The Speed of Light - Learn

The Speed of Light – Learn

Early Ideas

Leading up to the 17th century, scientists and physicists believed that light would travel from one place in space to another instantaneously. This idea was accepted until Galileo challenged the theory and began to attempt to measure the speed of light.

Galileo (1638)

When Galileo was in Florence he attempted to measure the speed of light in 1638. He had his assistant stand on a hill at a known distance with a lantern. Galileo would open a shutter on his own lantern and start a timer – possibly a sand or water timer. When his assistant saw the lantern on he would open the shutter on his lantern and Galileo would stop his timer when he noticed the light from the lantern. He determined that the speed of light was about ten times greater than the speed of sound. Whilst this result was a very poor estimation for the speed of light, it was the first known attempt to do so. Galileo understood the limitations of his method and concluded that light travelled too fast to be accurately measured using this method.

Ole Romer – Eclipses of Jupiters Moon Io (1676)

Romer noticed that the time that Io came into and out of eclipse varied by a time of about 16.6 minutes. The greatest and shortest differences coincided with when Jupiter was closest and furthest from Earth due to the different orbital speeds of the planets. Romer explained that the time difference was due to light travelling a distance equal to the Earth’s diameter around the Sun. He went on to calculate the speed of light using the orbital radius of the Earth that was known at the time. Romer estimated that the speed of light was 214000 km/s. This value was far from the true value of 300000 km/s, however, he was the first to suggest light travelled at a finite speed and he was at least in the correct order of magnitude.

James Bradley – The Aberration of Light (1728)

James Bradley used the aberration of light to improve the estimate of the speed of light. This involved close observation of the apparent motion of stars. Using the orbital velocity of the Earth and a precise measurement of the angles involved, Bradley determined the speed of light to be 301000 km/s.

Armand Hyppolite Louis Fizeau – The Toothed Wheel (1848)

Fizeau generated a light that was reflected from a distant mirror, giving a total path length of about 19 km. The light was shone through a wheel with 720 teeth evenly placed around its edge. The gaps between the teeth were the same width as the teeth themselves. The wheel was capable of rotating at hundreds of times per second. The light would shine out through a gap and the rotational speed of the wheel was adjusted until no light shone back through the gap – the light beam was prevented from passing through the wheel by the adjacent tooth. This allowed the time for the light’s round trip to be measured based on the distance the wheel had rotated at the set speed. Using this method, Fizeau determined the speed of light to be about 315000 km/s.

Leon Foucault – The Rotating Mirror (1849)

Foucault used a similar method to Fizeau but instead used a rotating mirror. A beam of light was reflected off the rotating mirror and to a fixed mirror. The fixed mirror would reflect the light back to the rotating mirror and this would in turn reflect the light back toward the observer. The beam of light would return at a slightly different angle to which it left. With accurate measurements of the rotating speed of the mirror and the angle that the beam returned, Foucault measured the speed of light to be 298000 km/s.

Modern Techniques

Modern method for determining the speed of light called for innovative techniques and precise measurements of variables.

Resonant Cavity and Interferometry (1946-1950)

Louis Essen and AC Gordon-Smith used a technique called cavity resonance. They used a resonant cavity which is a physical tube that is able to sustain a standing wave at particular frequencies – these frequencies correspond to an integral number of half wavelengths. To achieve a measurement for c, they needed to independently measure the frequency, f, and the wavelength, λ. They could then use the relationship c=fλ to determine the speed of light. They used gauges that were calibrated by interferometry and achieved an accuracy of ±0.8μm

Interferometry splits a beam into two different beams that travel different paths, are reflected back and recombine. They form an interference pattern that can be used to determine the wavelength.

SI Standard for c and the Metre

The definition of the metre is based on c. A metre is the distance that light travels in $\cfrac { 1 }{ 299 792 458 }$ of a second, in a vacuum. As a result of this we have an exact value for the speed of light equal to 299 792 458 m/s.