Measuring the Speed of Light: From Rømer to Modern Day

Expert reviewed • 22 November 2024 • 6 minute read

Early Astronomical Methods

Rømer's Revolutionary Discovery (1675)

Ole Rømer made the first quantitative measurement of light's speed by observing Jupiter's moon Io. He noticed that Io's orbital period appeared to vary depending on Earth's motion relative to Jupiter. This variation occurred because:

When Earth moved away from Jupiter, Io's eclipses appeared delayed
When Earth moved toward Jupiter, eclipses appeared to occur earlier

The maximum time difference Rømer observed was 22 minutes, representing the time light took to travel across Earth's orbital diameter. While his calculated value of 200,000 km/s was imprecise due to uncertainties in Earth's orbital size, his work proved that light's speed was finite.

Bradley's Stellar Aberration (1728)

James Bradley discovered stellar aberration - an apparent displacement of stars due to Earth's orbital motion combined with light's finite speed. Using the equation:

\tan \theta = \frac{v}{c}

Where:

$\theta$ is the aberration angle
$v$ is Earth's orbital velocity
$c$ is light's speed

Bradley calculated light's speed to be 301,000 km/s.

Terrestrial Measurements

Fizeau's Toothed Wheel (1849)

Hippolyte Fizeau developed the first terrestrial method using a rotating toothed wheel. The speed could be calculated using:

c = \frac{2Dn}{t}

Where:

$D$ is the distance to the mirror
$n$ is the number of teeth
$t$ is the rotation period

This method yielded 313,300 km/s.

Foucault's Rotating Mirror (1862)

Léon Foucault refined the measurement using rotating mirrors, achieving greater accuracy with a value of 298,000 km/s. His setup also demonstrated that light travels slower in water than in air, supporting the wave theory of light.

Modern Methods

Rosa & Dorsey's Electromagnetic Approach (1907)

Following Maxwell's electromagnetic theory, Rosa and Dorsey calculated light's speed using electric and magnetic constants:

c = \frac{1}{\sqrt{\varepsilon\mu}}

Where:

$\varepsilon$ is electric permittivity
$\mu$ is magnetic permeability

Their result: 299,788 km/s.

Laser Interferometry (1973)

Evenson et al. achieved high precision using laser interferometry. The technique involves:

Splitting a laser beam with known frequency
Measuring wavelength through interference patterns
Calculating speed using $c = f\lambda$

This yielded the highly accurate value of 299,792,457 m/s.

Modern Definition and Relativity

The speed of light's constancy in vacuum, as postulated by Einstein's Special Relativity, led to fundamental changes in how we define measurement units:

The meter is now defined as the distance light travels in 1/299,792,458 seconds
This makes light's speed exactly 299,792,458 m/s by definition

Special relativistic effects include:

Time dilation: $t' = \frac{t}{\sqrt{1-v^2/c^2}}$
Length contraction: $L' = L\sqrt{1-v^2/c^2}$

Where primed quantities represent measurements in moving frames.

Maxwell's Unification of Electromagnetic Theory

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Understanding Spectroscopy and Atomic Spectra

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