How We Came to Know the Cosmos:
Light & Matter

by Dr Helen Klus

# Chapter 4. Measuring the Speed of Light

## 4.1 Galileo Galilei

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.

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, using the equation:

 v = d/Δt (4.1)

Here, v is velocity, d is distance, Δ should be read as ‘change in’, and t is time. Velocity is a vector quality (discussed in Book I), which means that it contains two pieces of information: a value and a direction. The value in this case is the value of the speed. Assuming the direction is positive and c is the speed of light:

 c = d/Δt (4.2)

In Galileo’s experiment, 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]

## 4.2 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.[3,4]

Jupiter’s moon Io orbits Jupiter once every 42.5 hours, and for much of this time, it’s 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.

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 (discussed in Book I). They concluded that the Sun is about 140 million km from the Earth, underestimating the distance by less than 10 million km.[6]

 Figure 4.1Image credit Rømer’s diagram of Jupiter (B) eclipsing Io (D and C) as viewed from different points in Earth’s orbit around the Sun (A).

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).[4]

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 (discussed in Book I). 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 one orbit, and so he could use Richer and Cassini’s estimation of the distance between the Earth and the Sun to determine the distance that the Earth must travel in that time.[7,8]

## 4.4 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]

 Figure 4.2Image credit Diagram showing a modern approach to measuring the speed of light using Foucault’s rotating mirror method.

## 4.5 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 light can be found using c = d/Δt. A wavelength (λ) is a distance, and frequency (ν) refers to the number of wavelengths that pass in that time (i.e. ν = 1/Δt ), and so:

 c = λν (4.3)

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 (discussed in Book I) showed that it would take an infinite amount of energy to accelerate an object from rest to the speed of light.[14]

## 4.6 References

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

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

3. Rømer, O., Philosophical Transactions of the Royal Society of London 1676, 12, 893–894.

4. Helden, A. van, Journal for the History of Astronomy 1983, 14, 137–140.

5. Heath, T., Aristarchus of Samos, the Ancient Copernicus, Cambridge University Press, 2013.

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

7. Bradley, J., Philosophical Transactions of the Royal Society 1728, 35, 637–661.

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

9. Fizeau, H., Breguet, L., Sessions of the Academy of Sciences 1850, 30, 562–563.

10. Foucault, L., Sessions of the Academy of Sciences 1850, 30, 551–560.

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

12. Essen, L., Gordon-Smith, A. C., Journal of the Institution of Electrical Engineers-Part I: General 1946, 93, 147.

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

14. Einstein, A. in The principle of relativity; original papers, The University of Calcutta, 1920 (1905).