Ground Rules

The Integrated Systems Bonding Project

Velocity Factor Computation

Absolute Refractive Index Ratio [ n ]

•  [ n = c₀ / v_m ]
•  [ n = c₀ / v_phase ]
•  [ n = v₀ / v_m ]
•  [ n = λ₀ / λ ]
•  [ n = | f | ]

Convergence of Frequency and Wavelength

• Values for the measurements of frequency and wavelength in the electromagnetic spectrum converge at the square root of the speed of light and electromagnetic waves.
•  [ f = | √c₀ | Hz ] = 17,314.515817660047983788339758548 Hz.
•  [ λ = | √c₀ | m ] = 17,314.515817660047983788339758548 m.
•  [ n = | √c₀ | ] = 17,314.515817660047983788339758548.
•  [ n^-1 ] = 0.000057755008025118657200470132435913.
•  [ T ] = 57.755008025118657200470132435913 microseconds (μs).

Frequency [ f ]

•  [ f = c₀ / λ Hz ]
•  [ f = n Hz ]
•  [ f = T^-1 Hz ]
•  [ f = v₀ / λ Hz ]
•  [ f = v_m / λ₀ Hz ]
•  [ f = λ₀ / λ Hz ]
•  [ f₀ = 1.0 Hz ]
•  [ f₀ = c₀ / λ₀ Hz ]
•  [ | f^-1 | = n^-1 ]

Period [ T ]

•  [ t =  d / v ] (time equals distance divided by velocity)
•  [ T = | f^-1 | s ]
•  [ T = n^-1 s ]
•  [ T_A = au / c s ] (light-time for astronomical unit distance)
•  [ T_A = 499.004783836156411913 seconds per astronomical unit (s/au or s*au^-1) ]
•  [ T_c0 = 5.36819375222574812072 microseconds per statute mile (μs/mi or μs*mi^-1) ]
•  [ T_c0 = 3.3356409519815204957557671447492 nanoseconds per meter (ns/m or ns*m^-1) ]
•  [ T_c0 = 3.05011008649190234132 nanoseconds per yard (ns/yd or ns*yd^-1) ]
•  [ T_c0 = 1.0167033621639674471063578257196 nanoseconds per foot (ns/ft or ns*ft^-1) ] (light foot)

Relative Refractive Index Ratio [ n ]

•  [ n = | f | ]
•  [ n = T^-1 ]
•  [ n = v₁ / v₂ ] (one perspective)
•  [ n = v₂ / v₁ ] (another perspective)

Snell's Law

•  [ sinΘ₁ / sinΘ₂ ] = [ v₁ / v₂ ] = [ n₂ / n₁ ]

Speed of Light and Electromagnetic Waves in Free Space (Vacuum) [ c ]

•  [ c = c₀ ]
•  [ c = f * λ₀ ]
•  [ c₀ = v₀ ]
•  [ c₀ = 299,792,458.0 meters per second (m/s or m*s^-1) ]
•  [ c₀ = 29.9792458 centimeters per nanosecond (cm/ns or cm*ns^-1) ]
•  [ c₀ = 186,282.03962746 statute miles per second (mi/s or mi*s^-1) ]
•  [ c₀ = f₀ * λ₀ ]
•  [ c₀ = f * λ ]

Velocity Factor Ratio [ n^-1 ]

•  [ n^-1 = | f^-1 | ]
•  [ n^-1 = s ]
•  [ n^-1 = T ]
•  [ n^-1 = v_m / c₀ ]
•  [ n^-1 = v_m / v₀ ]
•  [ n^-1 = λ / λ₀ ]
•  [ n^-1 = 1 * √ε_r^-1 ]
•  [ n^-1 = 1 / √ε_r ]

Velocity of Light and Electromagnetic Waves through a Medium [ v_m ]

• Velocity of light and electromagnetic waves through a medium equals the speed of light divided by absolute refractive index.  
   [ v_m = c₀ / n ]


• Velocity of light and electromagnetic waves through a medium equals the speed of light multiplied by the velocity factor.  
   [ v_m = c₀ * n^-1 ]

Velocity of Propagation [ V_P ]

• Velocity of propagation equals the speed of light divided by the square root of relative electric permitivity.  
   [ V_P = c₀ / √ε_r ]


• Velocity of propagation equals the speed of light multiplied by the quantity of the square root of relative electric permitivity to the power of minus 1.  
   [ V_P = c₀ * √ε_r^-1 ]

Wavelength [ λ ]

•  [ λ₀ = | c₀ | m ]
•  [ λ₀ = | v₀ | m ]
•  [ λ₀ = 299,792,458.0 m ]
•  [ λ₀ = 186,282.03962746 statute miles ]
•  [ λ₀ = c₀ / f₀ ]
•  [ λ = c₀ / f ]
•  [ λ = v₀ / f ]
•  [ λ_m = λ₀ * n^-1 ]
•  [ λ_m = λ₀ / n ]

  

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