# Measuring the Speed of Light

The history of physics from ancient times to the modern day, focusing on light and matter. There have been many attempts to measure the speed of light. Danish astronomer Ole Rømer showed that light travels at a finite speed in 1676, and the first accurate measurements were made in the mid-1900s.

Last updated on 5th June 2017 by Dr Helen Klus

The first attempts to measure the speed of light were made in the 1600s. During this time, no one knew if light was composed of waves, as Dutch natural philosopher Christiaan Huygens claimed, or particles, as English natural philosopher Isaac Newton suggested, and no one knew if the speed of light was infinite.

## 1. Galileo Galilei ↑

In 1638, Italian natural philosopher Galileo Galilei attempted to determine the speed of light by measuring the time it takes to travel between two observers. The first observer flashed their lantern at the second, and they replied by flashing their own lantern back.

Galileo suggested that the experiment was best performed if the observers remain about three miles apart, giving a total distance of six miles. He claimed to have tried the experiment at less than a mile, but was unable to determine whether or not the speed of light is infinite[1].

This experiment was later repeated by the Accademia del Cimento (Academy of Experiment), which was founded in Florence 15 years after Galileo's death. However, their results were equally inconclusive[2].

## 2. Ole Rømer ↑

Danish astronomer Ole Rømer was able to show that light travels at a finite speed in 1676. He did this by utilising another of Galileo's discoveries, the moons of Jupiter[3][4a].

Jupiter's moon Io orbits Jupiter once every 42.5 hours, and for much of this time, it is shrouded by the shadow of Jupiter. Rømer kept a record of how long these eclipses lasted and found that they vary over a year, as the Earth moves around the Sun.

Rømer knew that Io appears to remain shrouded for about 22 minutes longer when Jupiter is furthest away from the Earth than when it is closest. He realised that this was because the light from Jupiter had to travel an extra distance.

Rømer was then able to estimate the speed that light must be travelling in order to cover the extra distance in this time.

Rømer's diagram of Jupiter (B) eclipsing Io (D and C) as viewed from different points in earth's orbit around the Sun (A). Image credit: Ole Rømer/Public domain.

Ancient Greek astronomer Aristarchus of Samos had previously estimated the distance between the Earth and the Sun in about 300 BCE[5], and it was first accurately calculated by French astronomer Jean Richer and Italian astronomer Giovanni Domenico Cassini in 1672. They concluded that the Sun is about 140 million km from the Earth, underestimating the distance by less than 10 million km[6].

Rømer had found that Io is shrouded for about 22 minutes longer when Jupiter is furthest away, and so estimated that light takes about 11 minutes to travel between the Sun and the Earth. This led him to calculate that light travels at about 200,000 km/s (this is 760 million km/h, or 470 million mph)[4b].

Rømer was later shown to have underestimated the speed of light. This was partly due to his overestimation in the length of time it takes for light from the Sun to reach Earth, which is now known to be about 8 minutes.

English astronomer James Bradley measured the speed of light to be just over 300,000 km/s in 1728. Bradley was the first to measure how stars appear to change in position as the angle of the Earth changes as it orbits the Sun. This is known as stellar aberration.

The distance that the stars appear to move is proportional to the speed that the Earth moves, divided by the speed of light.

Bradley knew that it takes about 365 days for the Earth to complete its orbit, and so he could use Richer and Cassini's estimate of the distance between the Earth and the Sun to determine the distance that the Earth must travel in that time[7][8].

## 4. Hippolyte Fizeau and Léon Foucault ↑

In 1850, French natural philosophers Hippolyte Fizeau[9] and Léon Foucault[10] proved Newton's particle theory of light to be wrong when they showed that light travels faster in air than in water.

They did this by splitting a beam of light in two, and then passing half through water and half through air. In order to measure the speed of each beam, they reflected them from a rotating mirror towards a stationary mirror many miles away.

By the time the light was reflected back, the rotating mirror had moved slightly. The angle between this beam and the original could then be used to determine the speed that light must have travelled, in order to arrive in the time it took the mirror to rotate[11].

Diagram showing a modern approach to measuring the speed of light using Foucault's rotating mirror method. Image credit: Rhodesl/Public domain.

## 5. Louis Essen and A. C. Gordon-Smith ↑

By the mid-1900s, British physicist Louis Essen and his colleague A. C. Gordon-Smith were able to determine the speed of light by measuring its wavelength and frequency[12][13].

The velocity of something can be found using Velocity = Distance/Time. A wavelength is a distance, and frequency refers to the number of wavelengths that pass in that time (i.e. Frequency = 1/Time), and so Velocity = Wavelength × Frequency.

Essen and Gordon-Smith used a cavity resonance wavemeter - an electric circuit that oscillates at a known frequency - and calculated the wavelength based on the dimensions of the wavemeter. They determined that light travels at about 299,792 km/s (this is just over 1 billion km/h, or 670 million mph), the value accepted today.

In 1905, German-Swiss-American physicist Albert Einstein's theory of special relativity showed that it would take an infinite amount of energy to accelerate an object from rest to the speed of light[14].

## 6. References ↑

1. Galilei, G., Crew, H. (trans), and de Salvio, A. (trans), 1914 (1638), 'Dialogues Concerning Two New Sciences', Macmillan.

2. Seeger, R. J., 2016, 'Men of Physics: Galileo Galilei, His Life and His Works', Elsevier.

3. Rømer, O., 1676, 'A demonstration concerning the motion of light, communicated from Paris. the Journal des sçavans, and here made in English', Philosophical Transactions of the Royal Society of London, 12, pp.893-894.

4. (a, b) van Helden, A., 1983, 'Roemer's speed of light', Journal for the History of Astronomy, 14, pp.137-140.

5. Heath, T., 2013, 'Aristarchus of Samos, the Ancient Copernicus: A History of Greek Astronomy to Aristarchus, Together with Aristarchus's Treatise on the Sizes and Distances of the Sun and Moon', Cambridge University Press.

6. Schilling, G., 2011, 'Atlas of Astronomical Discoveries', Springer Science & Business Media.

7. Bradley, J., 1728, 'Giving an Account of a New Discovered Motion of the Fix'd Stars', Phil. Trans, 35, pp.637-661.

8. Lang, K. R., 2013, 'Essential Astrophysics', Springer Science & Business Media.

9. Fizeau, H. and Breguet, L., 1850, 'Note the relative experience the comparative speed of light in air and in water', Sessions of the Academy of Sciences, 30, pp.562-563.

10. Foucault, L., 1850, 'General method for measuring the speed of light in air and transparent media', Sessions of the Academy of Sciences, 30, pp.551-560.

11. Michelson, A. A., 1964, 'Experimental determination of the velocity of light', Honeywell.

12. Essen, L. and Gordon-Smith, A. C., 1946, 'The measurement of frequencies in the range 100 Mc/s to 10,000 Mc/s', Journal of the Institution of Electrical Engineers-Part I: General, 93, pp.147.

13. Maddaloni, P., Bellini, M., and De Natale, P., 2016, 'Laser-Based Measurements for Time and Frequency Domain Applications: A Handbook', Taylor & Francis.

14. Einstein, A., 1905, 'On the electrodynamics of moving bodies', Annalen der Physik, 17, pp.891-921, reprinted in 'The principle of relativity; original papers', 1920, The University of Calcutta.

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### Light & Matter

Pre 20th Century theories

1. Atoms and Waves

2. Reflection, Refraction, and Diffraction

3. Newton's theory of Light

4. Measuring the Speed of Light

5. 19th Century Wave Theories

6. 19th Century Particle Theories

7. Spectral Lines and Spectroscopy

Quantum Mechanics

1. Origin of Quantum Mechanics

2. Development of Atomic theory

3. Quantum Mechanical model

4. Sommerfeld's model

5. History of Quantum Spin

6. Superconductivity

7. History of Nuclear Physics

8. De Broglie's Matter Waves

9. Heisenberg's Uncertainty Principle

10. Schrödinger's Wave Equation

11. Quantum Entanglement

12. Schrödinger's Cat

Quantum field theories

1. Field Concept in Physics

2. Electromagnetic Force

3. Strong Nuclear Force

4. Weak Nuclear Force

5. Quantum Gravity