Maxwell Einstein SofL

The Theoretical Formula
Maxwell's equations show that in a vacuum, electromagnetic waves propagate at a speed (v) defined by the square root of the product of two fundamental constants:
(Vacuum Permeability): mu0
A measure of how easily a magnetic field forms in a vacuum.
(Vacuum Permittivity): epsilon0
A measure of how easily an electric field forms in a vacuum.

Using modern SI values for these constants, the calculation results in exactly 299,792,458 m/s, the universal speed of light (c ).

How Maxwell Made the Connection
Maxwell did not "measure" the speed of light in a lab; he derived it through mathematics and compared it to existing data:

Unity of Fields:
He added a "displacement current" term to Ampere's Law, which allowed electric and magnetic fields to sustain each other in a self-propagating wave.
Weber & Kohlrausch Results:
He used data from experiments by Wilhelm Weber and Rudolf Kohlrausch, who had measured the ratio of electrostatic to electromagnetic units of charge.
The "Aha!" Moment: Maxwell realized this ratio was almost identical to Foucault's 1862 measurement of the speed of light (approx. 298,000 km/s).

Historical Significance

Second Great Unification: This discovery unified optics (the study of light) with electromagnetism.

Foundation for Einstein:
Because Maxwell's speed depends only on the properties of space (mu0 and epsilon0), it appeared to be the same regardless of the observer's motion. This was a key insight that led Albert Einstein to develop the Theory of Special Relativity.

Confirmation: Heinrich Hertz later confirmed these waves existed experimentally in 1888, proving that invisible electromagnetic radiation (like radio waves) follows the same laws as light.

Foucault
The Experimental Apparatus
( https://en.wikipedia.org/wiki/ Foucault%27s_measurements_of_the_speed_of_light )

Foucault used a rotating mirror method to overcome the challenge of measuring light's extreme velocity over a short distance.

Mirror Setup:
A light source was reflected off a mirror rotating at high speed (400-800 revolutions per second) toward a distant fixed mirror.
The Return Trip:
The light reflected back from the fixed mirror to the rotating mirror. The Displacement: Because the mirror had rotated a tiny amount during the light's flight time, the returning beam was deflected at a slight angle from its original path.
Precision Timing:
Foucault achieved constant rotation using a small steam-powered air turbine and measured the speed stroboscopically against a precision clock.

Key Data Points

Path Length: approximately 20 meters (confined entirely within a laboratory).
Angular Displacement: Foucault measured a linear deflection of less than 1 mm (typically 0.7 mm) in the returning light spot.
Rotation Speed: The mirror typically spun at 400 or 500 revolutions per second.

Scientific Significance

Astronomical Accuracy:
His boss, Urbain le Verrier, predicted the previous speed of light was 4% too high based on planetary orbits. Foucault's result confirmed le Verrier's estimate, leading to a more accurate calculation of the distance between the Earth and the Sun.
Wave Theory Validation:
By performing the same experiment through a tube of water, Foucault proved that light travels slower in water than in air. This was considered the final blow to Newton's corpuscular (particle) theory, which predicted light would move faster in denser media.
Foundation for Future Work:
This method was later refined by Albert A. Michelson, who used larger mirrors and longer distances to reach 99.9% accuracy.