Measuring Light

In my office window, I have a chunk of clear glass with a clock mounted in it, which, when the light in the afternoon hits it, projects amazing rainbows around the walls and floor of my office.

I thought you might enjoy seeing one of the rainbows: such wonderful colors.


As I am determined to understand measurement, I look at the rainbows and think of ways that light can be measured.  There are a few that come to mind, but this list is surely not definitive  – measuring reflections, measuring refractions, figuring out where the colors come from and then measuring the wavelengths of the colors, measuring the speed of light.  What is the history of performing these four types of measurement?

First, do these measurement techniques meet or match the elements of measurement, as listed to the right?  Certainly they do: as I have written about these measurements in this post and posted it, others can read it, so the social element has been met.  The next element, when measuring light, the intention is to capture some characteristic of its behavior for understanding so that it can be communicated, at least.  Is there sufficient language to do that, not just the words but the concepts behind the words?  This is a tricky question, since there have been competing concepts about the nature of light over the centuries, the most recent of which is Einstein’s brilliant but weird synthesis.  There are ways to capture whatever insights into the nature of light we want to look at, and some standards that have been developed that can be used to make sure we are discussing common measurements.

Of course, once knowledge is there, the onboard computer (a.k.a. brain) doesn’t have to do a review each time, since one can look at the colors and be dazzled by them, with or without understanding the concepts or what has been measured.  For me, though, I find that anything in nature that is as beautiful as the rainbows cast by the prism/clock is enriched by knowing as much as I can about the phenomenon, although I rarely have to review the scientific understanding while viewing or experiencing the phenomenon because the knowledge is already there.

Looking at the history of the measurement of light provides some remarkable information about the development of measurement as well as the development of the concepts to understand light.

It is impossible to guess how primitive humans understood light: the first Greek to describe light with any accuracy is Empedocles (c 482 – c 432 BC), who “..claim[ed] that light has a finite speed.”1 Aristotle (384 – 322 BC) disagreed: he felt that light did not move, though in reading several interpretations of what he did say about light, his view seems a bit muddled.  It was almost as if he was saying that light is part of what we exist in, much like fish exist in water.  A further view of light was that developed by Euclid (around 295 BC) and subscribed to by Ptolemy (about 100 – 170): the eye sends out rays to see with.  Based on Euclid’s model, Heron of Alexandria (10 – 70) reasoned that the speed of light has to be infinite, because when you open your eyes at night, you immediately see distant stars: no time elapses between opening and seeing.

This is where the understanding of how the eye works, what light is and what the speed of light is, stood for nearly 1000 years.  In 1021, a very smart Islamic scientist named Abu ‘Ali al-Hasan ibn al-Hasan ibn al-Haytham (c 965 – 1041), westernized as Alhazen, completed an influential book called Kitab al-Manazir, translated as Book of Optics.  He accurately described a number of the behaviors of light, and also claimed that light from objects was delivered to the eye, not rays from the eye to the object.  The book was translated into Latin in the late 12th or early 13th century, and was printed in 1572.  This work influenced Roger Bacon and Johannes Kepler, among others – though it is not clear if Isaac Newton knew of it or of its commentaries.

Some of the contents of his book include:

  • Proof that light travels in straight lines.
  • Accurate descriptions of light being reflected by reflective surfaces.
  • Accurate descriptions of light being refracted by clear media other than air – stating that light travels more slowly through water and glass.
  • A clear and accurate description of how camera obscuras work.
  • The nearly correct presentation of the physiology of the eye – though he thought the pupil was the receptive organ of light, he hinted that the retina would be involved, and he also stated that the optic nerve delivers what the eye captures to the brain for the brain to turn it into vision.

Al-Haytham’s near contemporary, Abu Rayhan al-Biruni (973 – 1048), westernized as Alberonius, added one more piece to the puzzle: he discovered that light traveled faster than sound.  And some years later, Kamal al-Din Farisi (1267 – 1319) wrote a correction to al-Haytham’s Book of Optics, in which he corrects al-Haytham’s theory of color, and correctly describes rainbows.  He used a clear glass sphere filled with clear water inside a camera obscura, and introduced light into the camera obscura through the pinhole.  The result was the “decomposition” of white light into the various colors of the rainbow.  At nearly the same time as al-Farisi’s discovery of how the rainbow phenomenon works, Theodoric of Freiberg discovered the same thing: there is no evidence of contact between the two, so the discoveries were most likely independently made.

The foundation of the modern understanding of how light behaves, then, had been developed by the late 13th, early 14th century.  The baton of scientific endeavor was passed to Europe around then, and work on light continued.

Johannes Kepler (1571 – 1630) evidently believed that the speed of light was infinite, as did Rene Descartes (1596 – 1650).  Galileo Galilei (1564 – 1642) performed an experiment to see if there was a speed of light, in about 1638.  He used a method similar to that used to figure out the speed of sound, an experiment done in the years preceding his light experiment.  The speed of sound was determined by firing a cannon, and having an observer a mile or so away time the difference between seeing the flash from the muzzle of the cannon and the sound of the cannon.  Galileo had an assistant with a lantern go to a hill a mile or so away from him, he uncovered his lantern and the assistant uncovered his when he saw the light from Galileo’s.  Galileo timed how long it took from when he uncovered his to the time he saw the light from his assistant’s lantern.  He concluded that if light is not infinitely fast, it is very very fast, since the timed interval was the same as when his assistant was six feet away, so the interval depended on human reaction time, not the speed of light.  “Based on the modern value of the speed of light, the actual delay [attributable to the speed of light] in the experiment would be about 11 microseconds.”2

In order to time the speed of light, the timing mechanism had to be accurate and standardized.  In an earlier post, “Marking Time (or at least calibrating it)”, I mentioned the work of Christiaan Huygens (1629 – 1695), who developed the first pendulum clock in 1656, increasing the accuracy of clocks to within 15 seconds per day.  I also mentioned Ole Roemer (1644 – 1710) who in 1676 realized that the movement of one of Jupiter’s moons seemed to have some timing problems.  Rather than re-write what I said, I will quote:

…the transit of the moons of Jupiter had been precisely timed: when several of the moons went behind Jupiter and reappeared had been timed precisely enough that one astronomer, Ole Roemer in 1676, had proved that the speed of light was finite using the occultation of Io, one of Jupiter’s moons.  He timed the occultation when the earth in its orbit was nearer to Jupiter, then when earth was at a different part of its orbit, much further from Jupiter, and noted that the times of occultation took much longer when the earth was farther from Jupiter.  This he correctly assumed was because the distance was so much greater, and reasoned that because of that, light had a finite speed and was not infinitely fast.

Roemer did not calculate a speed for light, but based on the timings he published, Christiaan Huygens did a calculation that came up with a speed for light of about 220,000 kilometers per second (km/s), which is not quite enough: the modern measure is about 300,000 km/s.  It should also be pointed out, while mentioning Huygens, that he published work on optics in which he stated his belief that light was composed of waves.  But more on the speed of light a little later.

A contemporary of Roemer and Huygens, Isaac Newton (1642 – 1727)3, the English genius, studied and wrote about optics.  He is associated with prisms being used to decompose white light into its constituent colors, among other things, and for his stance on the nature of light.  By his time, light was showing behavior that was like that of particles as well as of waves.  He used the measurements of reflection to “prove” that light consists of particles.

A light is reflected at the same angle to the perpendicular (the “normal”) of a flat mirror (a plane) as the angle of the incoming light ray to the perpendicular.  In math-ese, the angle of incidence to the normal is the same as the angle of the reflectance to the normal, very much like a billiard ball being shot at a cushion on a billiard table.  And even though light also showed wave-like behaviors, Newton felt the wave-like behaviors were not significant.  Because of his great prestige, scientists only looked for and used particle-like behavior in their experiments.  Until about 1801.

In 1801 or thereabouts, the results of the double-slit experiment, attributed to Thomas Young (1773 – 1829), became known.  Shining a light through a card with two slits near to each other and letting the light project onto a screen beyond the card shows a pattern of light and dark which is best explained by the interference of waves.  This “proved” that light was waves, not particles, and so the description remained until Albert Einstein redefined the nature of light.  But for much of the 19th century, many of the measurements of light were devoted to its wave nature, with Newton’s particle theory being eclipsed.

One concept related to waves is that they require a medium in which to travel, much like waves in water, or sound waves in air.  As an example of an inaccurate analogy applied incorrectly, this led to a hypothesis that space, whether between the celestial bodies or here on Earth, was filled with a medium that transmits light waves, called “ether” or, as it was called in the 19th century, “luminiferous ether”, meaning “light-carrying ether”.  We’ll get to an experiment that was done to figure out the effect of the ether in a little bit, but first, another consequence of the double-slit experiment: the measurement of wavelengths – the measurement of color.

“Furthermore, from the spacing of the interference bands of light and dark, Young could calculate the wavelength of light.”4 The figure he came up with was on the order of a fifty-thousandth of an inch.  This figure was improved upon by Anders Jonas Angstrom (1814 – 1874) who not only measured the wavelengths of the various colors, but developed a unit scale for the size.  The unit is equal to one-tenth of a millimicron (1 millimicron = a ten-millionth of a centimeter), and was subsequently named after him: an Angstrom.  So, although there are no sharp divisions between the colors, the ranges for colors are:

Red = 7600-6300 angstroms

Orange = 6300-5900 angstroms

Yellow = 5900-5600 angstroms

Green = 5600-4900 angstroms

Blue = 4900-4500 angstroms

Violet = 4500-3800 angstroms5

A further consequence of this work with spectrums was the development of spectroscopy.  Without going into spectroscopy too deeply, during the 19th century, Joseph von Fraunhofer (1766 – 1826) discovered black lines in the spectrum from the Sun and from other heavenly bodies.  He measured them meticulously, but his work was ignored until Gustav Robert Kirchhoff (1824 – 1887) working with a collaborator, Robert Wilhelm Bunsen (1811 – 1899) (he of the famed burner…) explored the emission colors of various elements.   Kirchoff and Bunsen found that each element had a characteristic pattern of wavelengths/colors which could be used to define them, which were produced when they were heated to incandescence.  He also figured out that when he used a carbon arc to produce white light, and ran the light through the vapor of a heated element, the dark lines seen and measured by Fraunhofer matched the wavelengths of the characteristic element signature in emitted light.  As a result, it was realized that one could figure out the elements in stars and other heavenly bodies by spreading the spectrum the way that Fraunhofer had done, and checking the wavelengths at which the dark lines, the absorption lines, appeared.  A whole new way of measuring the stars was born.  One of its great successes was the discovery of helium in the sun’s absorption lines well before helium was discovered here on Earth.

By the late 1800s, most physics work related to light was being done with the understanding that light was composed of waves: in fact James Clerk Maxwell (1831 – 1879) published A Dynamical Theory of the Electromagnetic Field, in which he described the unified theory of magnetism and electricity, and along with it, described light as a form of electromagnetic wave.  So at this point, detecting the ether was one of the problems that physicists were working on.

During the 19th century, several values for the speed of light were published: Hippolyte Fizeau (1819 – 1896) reported a result of 315,000 km/s, and Leon Foucault (1819 – 1868), improving on Fizeau’s method, published a value of 298,000 km/s.  The next worker of note is Albert Abraham Michelson (1852 – 1931), who began trying to measure the speed of light in about 1877, while an instructor at the U.S. Naval Academy.  He accepted a position as a full professor at Case School of Applied Science in 1883, and in 1887 he and Edward Morley (1838 – 1923) performed an experiment to detect the motion of the Earth relative to the ether.

The way that the experiment was designed was to have a single light source, split the beam of light from it and send one beam in the direction of the Earth in its orbit, and the other at 90 degrees from it, essentially across the motion of the orbit.  Both of the beams of light were reflected back to the same place from mirrors that were placed to be exactly the same distance from the split, and based on the interference pattern, the experiment should have allowed Michelson and Morley to determine the speed of the Earth relative to the ether.  The concept was very much like firing a cue ball at two other billiard balls, placed in a way that they would move at 90 degrees from each other, hit cushions placed so that the distances were the same, bounce back, and if they collided in the same place that they had started from, the billiard table could be considered stationary.  But if it had been done on a train, the billiard ball traveling with the direction of the train, then bouncing back, against the direction of the train, would take slightly more time than the billiard ball traveling across the direction of the train.  So at least was the theory.

Michelson and Morley got a null result – meaning that no matter how precisely they could measure it, there was no effect on light from traveling through the ether.  Michelson continued to make improvements on his equipment, and still could not determine the effect of the ether.  He did provide more and more accurate measurements of the speed of light, over time, with his final determination while he was alive being 299,706 ± (meaning plus or minus) 4 km/s.  He made this measurement in 1924 in California, after the U.S. Coast and Geodetic Survey had taken two years surveying an accurate baseline for projecting light: the precise distance between Mount Wilson Observatory and Mount San Antonio, about 22 miles away.  The survey, no doubt, used some of the instruments discussed in the earlier posts about geodetic surveys.  He set up his last experiment, but did not live to see the results: published posthumously as 299,774 ± 11 km/s.

The next big player was Albert Einstein.  His own reports conflict about whether he knew of the Michelson-Morley experiments results, though it is clear that he knew about the formula developed by Hendrik Lorentz (1853 – 1928)  which was created in response to the Michelson-Morley experiment, known as the Lorentz contraction.6

Einstein was less concerned with the precise speed of light than with the concept of pure energy waves traveling very fast.  In an autobiographical statement, he described how he came to understand light, which has been picked up by the physics community as the archetype of a gedankenexperiment – a thought experiment.  He imagined traveling with a light beam at the speed of light.  What he determined he would be able to see was contradictory to both experience and to Maxwell’s equations about electromagnetic waves, but only if time was considered to be absolute.

After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest.  However, there seems to be no such thing, whether on the basis of experience or according to Maxwell’s equations.  From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest.7

In other words, light could never be at rest, and even for an observer traveling at the speed of light, an impossibility, light would still have to appear to be moving at the speed of light.  The result of his thought experiment was the conclusion that the speed of light is absolute, a universal constant, that nothing with any mass could ever be accelerated to the speed of light, and nothing could ever exceed it.  Oh, and by the way, there was no need to talk about the ether.  Most likely, it didn’t exist.

This concept is only part of the weirdness Einstein left us with.  The other part was his realization that energy was not continuous.  Energy came in very small bundles, but could not be split down smaller than a single one of these bundles, called a photon.  And that light behaves like a particle when the experiment is set up to measure particle-like behavior and it behaves like a wave when the experiment is set up to measure wave-like behavior, since it is, in fact, both.

These two concepts were major changes in the way that light is understood.  The consequences of this new set of concepts are so many that it would take (actually has taken) years to fully elucidate them, and there may still be surprises left.

However, to wrap this up, the speed of light, then, as a constant continued to be measured against the standards that had been defined here on earth: the second, distance in terms of meters or miles, etc., until 1983.  In 1972, the U.S. National Bureau of Standards measured the speed of light in a vacuum to be 299,792,456.2 plus or minus 1.1 m/s (notice that this is meters per second: move the decimal point three places left for kilometers/sec).  In 1975, the 15th Conference Generale des Poids et Mesures (CGPM) set the value at 299,792,458 m/s.  Then in 1983, evidently the 17th CGPM changed the way that a meter was defined: it used the speed of light to define the length of a meter as “The metre is the length of a path travelled by light in a vacuum during the time interval of 1/299,792,458 of a second”8

So, by measuring light and re-conceptualizing it, light has become the standard length by which all other length systems are now measured.  Who else saw that in the refraction from the prism/clock?  Go ahead, raise your hands.

Sources relied on for this post are:

Albert Einstein: Philosopher-Scientist, The Library of Living Philosophers, Volume VII, Schilpp, Paul Arthur, ed. Open Court Publishing Company, La Salle, Illinois, 1949, 1951, third edition, fourth printing 1988.

Asimov, Isaac, Understanding Physics: Light, Magnetism, and Electricity, New American Library, New York, N.Y., 1966.  Volume II of three, an old source, but clear, accurate and helpful.  And you thought Isaac Asimov only wrote science fiction?

Freely, John, Aladdin’s Lamp, How Greek Science Came to Europe Through the Islamic World, Alfred A. Knopf, New York, 2009.  Good discussions of the Greek science, and an extensive run-through of the work of the Islamic scientists and scholars.

Isaacson, Walter, Einstein, His life and Universe, Simon & Schuster, New York, N.Y., 2007.  A thorough and warm biography, with a great quote from Einstein after the dedication: Life is like riding a bicycle.  To keep your balance you must keep moving.

Rubenstein, Richard E., Aristotle’s Children, How Christians, Muslims, and Jews Rediscovered Ancient Wisdom and Illuminated the Dark Ages, Harcourt, Inc., Orlando, FL  2003.  With the focus on the transmission of Aristotle’s works, detail about other aspects of the Islamic custodianship of knowledge is just skimmed over.

And the ever-present, really convenient Wikipedia.


3 At the time that Isaac Newton was born, the Julian calendar was in use in England, and his birth date was December 25, 1642.  On the Gregorian calendar, later adopted by England in 1752, the date was January 4, 1643.  I prefer to provide cover for all those atheists and others of little faith to have a reason to celebrate on the 25th of December.

4 Asimov, Isaac, Understanding Physics: Light, Magnetism, and Electricity, New American Library, New York, N.Y., 1966. p.67

5 Asimov, Isaac, Understanding Physics: Light, Magnetism, and Electricity, New American Library, New York, N.Y., 1966. p. 68.

6 Strictly known as the Lorentz-Fitzgerald contraction: George F. FitzGerald (1851 – 1901) did the initial work in 1889 as a result of the Michelson-Morley experiment, and the formula was more fully developed by Lorentz in 1892.

7 Einstein, Albert, “Autobiographical Notes” (in German, and in English translation) in  Albert Einstein: Philosopher-Scientist, The Library of Living Philosophers, Volume VII, Schilpp, Paul Arthur, ed. Open Court Publishing Company, La Salle, Illinois, 1949, 1951, third edition, fourth printing 1988.  p. 53.

8 “Resolution 1 of the 17th CGPM” ( http://www.bipm.org/en/CGPM/db/17/1/ ), as quoted in http://en.wikipedia.org/wiki/Speed_of_Light

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