How Fast Is Light In Speed?
Light from a stationary source travels at 300,000 km/sec (186,000 miles/sec).
The first non-astronomical measurement of the speed of light in air was done by Foucault in 1849 and successfully determined the speed of 315 000km/s, which was only approximately 5% larger than today’s accepted value.
Using a rapidly rotating mirror, he measured the small changes in position of a reflected beam using a microscope, and by plotting said position changes against the rotation frequencies of the mirror, obtained a reasonably accurate value for c. However, the invention of the laser in 1960 opened a new realm of accuracy for such measurements, and in 1972, the speed of light was measured as
c=299 792 458 m/s, with an uncertainty of under 1 m/s. Various laser-based experiments could produce relatively reliable results, including the measurement of the delay of a short laser light pulse reflected off several mirrors into a photodetector. This same technique can be generalized for measuring the speed of light in different mediums of propagation (water tank, fiber optic cable).
Today, most optics labs possess the materials required to accurately measure the speed of light. In our lab, we set out to gain a better understanding of the workings of such optical measurement methods by recreating the rotating mirror and the pulsed laser experiments, and using them to experimentally determine the speed of light in air. Here, we show how changes in laser beam position and pulse delay can be used to determine the speed of light in Foucault’s experiment and the pulsed laser experiment respectively, as well as how this speed changes in an optical fiber and BNC cable. Using multiple lenses, mirrors, beam splitters, a microscope, a BNC cable, fiber optic cable and an oscilloscope, we successfully determined increasingly accurate experimental measurements of the speed of light, all while taking data at various stages to illustrate our experimental approach. Our results demonstrate how varying our experimental setup allowed for increasingly accurate measurements of the speed of light.
The speed of light is a constant which lends itself well to measurement via time of flights experiments, which consist of experiments measuring the time taken for an object to travel a known distance and deducing its speed accordingly. In this lab, we used basic optical table components (mirrors, lenses, beam splitters) and auxiliary components (oscilloscope, BNC cable, optical fiber, microscope) to recreate Foucault’s rotating mirror experiment. Then, we conducted our own time-of-flight measurements of the speed of light in different media.
We began our work on Foucault’s speed of light measurement experiment by measuring the distances between several particularly relevant components of the prearranged optical system, which is represented in Figure 1. This system consisted of a focused laser, two lenses, a beam splitter, rotating mirror, fixed mirror, quarter waveplate, linear polarizer and microscope. The laser first passed through a converging lens L1, which focused it midway between L1 and the beam-splitter. At the beam-splitter, the beam split into two parts, with its reflected component passing straight to the microscope, and the transmitted component continuing on to the second lens L2. However, the beam was polarized along the z direction, whereas the polarizer’s axis was aligned along the y axis, preventing any reflected light from being seen when looking through the microscope.
Meanwhile, the transmitted laser component, after passing through lens L2, was reflected off the rapidly rotating mirror, which could be set to either 750Hz or 1500Hz (counterclockwise and clockwise). The beam then came to a focus on the fixed mirror after passing through a quarter-wave plate, thus circularly polarizing the light. Reflecting off the fixed mirror passed the beam through the quarter-waveplate once again, completing a 90-degree polarization change to y polarization. The y polarized light, reflected across the rotating mirror, was focused by L2, then partially reflected by the beam-splitter and focused on the microscope slide. However, this y-polarized light could pass through the linear polarizer since it was aligned along the same axis and was ultimately the light we observed during our experiment.
Figure 1: Diagram of the optical system used during our recreation of Foucault’s rotating mirror experiment.
During this experiment, we used a camera placed at the microscope’s visual output to provide real-time data on reflected beam position while minimizing risks to our eyesight. We began by setting the mirror rotation speed to 750Hz, then centered the microscope crosshairs on the reflected light beam using a micrometer to complete small positional adjustments. We noted the micrometer measurement, then repeated this procedure for the three other rotation speeds, thus obtaining 4 data points illustrating the relation between reflected beam position and rotation speed.
Results and Discussion
Over the course of this experiment, we established multiple different approximations of the speed of light using a variety of measuring techniques and procedures. A common point to all our results was their relative closeness to the expected theoretical value of c, with respective percentage errors of 0.66%, 0.53%, 0.17%, 1% and below 0.5%. Our success in obtaining experimental data to a high degree of accuracy can be attributed in part to the highly improved sampling rate of the oscilloscope used. Indeed, our initial round of data collection was unsuccessful due to a low oscilloscope sampling rate of less than 1 data point per nanosecond. However, replacing the apparatus with another oscilloscope with over double the sampling speed allowed us to massively decrease uncertainty in our time variable, which, as shown previously, was the primary factor in our uncertainty calculations. Our optical setups were also designed so as to maximize path length difference and reduce the effect of measurement uncertainties, though their impact was relatively minor regardless. In part thanks to these measures, the theoretical speed of light was always contained within the uncertainties of our measurements, which were themselves restricted to a relatively narrow range of values (save for experiment 1).
As stated previously, the large uncertainty in experiment 1 is still cause for concern but is most likely due to lack of available data rather than errors in measuring. Indeed, this experiment only made use of 4 manually collected data points, as opposed to the hundreds of automatically sampled points obtained by the oscilloscope for all other experiments. Therefore, the large uncertainty in experiment 1’s value could be massively reduced by the inclusion of additional data points, which could be readily obtained by using a rotating mirror apparatus with a larger variety of rotation frequencies. In a similar fashion to, and following from our definition of uncertainty for the time delay variable, using an oscilloscope with an even greater sampling rate might further reduce uncertainty estimates for the time-of-flight experiments. Finally, increasing path-length difference would clearly improve the accuracy of results, as a large path-length implies a longer time-delay and distance travelled, reducing the effects of experimental error and uncertainty on both variables used in the calculation of c.
This experiment allowed us to apply our knowledge of optics and light propagation to the construction of multiple optical setups incorporating multiple mirrors, lenses, oscilloscopes, lasers and beam-splitters. By modifying parameters such as path-length and medium of propagation, we could calculate several experimental values for the speed of light and ascertain their uncertainties and proximities to the actual speed of light in a vacuum or optical fiber. Using a microscope, we observed the shift in position of a reflected laser beam to calculate c using a previously derived formula, after which we analyzed the output voltage from a photodetector receiving two temporally delayed laser pulses to calculate c using a simple velocity formula. We also completed an in-depth analysis of our uncertainties and explored how we might further refine our measurements during a future experiment. A potential future avenue of interest would be laser interferometry, which utilizes optical interference effects and has produced some of the most accurate experimental measurements of the speed of light to date. Knowing the exact speed of light also broader significance, as it allows for the development of modern technologies such as Lidar, which maps object and surface topography using laser pulse reflection methods applied to large surfaces. However, the implementation of such technologies requires knowledge of the speed of light to accuracies far beyond those we achieved in our lab.
Written by Sebastien Brown
How Fast Is Light In Speed?