How Did We Get To The Speed Of Light?

Every high school physics student knows c, or the speed of light, it’s 3 x 10^8 metres per second. More advanced or more curious students will know that this is an approximation, and the figure of 299,792,458 metres per second that forms the officially accepted figure comes from a resonance of the caesium atom from which is derived a value for the second.

Galileo Galilei, whose presence in this story should come as no surprise. Justus Sustermans, Public domain.

But for those who are really curious about measuring the speed of light the question remains: Just how did we arrive at that figure and how long have we been measuring it? The answer contains some surprises, and some exceptionally clever scientific thought and experimentation over the centuries.

The nature of light and whether it had a speed at all had been puzzling philosophers and scientists since antiquity, but the first experiments performed in an attempt to measure it were you will not be surprised to hear, performed by Galileo sometime in the early 17th century. His experiment involved his observation of assistants uncovering lanterns at known distances away, and his observations  failed to arrive at a figure.

Later that century in 1676 the first numerical estimate of the speed of light was made by the Danish astronomer Ole Rømer, who observed an apparent variation in the period of one of Jupiter’s moons depending upon whether the Earth was approaching it or moving away from it. From this he was able to estimate the time taken for light to cross the Earth’s orbit, and from there the mathematician Christiaan Huygens was able to produce a figure of 220,000,000 metres per second.

Spinning Cogs And Mirrors: Time Of Flight

The mile-long evacuated tube used in Michelson's time-of-flight experiment. H.
The mile-long evacuated tube used in Michelson’s time-of-flight experiment. H. H. Dunn, Public domain.

The experiments with which we will perhaps be the most familiar are the so-called time of flight measurements, which take Galileo’s idea of observing the delay as light travels over a distance, and bring to it ever higher precision. This was first performed in the middle of the 19th century by the French physicist Hippolyte Fizeau, who reflected a beam of light from a mirror over several kilometres, and used a toothed wheel to chop it into pulses. The pulses could be increased in frequency by moving the wheel faster until the time taken for the light to travel the distance from wheel to mirror and back again matched the separation between teeth and the returning pulse could be observed. His calculation of 313,300,000 metres per second was successively improved upon through the work of succession of others including Léon Foucault, culminating in the series of experiments by the American physicist Albert A. Michelson in the 1920s. Michelson’s final figure stood at 299,774,000 metres per second, measured through a multi-path traversal of a mile-long evacuated tube in the California desert. In the second half of the century the techniques shifted to laser interferometry, and in the quest to define the SI units in terms of constants, eventually to the definition mentioned in the first paragraph.

The most fascinating part of the story probably encapsulates the essence of scientific discovery, namely that while to arrive at something takes the work of many scientists building on the work of each other, it can then often be rendered into a form that can be understood by a student who hasn’t had to pass through all that effort. We could replicate Fizeau and Michelson’s experiments with a pulse generator, laser diode, and oscilloscope, which while of little scientific value nearly a century after Michelson’s evacuated tube, is still immensely cool. Has anyone out there given it a try?

Header image: Tommology, CC BY-SA 4.0.

Measuring The Speed Of Light In 1927

It is hard to remember that a lot of high tech research went on well before the arrival of electronic computers, lasers, and all the other things that used to be amazing but are now commonplace. That’s why we enjoyed [Michel van Biezen’s] two part post on how Michelson computed the speed of light in 1927. You can see the videos below.

Michelson wasn’t the first, of course. Galileo tried. He sent an assistant to the top of a hill with a lantern. When the assistant saw Galileo’s lantern, he was to uncover his lantern. They practiced near each other to account for reaction time. But when the assistant was 3 km away, it didn’t take any more time. The implication was that light traveled instantaneously, but, of course, it is actually just really fast.

By 1927, Michelson tried what was in effect the same technique but with better technology, and this time they put a reflector about 35 km away meaning the light had to go to the reflector and back for a total of about 70 km.

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Fast Video Covers Coax Velocity Factor

We once saw an interview test for C programmers that showed a structure with a few integer, floating point, and pointer fields. The question: How big is this structure? The correct answer was either “It depends,” or “sizeof(struct x).” The same could be said of the question “What is the speed of light?” The flip answer is 186,282 miles per second, or 299,792,458 metres per second. However, a better answer is “It depends on what it is traveling in.” [KB9VBR] discusses how different transmission lines have different velocity factors and what that means when making RF measurements. A cable with a 0.6 velocity factor sees radio signals move at 60% of that 186,282 number.

This might seem like pedantry, but the velocity factor makes a difference because it changes the actual measurements of such things as dipole legs and coax stubs. The guys make a makeshift time domain reflectometer using a signal generator and an oscilloscope.

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Testing The Speed-of-Light Conspiracy

There are a number of ways to measure the speed of light. If you’ve got an oscilloscope and a few spare parts, you can build your own apparatus for just a few bucks. Don’t believe the “lies” that “they” tell you: measure it yourself!

OK, we’re pretty sure that conspiracy theories weren’t the motivation that got [Michael Gallant] to build his own speed-of-light measurement rig, but the result is a great writeup, and a project that includes one of our favorite circuits, the avalanche transistor pulse generator.

setupThe apparatus starts off with a very quickly pulsed IR LED, a lens, and a beam-splitter. One half of the beam takes a shortcut, and the other bounces off a mirror that is farther away. A simple op-amp circuit amplifies the resulting pulses after they are detected by a photodiode. The delay is measured on an oscilloscope, and the path difference measured with a tape measure.

If you happen to have a photomultiplier tube in your junk box, you can do away with the amplifier stage. Or if you have some really fast logic circuits, here’s another project that might interest you. But if you just want the most direct measurement we can think of that’s astoundingly accurate for something lashed up on breadboards, you can’t beat [Michael]’s lash-up.

Oh and PS: He got 299,000 (+/- 5,000) km/sec.

Hackaday Prize Entry: Optical Experiments Using Low Cost Lasercut Parts

Experimenting with optics can be great fun and educational. Trouble is, a lot of optical components are expensive. And other support paraphernalia such as optical benches, breadboards, and rails add to the cost. [Peter Walsh] and his team are working on designing a range of low-cost, easy to build, laser cut optics bench components. These are designed to be built using commonly available materials and tools and can be used as low-cost teaching tools for high-schools, home experimenters and hacker spaces.

They have designed several types of holders for mounting parts such as lasers, lenses, slits, glass slides, cuvettes and mirrors. The holder parts are cut from ¼ inch acrylic and designed to snap fit together, making assembly easy. The holders consist of two parts. One is a circular disk with three embedded neodymium magnets, which holds the optical part. The other is the base which has three adjustment screws which let you align the optical part. The magnets allow the circular disk to snap on to the screws on the base.

A scope for improvement here would be to use ball plunger screws instead of the regular ones. The point contact between the spherical ball at the end of the screw and the magnet can offer improved alignment. A heavy, solid table with a ferrous surface such as a thick sheet of steel can be used as a bench / breadboard. Laser cut alignment rods, with embedded magnets let you set up the various parts for your experiment. There’s a Wiki where they will be documenting the various experiments that can be performed with this set. And the source files for building the parts are available from the GitHub repository.

Check out the two videos below to see how the system works.

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Light Speed: It’s Not Just A Good Idea

[Kerry Wong] took apart a PM2L color analyzer (a piece of photography darkroom gear) and found a photomultiplier tube (PMT) inside. PMTs are excellent at detecting very small amounts of light, but they also have a very fast response time compared to other common detection methods. [Kerry] decided to use the tube to measure the speed of light.

There are several common methods to indirectly measure the speed of light by relating frequency to wavelength (for example, using microwave ovens and marshmallows). However, measuring it directly is difficult because of the scale involved. In only a microsecond, light travels almost 1000 feet (986 feet or 299.8 meters).

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image of the face of einstein

The Spooky Nature Of Electromagnetic Radiation

Our story begins a little over one hundred years ago in Bern, Switzerland, where a young man employed as a patent clerk went off to work. He took the electric trolley in each day, and each day he would pass an unassuming clock tower. But today was different, it was special. For today he would pose to himself a question – a question whose answer would set forth a fascinating dilemma.

The hands of the clock appeared to move the same no matter if his trolley was stopped or was speeding away from the clock tower. He knew that the electromagnetic radiation which enabled him to see the clock traveled at a finite speed. He also knew that the speed of the light was incredibly great compared to the speed of his trolley. So great that there would not be any noticeable difference in how he saw the hands of the clock move, despite him being at rest or in motion. But what if his trolley was moving at the speed of the reflected light coming from the clock? How would the hands of the clock appear to move? Indeed, they could not. Or if they did, it would not appear so to him. It would appear as if all movement of the clock’s hands had stopped – frozen in an instant of time.  But yet if he looked at the hands of the watch in his pocket, they would appear to move normally. How does one explain the difference between the time of the clock tower versus the time of his watch? And which one was correct?

There was no way for him to know that it would take three years to answer this question. No way for him to know that the answer would eventually lead to the discovery of matter and energy being one and the same. No way to know that he, this underemployed patent clerk making a simple observation, would soon unearth the answer to one of the greatest mysteries that had stumped every mind that came before his – the very nature of time itself.

Now it might have taken Einstein a few years to develop the answer we now know as the Special Theory of Relativity, but it most certainly took him no longer than a few days to realize that Isaac Newton…

must be wrong.

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