Mass  
WAVE AND PHOTON 

WA. Fundamental of Wave  WB. Photon  WC. Kong Vector  
WE. Behaviors of Photon 


WB. PHOTON 

1. Photon  2. Electric Field of a Finite Gaussian Surface  3. Stored Energy  4. Stored Energy Density 
5. Total Energy of Electromagnetic Wave  6. Size of Photon  7. Photon Electric Field  8. Photon Intensity and Light Intensity 
9. Photon Power and Light Power  
INTRODUCTION
The relationship between photon and light is postulated. The size of photon is derived from a finite Gaussian surface. The power and intensity of light is postulated in terms of quanta energy.
OBJECTIVES
1) To introduce and brief the new relationship between photon and light. 2) To develop the electric field and stored energy of photon using finite Gaussian surface method. 3) To find out the size of photon. 4) To develop the intensity and power of light base on photon model.


WB.1.0 PHOTON
Photon is a discrete energy of light. The photon energy is the Plank constant multiply by the frequency of light as described by eq. WB.1.1. In another definition as shown by eq. WB.1.2, photon also can be defined as the energy of one unit of wave length or lambda. Light is the chain of photon; linking photons continuously one by one in straight line.
... eq. WB.1.1 ... eq. WB.1.2 where, c = fl E = Energy h = Plank constant f = frequency λ = wave length
Figure WB.1.1
Figure WB.1.1 shows that light is made up of a chain of photons. The light travels through a surface 'A' at the speed of light.
Light is a series of continuous photons. The energy of light is quantified by photon, but continuous in a long chain as described in figure WB.1.1. Light is a chain of photons travels in straight line as seen in the rays of sun shine.


WB.2.0 ELECTRIC FIELD OF A FINITE GAUSSIAN SURFACE
For a Gaussian surface that encloses an electron, the Gauss’s law for electric is as follow, ... eq. WB.2.1
Expanding the above equation into finite area and solving the vectorial dotproduct, we obtain, ... eq. WB.2.2
Figure WB.2.1
Figure WB.2.1 shows an enclosed Gaussian surface of electron and a finite Gaussian surface dA. For a finite Gaussian surface, dA, we have, ... eq. WB.2.3


WB.3.0 STORED ENERGY
Refer to figure WB.2.1, for instant, the electric potential energy between the charge particle (electron) and the finite Gaussian surface is V.
... eq. WB.3.1 where C = Capacitance
The work required to bring the total capacitor charge up to a final value q is, ... eq. WB.3.2
Hence, the work is stored as potential energy U in the capacitor is, ... eq. WB.3.3
From eq. WB.3.1, we can also present eq. WB.3.3 as follow, ... eq. WB.3.4


WB.4.0 STORED ENERGY DENSITY
In an enclosed volume between electron and Gaussian surface, the electric field has the same value for all points between the finite Gaussian surfaces and electron. Thus the energy density u, that is the potential energy per unit volume between the finite Gaussian surfaces and electron, should be uniform. u can be found by dividing the total potential energy by the volume of the space between the electron and finite Gaussian surfaces.
Figure WB.4.1
Figure WB.4.1 shows a vibrating electron produces electromagnetic wave. Refer to figure WB.4.1, the vibrating electron and the finite Gaussian surface have the surface dA. The potential between the electron and the finite Gaussian surface is V. The distance between the electron and the finite Gaussian surface is D. Thus the energy density u, that is, the potential energy per unit volume between the two surfaces is, ... eq. WB.4.1 where U = Stored potential energy
Substitute eq. 3.4 into eq. 4.1, we have, ... eq. WB.4.2 For two parallel surfaces, the capacitance is, ... eq. WB.4.3 Substitute eq. 4.3 into eq. 4.2, we obtain, ... eq. WB.4.4
But, , therefore, the energy density of a volume between the electron and the finite Gaussian surface is, ... eq. WB.4.5


WB.5.0 TOTAL ENERGY OF ELECTROMAGNETIC WAVE
Figure WB.4.1 show a traveling electromagnetic (EM) wave, along with a thin “box” of thickness dx and face area dA. The box is fixed with respect to the axes and the EM wave moves through it. At any instant, the energy stored in the box is,
... eq. WB.5.1 where u_{E} = the electric energy density u_{B} = the magnetic energy density dAdx = dV = volume of box
From eq. WB.4.5 and analogy for the magnetic energy density, eq. WB.5.1 becomes as follow, ... eq. WB.5.2
Again, for traveling EM wave, it is known that the relation between electric and magnetic field is, ... eq. WB.5.3 where c = light of speed
Substitute eq. WB.5.3 into WB.5.2, we obtain, ... eq. WB.5.4 where


WB.6.0 SIZE OF PHOTON
From eq. WB.5.4, the energy carries by light across a surface in a distance of dx is, ... eq. WB.5.4
The energy carried by a photon is, ... eq. WB.6.1 where U is also expressed as the energy of photon per unit of wavelength.
From eq. WB.5.4, we substitute the dx with the photon wavelength, λ, where the volume of box captures a photon energy, eq. WB.5.4 becomes, ... eq. WB.6.2
Combining eq. WB.6.1 and WB.6.2, we obtain, ... eq. WB.6.3
Rearrange eq. WB.6.3, becomes, ... eq. WB.6.4
From eq. WB.2.3, we also know that the electric field for a finite Gaussian surface is, ... eq. WB.2.3
Substitute eq. WB.2.3 into eq. WB.6.4, we obtain, ... eq. WB.6.5
Rearrange to get surface dA, ... eq. WB.6.6 where,
Hence, a photon has the size of ... eq. WB.6.7 where,
Hence, we can conclude that the size of photon is proportional to the wavelength. Different photon has different size and it depends on the size of the wavelength.
For high frequency EM wave such as Xray and above, where the wavelength is small, the size of photon is small enough to penetrate most of the solid substance, such as bone and etcetera.


WB.7.0 PHOTON ELECTRIC FIELD
From eq. WB.6.4, the electric field of a photon is, ... eq. WB.6.4
Substitute eq. WB.6.6 into eq. WB.6.4, we obtain, ... eq. WB.7.1
The quantized electric field of a photon is, ... eq. WB.7.2


WB.8.0 PHOTON INTENSITY AND LIGHT INTENSITY
From eq. WB.6.2, the photon energy is, ... eq. WB.6.2
The quantized intensity of a photon is the energy per unit photon area as follow, ... eq. WB.8.1
The total intensity of EM wave is the summation of all the photon intensity as follow, ... eq. WB.8.2 where i = type of photon or the photon of frequency i j = total number of photons of type i that collected
The light energy captured by a collecting surface A is the dotproduct between light intensity and the collecting surface, where,
... eq. WB.8.3
where θ is the angle between the photon traveling direction to the collecting surface.
Similarly in term of quanta energy, the light intensity over a collecting surface A is also can be written as follow, ... eq. WB.8.4 where i = type of photon or the photon of frequency i j = total number of photons of type i that collected by a surface A


WB.9.0 PHOTON POWER AND LIGHT POWER
From eq. WB.5.4, the energy of a traveling EM wave is, ... eq. WB.5.4
The quantized power of a photon is, ... eq. WB.9.1
The total power of EM wave is the summation of all the photon power as follow, , ... eq. WB.9.2 where i = type of photon or the photon of frequency i j = total number of photons of type i that collected
The total power collected by a surface A over a period of time is as follow, ... eq. WB.9.3 where i = type of photon or the photon of frequency i j = total number of photons of type i that collected within a period of time, T


DISCUSSIONS AND CONCLUSIONS
In this chapter, photon is fully dissected into a quantized property, which is fully particlelike photon. Photon possesses discrete size depending on the wavelength. Different from conventional wave model, the energy, the intensity, the power of lights are quantized and expressed in term of particle count.

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