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Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
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Semiconductor Electron Energies and Band Gap 1D Semiconductor Electron Energies and Band Gap 2D Simple Fermi Surface p-nJunctionDiode Depletion Width Temperature Dependence of 2D Fermi-Dirac Particles
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Assembly of 3D Parts Using Javascript Web Graphics Library 3D Compared to Javascript 3D Graphics 3D Graphics Tutorial Beginnings Proof of Pythagoras a^2+b^2=c^2
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Chapter 5
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Multiple Slider Animation Template for Plotting with HTML Enhanced Sliders or Ranges Collapsible Dropdown Menu Example Arrow Functions Fast Fourier Transform (FFT) Demonstration
Animation of a Progress Bar
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Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Probability of Birthday Match Random Creation of Probability Function Profiles Two Dies Probability Distribution Three Dies Probability Distribution
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
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Chapter 10
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Light Rays in a Transparent Isosceles Prism Light Ray in a Series of Wedges of Various Index of Refraction Snells Law of Refraction Refraction Due to Dipoles in Two Media Refraction and Reflection Two Media Animation of Concave Mirror Reflection Animation of Convex Lens Refraction Prism Refraction-Wave Picture Thick Lens Ray Trace Monochromator (Czerny-Turner Type) Wavelets from Concave Mirror> Thick Lens Focusing
Chapter 4
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Chapter 6
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Chapter 9
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Chapter 11
Chapter 12
Sagnac Effect Fiber Optical Gyro (FOG) Ring Laser Gyro (RLG)
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
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Paticle Motion in a Venturi: Wall Reflections Paticle Motion in a Venturi Potential Elliptical Ion Trap Using Boundary Potential Distribution Prediction of Hard Disc Collision Time and Position Rigid Rotor Collisions
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
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Acoustic Wave with Built-in Pressure Acoustic Waves in 2D Numerically Modeled Solid Wave 1D on a Linear Array Waves on Discrete Model of Vibrating String Linear Acoustic Wave in a 3D Gas Spherical Acoustic Wave in a 3D Gas Laterally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces Longitudinally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces
Chapter 4
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Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
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Chapter 12
Bicep and Forearm Animation Blood Pressure Measurement Multiple Dose Residual Medicine Vs Time The Eye and its Resolution Breathing Animation Scoliosis Animation Muscle Animation
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
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Chapter 12
Scattering from a Crystalline Target 2D Scattering from a Crystalline Target 3D
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Energy Conduction in a 2D Numerically Modeled Solid Lattice Unbalanced Gas Dynamics:Energy Flow in a Gas
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12

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Wall Emission of Black Body Radiation

For a black body cavity, the photon group inside the cavity is in equilibrium with emitters and absorbers in the inner walls of the cavity. Here we show two versions of these emitters:either circular waves emnaniting from the walls or photons coming from the walls. Both of these entities propagate at the speed of light, c. However, the directions of the photons are quantized here in order to have an integer number of half waves between between vertical walls and horizontal walls which allows us to have zero tangential field at the boundaries. If there are to be some integer number of half waves in both x and y directions, then we must have

`f=(c/2)sqrt[(n_x/w)^2+(n_y/h)^2] `

where `f` is the frequency, `c` is speed of light, and `(n_x,n_y)` are integers and `w` and `h` are width and height of the cavity. In any case, the frequency to be used in the black body radiant power equation of a square cavity varies in a manner proportional to `n=sqrt(n_x^2+n_y^2)`. The velocity of a photon depends on the x and y components of its wave vector `k` which are `k_x=(pin_x)/w` and `k_y=(pin_y)/h` so that, for a square cavity, the speeds of these components are

`(v_x,v_y)=(n_x,n_y)c/sqrt(n_x^2+n_y^2)`

An important goal of this animation is to show that the emitted frequency photon distribution matches the black body curve for the parameters being used. In order to achieve this coal in as little time as possible, I have chosen to stop the photon motion after 2000 photons have been emitted. From 2000 photons on up, the new photons are shown in the body of the cavity but the bins of the "experimental" plot are still being updated so that the learner can see the improved match to the black body curve. The expression for the radiant power as a function of frequency is

`P(f)=h(f^3/c^2)/(exp((hf)/(kT))-1)`

It is interesting to find the maximum of P versus f. Planck, when he worked to try to fit an expression such as this to experimental data, could not have been aware that photons are bosons so the expression he used was

`P(f)=hf^3/c^2/exp[-(hf)/(kT)] `

which is very similar the the correct expression. It is very easy to solve for the peak value for this expression. The result is `hf_(Peak)=3kT`. A very simple way to correct the factor 3 in this expression is to multiply it by [exp(3)-1]/exp(3) and then the factor becomes 2.8506... while the more accurate numerically solved value from Wien's Displacement Law is 2.821439. For our purposes here we will use the expression

`P=Cn^3/(exp(n/(n_(avg)))-1) `

where `C` is a constant, `n` is the rms value of the mode indices given above and `n_(avg)` will be an adjustable parameter like the temperature.