# M7-S2: Determination of Speed of Light

#### Historical Methods

• 1638 – Galileo Galilei ten times faster than sound, if not instantaneous or extraordinarily fast.

Galileo’s experiment involved using lamps and water clock to measure the time taken for light to travel from these lamps. With pre-determine distance set between him and lamps (source of light), he would qualitatively determine the speed at which light from the lamp travels to and reaches his eyes. The method essentially utilises the relationship between speed, distance and time.

• 1675 – Ole Roemer 200,000 km/sec
Ole Roemer was a Danish astronomer was observing the orbital motion of Io (one of the four satellites of Jupiter), when he determined the speed of light. The orbital period of Io around Jupiter is about 1.7 Earth days, and during each orbit, Io is eclipsed by Jupiter once as viewed from Earth.

However, after multiple viewings, Roemer realised the time between each eclipse varies depending on the relative position of Earth to Jupiter. In specific, when Earth is closer to Jupiter, the time difference between successive eclipses becomes shorter. Roemer proposed that this time disparity is caused by the finite speed of light as it would take long for light to travel from Jupiter & Io when Earth is further away, resulting in a longer observed time.

From using the accepted value of Earth’s orbital diameter (around the Sun) at the time, Roemer calculated the speed of light by dividing the diameter by the observed time difference between eclipses. This discovery, although not accurate, was very impactful as it showed the speed of light was not infinite.

• 1728 – James Bradley 301,000 km/sec

Bradley used stellar aberration to calculate the relative speed of light. Stellar aberration refers to the astronomical phenomenon of when stars appear to be moving about their true position. This causes them to seem displaced when in fact their position has not changed. Bradley used the angle of displacement measured from Earth as well as the relative velocity of Earth to calculate the speed of light. The angle of aberration is related to the ratio between Earth (observer)’s relative speed to the speed of light.

• 1849 – Hippolyte Louis Fizeau 313,300 km/sec

Fizeau used optics and carefully a manipulated toothed wheel to investigate the speed of light. A reflective mirror was placed far away from the source of light. Upon reaching the mirror, the light would return back to the observer standing next to the source of light. Depending on the rotational speed of the wheel, the reflected light may or may not pass through the same gap between the teeth on the spinning wheel. Fizeau adjusted the frequency of the wheel and along with the known distance between the wheel and the mirror, he was able to calculate the speed of light to be 313,300 km/sec.

• 1862 – Leon Foucault 298,000 km/sec

Foucault’s experiment exploited the same principle as Fizeau, but he utilised rotating mirrors instead of a toothed wheel.

A beam of light was shone onto a distant rotating mirror which reflected the light onto a nearby fixed mirror. This fixed mirror then directed the light back to the first rotating mirror. Since the first mirror was constantly rotating, the angle at which the light first reached the rotating mirror would be different to the angle the light makes when it returns from the fixed mirror.

Foucault was able to use the time difference between the two angles and the distance between the rotating and fixed mirrors to determine the speed of light. The value he attained is much closer to the current accepted value of 299,792,458 m/sec.

#### Contemporary Methods

• 1907 – Rosa & Dorsay 299,788 km/sec

The scientific breakthrough in electromagnetism by James Maxwell in 1860s shed light on a new way of measuring speed of light. Rosa and Dorsay used the electric and magnetic permeability of air to indirectly obtain speed of light.

• 1958 – Froome 299,972,500 m/s

Froome’s methodology could not have been possible without Maxwell’s contribution to electromagnetic waves. Froome studied the interference pattern of radiowaves to obtain the speed of light.

• 1973 – Evanson et al 299,972,457 m/s

Evanson et al utilised lasers with high spectral stability to measure the speed of light. Along with the invention of highly accurate atomic clocks, the precision of measurement was significantly greater in contemporary methods compared to historical ones. In addition, the degree of error was also reduced.

#### Light’s Relationship with Time and Distance

• In the modern age, due to the constancy of light’s speed, standard distance and time units are defined using speed of light.
• The concept of distance and time is not constant as they change with frames of reference. This is due to Albert Einstein's theory of Special Relativity and his postulate - speed of light is constant in a vacuum, regardless of the observer. ﻿This will be covered in more detail later in the module.

Constancy of light has two effects:

• Time becomes dilated (each second becomes longer) when an observer is at relativistic motion with the observed frame of reference.
• Length becomes shorter when an observer is travelling at relativistic motion.

As a result, distance (metre) and time (second) are measured and defined in terms of speed of light, which is a constant value.

• The definition of a metre is the distance light travels in 1/299,792,458 second.
• The definition of a second is the time light takes to travel 299,792,458 metres.

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