An Educational Physics Laboratory Experiment for Directly Measuring the Speed of Light | ATI, April, 2010

An educational physics laboratory experiment for directly measuring the speed of light | ATI, April, 2010

Peer-reviewed & Open access journal ATI – Applied Technologies & Innovations ISSN: 1804-1191 | www.pieb.cz Volume 1 | Issue 1 | April 2010 |pp. 29-32

An educational physics laboratory experiment for directly measuring the speed of light

Krassimira Kardjilova, Peicho Popov, Valentin Lyutskanov, Vladimir Pulov, Mariela Mihova Department of Physics, Technical University-Varna, Bulgaria, e-mails: [email protected], [email protected], [email protected] [email protected], [email protected]

With the aid of modern electronics the speed of light was directly measured by timing the delay of a light pulse from a laser in reflecting from a mirror in experiment performed in educational Physics Laboratory.

Key words: Speed of light, student physical laboratory, lidar experiment.

Introduction

This paper aims to present an idea and its practical implementation for experimental determination of the fundamental physical constant - the speed of light. The known classical experiments require complicated and expensive instrumentation that is unsuitable for demonstrations and laboratory exercises in the general courses of physics. Contemporary laser physics and electronics are capable of producing light pulses and providing techniques for measuring time intervals with a few nanoseconds duration. These techniques are already accessible for the educational process. In view of these we have formulated a task to construct a system for generation of short laser pulses and measurement of the distance and the time of travel of these light pulses in order to determine the speed of light.

Historical overview

The idea that light is something that moves and takes time to go a distance comes from the time of Empedocles. Persian physicist from the 11th century Alhazen argued that light has finite speed that varies in different transparent media. Due to inaccuracies in the measurement of the time intervals, the first attempts to determine the speed of light in the early 17th century, including that of Galileo Galilei, though clever, had only led to the conclusion that it should be rated very high. The first quantitative measurement of the speed of light was carried out by the Danish astronomer Ole Christensen Römer in 1676 in an experiment based on the observation of the delay of the eclipse of Jupiter’s satellite Io. The speed of light was estimated with a great mistake (25%) that was mainly due to the bad accuracy in the estimation of the Earth’s orbit; even so, it became a well known fact - the speed of light is about several hundred thousand kilometers per second. Later on, new and more accurate methods have been developed, such as: -- the method of Fizeau (1849), using an amplitude modulated light beam, a rotating cog wheel and a mirror;

-- the method of Foucault (1862), using a rotating mirror; & Innovations Applied Technologies -- the method of Louis Essen (1946), using a standard wave in a microwave resonator; -- the method of Kate Davey Frum (1958), using radio-interferometer; -- the method of Kenneth Evenson (1972), using a kind of interferometer based on helium-neon laser with stabilized frequency; the speed of light was estimated at c = 299792.4574 ± 0.011 km/s. The method of optical radar, applied by Cooke et al. (1968), and by Aoki et al. (2008), although relatively imprecise in comparison with the interference methods (see James et al., 1999), enables direct measurement of the speed of light in the university/school physics laboratory. In the standard optical location methods the distance is determined by knowing the light velocity and measuring

© Prague Development Center www.pieb.cz - 29 - An educational physics laboratory experiment for directly measuring the speed of light | ATI, April, 2010 the time that it takes to the optical signal to travel along the distance. In the method applied here we know the optical path and by measuring the time of travel we directly determine the speed of light.

Justification

Standard General Physics courses include electromagnetism, optics, elements of quantum mechanics and special relativity. In the core of these courses stands the understanding of the fundamental role in nature of the universal physical constant - the speed of light in vacuum. Realization of an experiment for measuring the speed of light in a school Physics Laboratory is important mainly for: 1. The methodological perspective - conducting an experiment by the students themselves in order to determine a universal constant of nature, standing in the foundation of contemporary physics. 2. The applied perspective - creating a compact, reliable and affordable as a price experimental apparatus based on the most modern electronics, allowing direct measurement of the speed of light.

Method

The proposed method consists of creating short light pulses and measuring the time these pulses propagate from the source to the mirror and then back to the detector (Figure 1). Knowing the total distance 2L and the time of propagation allows to calculate the speed of light in the air: c = 2L ∆t .

Experimental solution and working principle

ALTERAs FPGA chip EP1C3T144 (Figure 1) is used to produce triggering LVDS pulse sequence with a period of 80 ns and pulse duration of 5 ns (Duty Cycle = 1/16).

Fi g u r e 1. Bl o c k Sc h e m e o f t h e experimental s e t u p

This is achieved using its PLL module with input frequency of the quartz oscillator of 120 MHz. MAXIMs laser driver MAX3643 converts this sequence into light pulses with almost the same time characteristics. The collimated laser beam is directed to a mirror that reflects it back to the detector placed near the laser. The distance between the mirror and the laser (and the detector) is L , so 2L is the distance that the light passes through the air illuminating the detector. MAXIMs transimpedance preamplifier MAX3665 and ANALOG DEVICES LVDS comparator AD8465 are used to convert light pulses again into electric ones. The detected LVDS pulses enter the FPGA chip and exit it converted into LVCMOS standard. The triggering sequence exits from another pin of the FPGA in the same LVCMOS standard. Both the trigger and the signal pulses (Figure 2) in the same standard are monitored by AGILENTs DS03202A oscilloscope. The time delay in nanoseconds between the trigger and the signal pulses is measured at certain distance L . It was found that the total time delay in the electronic circuitry (when L ~ 0) does not exceed 20 ns.

- 30 - © Prague Development Center www.pieb.cz An educational physics laboratory experiment for directly measuring the speed of light | ATI, April, 2010

Fi g u r e 2. De f i n i t i o n s o f t h e s i g n a l a n d t h e t r i g g e r p u l s e s b y t h e o s c i l l o g r a m s

Results

The results obtained for five different distances (see the oscillogram on Figure 3 for distance L =1.730 m ) are summarized in Table 1. A graph fitting the data points with a linear function through the least square method is plotted on Figure 4. The average speed of light in the air is calculated by using the formula c = 2/η , where η is the slope of the line of best fit. The result obtained is c = 291 262 km/s, which differs from the actual value of the speed of light by approximately 3%. This is mainly due to the error of the measurement of the time delay that is estimated at ~ 1 ns. As it is seen from the ∆t - intercept of the graph the electronics time delay at zero propagation distance is about 15 ns. Note that there is no influence of the duration of the received pulse on the accuracy of measurement. This is a consequence of the fact that only the rising edge of the received pulse is that stops the measurement of the time interval between the trigger pulse and the received pulse.

Ta b l e 1. Experimental Da t a

L , m 1.730 1.565 1.400 1.235 1.070 27.21 26.08 24.94 23.81 22.68 ∆t , ns

Fi g u r e 3. Os c i l l o g r a m o f t h e s i g n a l a n d t h e t r i g g e r p u l s e s w h e n t h e d i s t a n c e b e t w e e n t h e m i r r o r a n d t h e t r a n s c e i v e r is L = 1.730 m Applied Technologies & Innovations Applied Technologies

Fi g u r e 4. A p l o t o f t h e d a t a p o i n t s a n d t h e l e a s t s q u a r e s l i n e o f b e s t f i t

General Physics laboratory exercise

Given the good results of the tests, a set of equipment for making a laboratory exercise named “Direct measuring of the speed of light in the air” has been prepared. It can be used in General Physics training courses. In accordance with the primary objective of this exercise the student must fulfill the following tasks: 1. Measure the time ∆t that it takes the light pulses to propagate several different distances 2L in the air; 2. Plot a graph ∆t versus L of the experimental points; 3. Plot a linear function ∆t = τ + ηL that best approximates the experimental points by applying the least square method; 4. Calculate the speed of light in the air by using the slope of the plotted line: c = 2/η; 5. Evaluate the error in the resulting value of c by taking into account the errors in the measurement of the time ∆t and the distance L ; 6. Estimate the time delay in the electronics at zero distance between the light source and the detector by recording the parameter τ, i.e. the value of the ∆t - intercept of the plotted line. The accuracy of the method is determined by the resolution of the method of measuring the time delay, which is estimated at ~ 1 ns. This accuracy meets the requirements for school experiment and is of the same order as the accuracy achieved by Aoki et al. (2008).

Conclusion

In this paper we present an experimental technique for determining the speed of light in the air. The method is completely accessible to students who study General Physics at school, or as well as, in the university. The experiment is based on the direct measurement of the time delay accumulated during the propagation of light on its way from the source to the reflector and back to the detector. The obtained speed of light differs from the actual value of c by only 3%, which is achieved by highly precise measuring (with only 1 ns resolution) of the time delay. A set of laboratory equipment was prepared and tested to be used in General Physics courses. The laboratory experiment for determining the speed of light in the air has been financed by the research project “Experiments that prove the quantum nature of light.”

References

Aoki, K., Mitsui, T., 2008. “A tabletop experiment for the direct measurement of the speed of light”, American Journal of Physics, Vol. 6, No.9, pp.812-815. Cooke, J., Martin, M., McCartney, H., Wilf, B., 1968. “Direct determination of the speed of light as a general Physics Laboratory experiment”, American Journal of Physics, Vol.36, No.9, pp.847-847. James, M., Ormond, R., Stasch, A., 1999. “Speed of light measurement for the myriad”, American Journal of Physics, Vol. 67, No.8, pp.681-684.