present.

 

At the time, some of the experiments conducted on light theory, both the wave theory and particle theory, had some unexplained phenomenon, Newton could not explain the phenomenon of light interference, this forced Newton's particle theory in favor of the wave theory. This difficulty was due to the unexplained phenomenon of light Polarisation - scientists were familiar with the fact that wave motion was parallel to the direction of wave travel, NOT perpendicular to the to the direction of wave travel, as light does.

 

In 1803, Thomas Young studied the interference of light waves by shining light through a screen with two slits equally separated, the light emerging from the two slits, spread out according to Huygen's principle. Eventually, the two wave fronts will overlap with each other, if a screen was placed at the point of the overlapping waves, you would see the production of light and dark areas (see interference).

Later in 1815, Augustin Fresnel supported Young's experiments with mathematical calculations.

 

In 1900 Max Planck proposed the existence of a light quantum, a finite packet of energy which depends on the frequency and velocity of the radiation.

 

In 1905 Albert Einstein had proposed a solution to the problem of observations made on the behavior of light having characteristics of both wave and particle theory. From the work of Plank on the emission of light from hot bodies, Einstein suggested that light is composed of tiny particles called photons, and each photon has energy.

Wave theory of light:-

Light can exhibit both a wave theory and a particle theory at the same time. Much of the time, light behaves like a wave. Light waves are also called electromagnetic waves because they are made up of both electric (E) and magnetic (H) fields. Electromagnetic fields oscillate perpendicular to the direction of wave travel and perpendicular to each other. Light waves are known as transverse waves as they oscillate in the direction traverse to the direction of wave travel.

Consider the case of a point source located at a point P0, vibrating at a frequency f. The disturbance may be described by a complex variable U0 known as the complex amplitude. It produces a spherical wave with wavelength λ, wavenumber k = 2π/λ. The complex amplitude of the primary wave at the point Q located at a distance r0 from P0 is given by:

 

U(r0)=U0e^{ikro} / r0

since the magnitude decreases in inverse proportion to the distance traveled, and the phase changes as k times the distance traveled.

The Speed Of Light

The speed of light in a vacuum is a universal constant, about 300,000 km/s or 186,000 miles per second. The exact speed of light is: 299,792.458 km/s 
It takes approximately 8.3 min for light from the sun the reach the earth ( 150,000,000 / 300,000 / 60 = 8.3 ) 
Taking the distance of the sun from Earth into account, which is 150,000,000 km, and the fact that light travels at 300,000 km/s, it shows in someway how fast light actually travels. 

With the use of the SI units for wavelength (l), frequency (¦) and speed of light (c), we can derive some simple equations relating to wavelength, frequency, and speed of light:

l = c / ¦¦ = c / l

Photon Model of Light

As proposed by Einstein, light is composed of photons, very small packets of energy. The reason that photons are able to travel at light speeds is due to the fact that they have no mass and therefore, Einstein's infamous equation - E=MC2 cannot be used. Another formula devised by Planck is used to describe the relation between photon energy and frequency - Planck's Constant (h) - 6.63x10-34 Joule-Second.
 

E = hl

or

E = hc / l


E is the photonic energy in Joules, h is Planks constant  and f is the frequency in Hz

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