ХИМИЧЕСКАЯ ФИЗИКА, 2004, том 23, № 2, с. 116-127
ЭЛЕМЕНТАРНЫЕ ^^^^^^^^^^
ФИЗИКО-ХИМИЧЕСКИЕ ПРОЦЕССЫ
УДК 532.22;535.1
USE OF TIME-CORRELATED SINGLE PHOTON COUNTING DETECTION TO MEASURE THE SPEED OF LIGHT IN WATER
© 2004 r. P. L. Muin o*, A. M. Thompson*, R. J. Buenker**
*Department of Chemistry, Mathematics and Physical Science, St. Francis College, Loretto, Pennsylvania 15940 USA **Bergische Universität-Gesamthochschule Wuppertal, Fachbereich 9-theoretische Chemie, Gaussstr. 20, D-42097
Wuppertal, Germany Received 16.11.2002
Traditional methods for measuring the speed of light in dispersive media have been based on the detection of interference between light waves emitted from the same source. In the present study the elapsed times for single photons to move from a laser to a photomultiplier tube are measured electronically. Time-correlated single photon counting detection produces a characteristic instrument response which has the same shape independent of both the path length the light travels and the nature of the transparent media through which it passes. This allows for an accurate calibration of the chronograph by observing shifts in the location of the instrument response for different distances traveled by the light. Measurement of the corresponding shift which occurs when light moves the same distance through air and water then enables an accurate determination of the ratio of the photon velocities in these two media. Three different wavelengths of light have been used. In two cases good agreement is found between the present measured light speeds and those which can be inferred from existing refractive index measurements in water. The shortest wavelength studied is too far in the uv to obtain a reliable estimate on the same basis, and so the ng value (1.463) measured in the present work awaits independent confirmation. A theoretical discussion of the present results is undertaken with reference to Newton's original corpuscular theory of light. It is argued that his failure to predict that light travels more slowly in water than in air arose from the inadequacy of his mechanical theory rather than his assumptions about the elementary composition of light.
1. INTRODUCTION
Measurements of speed of light in liquids and solids have had a decisive influence on the development of mechanical theories in science and in formulating models on which to visualize the fundamental processes of nature. the phenomenon of light refraction was already a subject of keen interest to the ancient scholars in Greece and Egypt, but it took many centuries of further study before it became clear that such effects are directly related to the fact that light travels with different speeds through air and water and other transparent materials. Two laws of refraction were discovered very early on, but it was not until the seventeenth century before the Dutch astronomer, Snell, was able to show that the sines of the angles of incidence and refraction always have a constant ratio for a given pair of media.
Experiments of this genre became the focus of a seminal argument about whether light in its elementary form is a particle or a wave. Newton concluded on the basis of his corpuscular theory of optical phenomena that particles of light travel faster in a dense medium such as water or glass than they do in air or free space. Belief in this theory was virtually abandoned a century and a half later when in 1850 Foucault was able to show that light actually travels more slowly in water than in air. The latter experiment was based on Fizeau's mechanical shutter method, which has also been the model for most subsequent measurements of the speed of light
in dispersive media [1-3]. It involves the detection of interference between two light waves originating from the same source. The slower speed of light in dense media is explained by the fact that the wavelength of the radiation is decreased while the corresponding frequency remain unchanged. Little more than a decade later Maxwell formulated his electromagnetic theory and after another twenty years Hertz was able to confirm that it gave a correct description of the transmission of both visible light and radio waves of much lower frequency.
Yet Newton's theory of the particle nature of light received new impetus in 1905 through Einstein's interpretation of the photoelectric effect [4] and later from observations of collisions between X-rays and electrons in the Compton effect [5]. These experiments can only be successfully analyzed in terms of highly localized entities with a definite energy and momentum, later designated as photons by Lewis [6], which are very similar to the corpuscles of light envisioned by Newton.
The question thus arises whether it is possible to measure the speed of single photons without taking advantage of any of the wave properties of light such as interference. A fairer test of the particle hypothesis would be to accurately measure the elapsed time that it takes for a photon to travel a known distance from a light source to a suitable detector, much as one goes about determining the velocity of an ordinary object such as a train or a baseball. Recent advances in time-
correlated single photon counting detection [7] open up an interesting possibility in this direction, as will be discussed in detail in the following section. On the basis of the present experimental investigation it has proven possible to measure the speed of light in water for three different wavelengths by timing the motion of single photons emitted from a laser source. The subsequent discussion of these results then considers the question of why Newtonian mechanics led to an erroneous prediction of the relative speeds of light in air and water some 300 years ago.
2. EXPERIMENTAL PROCEDURE
The technique employed to measure the speed of light in water in the present study has been implemented in past work to study relaxation effects in biological materials [8]. The underlying idea is to detect single photons over a period of time which have been used to irradiate a given substance. The method makes use of electronics which can measure the elapsed time between the firing of a laser pulse and the arrival of one of its photons at a photomultiplier tube (PMT) located some distance away. Before discussing exact details of the experimental procedure, a brief introduction to the model on which it is based will be given below.
A. Statistics of speed measurements
A simple way to visualize how the present experimental procedure enables a quantitative measurement of the speed of light in dispersive media is shown in the schematic diagram of Fig. 1. Analogy is made to the common procedure used to evaluate the results of a swimming race over a fixed distance AB. The basic idea is to start the clock at the moment the swimmer dives into the water and then to stop it immediately after the designated position at the end of the pool is reached. There are clearly two sources of error, corresponding to inaccuracies in initiating the timing at the proper moment and then later in stopping it precisely. In addition, one must be certain that the clock itself is functioning properly so that it gives an accurate value for the elapsed time to be measured. Because of the high speed of light, the sizes of the errors associated with the setting and stopping of the clock electronically are too large to allow the speed of any one photon to be determined within the desired level of accuracy. The present method overcomes this deficiency by relying on the fact that the errors in question are quite systematic and follow a definite statistical pattern.
If the race is judged by a large number of official timers, one can catalog their individual errors as t1(n) for the time it takes each of them to set their clock after the swimmer starts to dive and t3(n) for the corresponding time it takes to stop their clock after the final position has been reached. In the photon experiments under discussion it is certain that each t1 and t3 value will be positive, but this characteristic is not critical to the suc-
Normal
Fig. 1. Schematic diagram showing the three time intervals which are involved in the electronic clocking of a racing event: ti for starting the clock after the object has left the starting gate A, t2 for the actual travel time from A to B, and t3 for stopping the clock after arrival of the object at B. The total elapsed time registered on the clock is thus t = t2 + t3 - ti.
cess of the overall determination. If the time actually required by the swimmer to complete the race in a fair manner is designated as t2, then the total elapsed time t on a given clock n will be
t(n) = t2 + t3 (n) - ti (n). (1)
without more specific knowledge of the individual t1(n) and t3(n) values, it is impossible to obtain an accurate measurement of the time t2 from these results, but if the distribution of these errors is reproducible to a sufficient degree, it is possible to obtain an accurate comA B
parison of the times t2 and 12 for two different swimmers. In other words, by subtraction of the total clock times for these two races as determined by each of the judges, through systematic cancellation of errors one obtains
tA (n) - tB (n) = tA - tB2 (2)
in all cases.
It is relatively easy to check how well the statistical distribution t3(n) - t1(n), which will hereafter be referred to as the instrument response, is reproduced in different situations. One can simply compare results for different sample sizes pertaining to the same race after appropriate normalization. In the experimental proce-
Pixel
Fig. 2. Experimental setup used for measuring the various time intervals needed to obtain the velocity of light in water for three different wavelengths of light.
dure to be described below it will be seen that the range of t3(n) values is far larger than for t1(n) because the detection of a single photon at the PMT is underst
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.