Electromagnetic constants
An option for deriving c that does not directly depend on a measurement of
the propagation of electromagnetic waves is to use the relation
between c and the vacuum permittivity ε0 and vacuum
permeability μ0 established by Maxwell's theory: c2 = 1/(ε0μ0). The vacuum
permittivity may be determined by measuring the capacitance and
dimensions of a capacitor, whereas the value of the vacuum permeability
was historically fixed at exactly 4π×10−7 H⋅m−1 through the definition of
the ampere. Rosa and Dorsey used this method in 1907 to find a value
of 299710±22 km/s. Their method depended upon having a standard unit of
electrical resistance, the "international ohm", and so its accuracy was limited
by how this standard was defined.[109][110]
Cavity resonance
Electromagnetic standing waves in a
cavity
Another way to measure the speed of light is to independently measure the
frequency f and wavelength λ of an electromagnetic wave in vacuum. The
value of c can then be found by using the relation c = fλ. One option is to
measure the resonance frequency of a cavity resonator. If the dimensions of
the resonance cavity are also known, these can be used to determine the
wavelength of the wave. In 1946, Louis Essen and A.C. Gordon-Smith
established the frequency for a variety of normal modes of microwaves of
a microwave cavity of precisely known dimensions. The dimensions were
established to an accuracy of about ±0.8 μm using gauges calibrated by
interferometry.[109] As the wavelength of the modes was known from the
geometry of the cavity and from electromagnetic theory, knowledge of the
associated frequencies enabled a calculation of the speed of light. [109][111]
The Essen–Gordon-Smith result, 299792±9 km/s, was substantially more
precise than those found by optical techniques. [109] By 1950, repeated
measurements by Essen established a result of 299792.5±3.0 km/s.[112]
A household demonstration of this technique is possible, using a microwave
oven and food such as marshmallows or margarine: if the turntable is
removed so that the food does not move, it will cook the fastest at
the antinodes (the points at which the wave amplitude is the greatest),
where it will begin to melt. The distance between two such spots is half the
wavelength of the microwaves; by measuring this distance and multiplying
the wavelength by the microwave frequency (usually displayed on the back
of the oven, typically 2450 MHz), the value of c can be calculated, "often
with less than 5% error".[113][114]
