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Each student must investigate the following:

The year and scientist(s) involved

The methodology used

The equipment available and limitations

An image if appropriate

The measured value of c and its accuracy

The significance of this method in the historical context

How it contributed to current understandings of time and distance

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Galileo came up with an experiment to measure light's velocity. He and his assistant took a shuttered lantern and they stood on hilltops one mile apart. Galileo flashed his lantern and as soon as his assistant saw Galileo's light he was supposed to flash his light.

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history of the speed of light and how its speed was determined

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Physics in a Nutshell: A Brief History of the Speed of Light

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We have estimates for the speed of light. But in truth, it is conceivable that further refinements will be made.

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Armand Fizeau (1894)

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Fizeau sent light pulses through a rotating toothed wheel. A distant mirror on the other side reflected the pulses back through gaps in the wheel. By rotating the wheel at a certain speed, each light pulse that went through a gap on the way out was blocked by the next tooth as it came around. Knowing the distance to the mirror and the speed of rotation of the wheel enabled Fizeau to obtain one of the earliest measurements of the speed of light.

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Ole Rømer publicised his findings in 1676, but worked on the calculations from

1668-1674

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1924-26 by Albert A. Michelson

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Albert A. Michelson

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In 1862 Leon Foucault used used a mirror to measure the speed of light.

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Albert Abraham Michelson

He designed the interferometer in 1887 to study the effect of the Earth's motion on the speed of light.

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c = 315,000 km/s

accuracy = 5.07% above

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Louis Essen 1950s-1960s (precise measurement pioneer)

Cornell researchers 1970s (refined laser-based methods)

CGPM (1983) (defined the current exact value)

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Hermann von Helmholtz

He is credited with discovering and describing cavity resonance in the 19th century, a phenomenon where an enclosed space (a cavity) vibrates at specific frequencies when stimulated.

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Method:

A beam of light is reflected off a rotating mirror toward a distant fixed mirror.

The light reflects back, but the rotating mirror has turned slightly in the meantime.

This causes a change in the returning beams angle.

By measuring this shift in angle and knowing the mirror's speed and distance, the speed of light is calculated.

Key formula:

c=2Lxω​/∆θ

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Galileo Galilei, using lanterns, tried to predict the speed of light in 1638. He was limited by both human reaction speed and lack of area for the light to travel.

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This cool guy couldn't get far enough away from his partner to find lights finite speed, thats why his experiment sucks for nowadays standards.

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Fizeau's experiment was the first terrestrial measurement of the speed of light. This was significant as not only did it prove that it was possible to measure the speed of light at a relatively small distance and to what is now considered an extremely close margin.

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1. Laser Measurements:

The measurements relied on the use of lasers locked on molecular absorption lines, which allowed for very precise measurements of wavelengths.

2. Wavelength and Frequency:

The speed of light (c) can be calculated using the formula c = fλ, where f is the frequency and λ is the wavelength of the electromagnetic wave.

3. The Value:

The recommended value for c was set to 299,792,458 meters per second. This value is now the standard, and the meter is defined as the distance light travels in a vacuum during 1/299,792,458 of a second.

4. Precision and Agreement:

The redefinition reflected the high degree of precision achieved in laser measurements, and the strong agreement between different measurements.

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The Equipment available and Limitations 

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The Equipment available and Limitations 

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Equipment

Rotating mirror

Stationary mirror

light source

Limitations

The displacement of the light beam had to be accurately observed which could be challenging

This experiment was limited by the technology of the time and more precise results were later recorded.

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A laser source is fired at a half reflective mirror that splits the ray into 2 perpendicular rays the travel to 2 stationary mirrors and back. The 2 mirrors are the same distance from the half mirror, so that it will take the same amount of time for the light to return. When they meet in the middle they will undergo constructive interference, resulting in a new wave with twice the amplitude.

This same experiment is repeated but this time one of the stationary mirrors is moved back. when the mirror is moved half a wavelength back, it will cause the 2 waves to undergo destructive interference. Therefore no wave will be detected.

In laser intferometory, laser source with known frequency is used and wavelength of the laser is measured by the distance in which the stationary mirror needs to move in order to cause destructive interference.

Lights speed is then calculated by multiplying the frequency times the wavelength.

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Michelson rotating mirror experiment - Methodology

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Michelson rotating mirror experiment - Methodology

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Michelson used a spinning mirror apparatus that allowed a better measurement than Foucault's apparatus (see doz and digs explanation). The mirror was rotating and eight sided, a beam of light hit one of the sides and reflected to a stationary mirror 35 km away on a mountain top. This beam bounced back to the rotating mirror. As long as the rotating mirror has spun exactly 1/8th of a turn, the next side is in the correct position to reflect the light to an observer looking through a telescope.

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c = 299 792 458 m / s

current value of c, considered highly accurate and is widely accepted.

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The Significance of this method in historical context.

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The Significance of this method in historical context.

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it was significant as it provided a more accurate and reliable laboratory-based measurement than previous astronomical observations.

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Initial interferometers, such as the Michelson interferometer, used partially monochromatic or white light sources, with limitations in coherence length and stability.

Detection and alignment technologies evolved from visual fringe evaluation using Vidicon cameras and analog methods in the 1970s to digital CCD detectors and computerised phase measurement in the 1980s and beyond.

Large-scale interferometers like LIGO use advanced Michelson–Fabry–Pérot configurations with Fabry–Pérot cavities to increase effective arm length by multiple reflections, enhancing sensitivity.

The cavity resonance technique, as used by Louis Essen and A.C. Gordon-Smith in the 1940s, employed cavity resonators (wavemeters) to measure radio-wave frequencies with high accuracy.

Earlier acoustic cavity resonators, such as the Helmholtz resonator invented in the 19th century, were simple rigid containers with a neck used to isolate specific sound frequencies, but these were mechanical rather than electromagnetic resonators. They were limited by the precision of cavity construction and the ability to control and measure resonant frequencies accurately.

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Rømer was able to calculate the speed of light using the discrepancies in the time between the eclipses of Jupiter's moons.

He measured the time delay of the eclipses, and noticed they were getting longer by up to 16.5 minutes.

He interpreted this as the difference in the times for light to travel from the sun to Jupiter, and back to earth.

Using this discrepancy, and the relative positions of the earth and Jupiter, he was able to calculate the speed of light.

This was extremely accurate for his time.

The speed of light he calculated was 214,000 km/s, which gives him a percentage error of 28.4% under the known value today.

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Its role as a fundamental constant of the universe, influencing everything from the definition of distance and time to the nature of space and time themselves.

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c=298,000 km/s or 298,000,000 m/s

Percentage error= 0.60%

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The Wheel had 720 teeth

spun at 13 rps or 780rpm

The light was measured crossing a distance of 16000m or 16km, crossing the same 8000m path forward and back

The wheels speed was recorded and altered until obtaining the required speed to block out light and then stabilised

He found the measurement found by using 1/13 X 2 X 720 = 1600/c

This gave him a value of 313,300 kilometres per second. This was roughly 5% too high than the known value now

this error can be attributed to either human error in the creation of the equipment or distance measurements or could be a design flaw in the teeth being too wide allowing for a larger room of error

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How to find the speed of light (Fizeau experiment)

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Maxwell’s Equations are presented in this tutorial. Gauss’s Law, Faraday’s Law, the non-existance of magnetic charge, and Ampere’s Law are described in an intuitive method, with a focus on understanding above mathematics.

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Because of Fizeau's experiment Foucault improved on Fizeau’s apparatus slightly when doing his experiment, replacing the cogwheel with a rotating mirror, it is now known as the Fizeau-Foucault Apparatus. Light was reflected at different angles as the mirror rotated. Since both the speed of rotation and the distance to the mirror were well established, it was possible to measure the difference between the angle of the light as it entered the apparatus and when it exited the setup, and calculate the speed of light from that. Foucault concluded in 1862 that the speed of light was 299,796 kilometres per second which was even closer than Fizeau only being off by 4.458 kilometres pre second off which is only 0.001% below the current accepted value of 299,792.458 kilometres per second as opposed to Fizeau who got 5.07% error above

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Significance and impact in the scientific community

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Significance and impact in the scientific community

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This experiment was extremely significant for the scientific community, as it was the first real confirmation that the speed of light was finite and measurable

It was the experiment that sparked the scientific community to find more and more accurate values of the speed of light, changing the way we view time and distance forever

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The faster the relative velocity, the greater the time dilation between them, with time slowing to a stop as one clock approaches the speed of light (299,792,458 m/s).

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Blud moved progressively further from another dude who also held a lantern. He opened his lantern and timed until he saw his partners lantern.

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Calculated Speed Of Light & Contributions

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Calculated Speed Of Light & Contributions

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This experiment has calculated the speed of light to be 299, 972, 457 m/s. Our most updated known value of the speed of light.

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Michelson's value for c turned out to be 299774000 ms^-1, which when compared to the current accepted value of 299,792,458 ms^-1, boasts a 99.9999384% accuracy.

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Laser Interferometry

Laser interferometry is essential in fields like gravitational wave detection, where tiny distortions in spacetime are observed using highly sensitive interferometers.

Cavity resonance

Cavity resonance is is crucial for laser operation, as it allows the light to build up and produce a coherent, powerful beam.

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The refined rotating mirror experiment challenged the long held assumption of the æther.