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diff --git a/chapters/spol.tex b/chapters/spol.tex deleted file mode 100644 index 6c0446e..0000000 --- a/chapters/spol.tex +++ /dev/null @@ -1,141 +0,0 @@ -%\chapter*{Measuring the Speed of Light} -%\addcontentsline{toc}{chapter}{Measuring the Speed of Light} -\documentclass{article} -\usepackage{tabularx,amsmath,boxedminipage,epsfig} - \oddsidemargin 0.0in - \evensidemargin 0.0in - \textwidth 6.5in - \headheight 0.0in - \topmargin 0.0in - \textheight=9.0in - -\begin{document} -\title{Measuring the Speed of Light} -\date {} -\maketitle - -\noindent - \textbf{Experiment objectives}: Determine the speed of light directly by - measuring time delays of pulses. - -\section*{History} - - The speed of light is a fundamental constant of nature, the value -we now take for granted. In 1983, the internationally adopted value in vacuum became: - -\[ -c = 2.99792458 \times 10^8 m/s\,\, \mbox{exactly} -\] - -But considering that light travels seven and a half times around the world in one second, you can imagine how -challenging a measurement it would be to determine the exact value of the speed of light. In fact, it took -several attempts over many centuries to determine the value (some of the measurements are shown in Table 1). -\begin{figure}[hbt] -\centerline{\epsfig{file=ctable.eps, width=6in, angle=0}} \label{fig:ctable} - -\end{figure} - -The first attempt at a measurement was made by Galileo in 1600 using two lanterns on hills. He had an assistant -on a distant mountain who would signal when he saw a lantern be masked, and then Galileo would measure the -interval between his own signaling and the response of his assistant. He only could find the speed of light to -be ``very fast''. But interestingly enough, the technique you will use is nowhere near the best, but it is -direct and in some ways similar to Galileo's. - -Several other experiments followed over the centuries until Michelson and Morely made a very accurate -measurement in 1887 using a specially design interferometer (which by lucky coincidence you explore during -another lab in our course). The currently accepted value was not determined until the advent of the laser. - -You might wonder why the speed of light is now a defined quantity. The -measurements at the end of the Table are measurements of the wavelength -and frequency of light, both referenced to the wavelength of atomic transitions -and to the frequency of atomic transitions. Distances can be measured to -small fractions of the wavelength of light, and this over distances of -meters. Frequencies are compared by beating one light signal against another -so that the difference frequency can be directly compared to atomic clocks. -You can estimate the accuracy of this by considering a meter to be measured -to $10^{-3}$ of $\lambda$ of some visible lightwave, and $\nu$, the frequency -can be measured to $10^{-5}$ Hz out of the frequency of an atomic transition. - -\section*{Procedure} - -\subsection*{Laser Safety} -While this is a weak laser caution should still be used. \textbf{Never look directly at the laser beam!} Align -the laser so that it is not at eye level. - -\subsection*{Set Up} -\textbf{Equipment needed}: diode laser, photodetector, lens, Pasco magnetic platform, large mirror on a rolling -table, small reference mirror, function generator, oscilloscope. - -In the experiment you modulate the power sent to the laser to produce short pulses of light, and then measure -the time it takes for these pulses to travel from the laser to the mirror and back to the photodetector, as -shown in the layout for the experiment in Fig. \ref{fig:solapp}. This measurement is repeated for several -displacements of the mirror (the more the better) by rolling the table with the mirror along the corridor (if -you like challenges, you can try to see how far you can go). - - -% -\begin{figure}[hbt] -\begin{center} -\epsfig{file=solapp.eps, width=5in, angle=0} -\end{center} -\caption{Speed of light Apparatus} \label{fig:solapp} -\end{figure} -% -\subsection*{Data acquisition} - -\begin{itemize} - -\item Put a rolling table as close as possible to the stationary table with the laser and the photodetector. Make -sure you have enough clearance to push the table along the corridor (you may need to move the tables). Make sure -that the laser beam hits the mirror relatively close to the center, and use fine tuning on the mirror to reflect -the beam to the photodetector - first without the lens, then with the lens in place. - -\item Plug in the output of the photodetector to the oscilloscope, and use a TTL pulse output as a trigger. If -everything works, you will see a train of nearly square pulses. Before starting the measurements, you first need -to think about two issues (\textit{the instructor will ask you about them}!): \\ -1) How will the detected signal change as you start pushing the mirror farther and farther? \\ -2) What is a suitable characteristic feature(s) of the detected signal to trace this change? Also, Make -yourself familiar with the scope features, such as ``measurements'' and ``save traces'' (your instructor or TA -will be able to help you with that). That will make your data acquisition easier. - - -\item Vary the position of the mirror by moving the rolling table from as close as possible to as far as possible -in about $10$ steps (the more measurements the more accurate final result you will have). For each step measure -the position of the table $D$. The floor tiles make a reasonable gauge - each tile is a 9 inch square (remember -to convert to meters!). Count the tile squares and double check. - -For each position each member of the group determine the light pulse time delay $T_{1,2,\cdots}$ by comparing -the time difference between the chosen characteristic features for the light reflected off the large ``distant'' -mirror and small ``reference'' mirror placed near the detector. Calculate average value $T_{ave}$ and the -uncertainty $\Delta T$. Below is the example of a table for data recording. - -\end{itemize} - -\vskip .1in - -\begin{tabular}{|l|l|l|l|l|l|l|}\hline -$D \pm \Delta D$ ($\#$ of tiles)& $D \pm \Delta D$ (m) &$T_1$($\mu$s)& $T_2$($\mu$s) -& $T_3$($\mu$s) & $T_{ave}$ ($\mu$s) & $\Delta T$ ($\mu$s) \\ -\hline &&&&&&\\\hline -&&&&&&\\$\dots$&$\dots$&$\dots$&$\dots$&$\dots$&$\dots$&$\dots$\\\hline -&&&&&&\\\hline &&&&&&\\\hline &&&&&&\\\hline - -\end{tabular} - -\vskip .2in -\noindent - -\subsection*{Analysis} - -Plot the results of the measurements as a distance vs time delay graph $D vs. T$. If the measurements are done -properly, the data will be scattered close to a straight line, and the slope of this line is inversely -proportional to the speed of light $1/v$. Thus, the measured $v$ and its uncertainty can be extracted from -fitting the experimental data. This method should give more accurate results than calculating $v$ from each -measurements, since it allows avoiding systematic errors due to an offset in the distance measurements. From -same fit determine the distance intercept. It the obtained value reasonable? - -In the lab report compare the measured speed of light with the theoretical -value. Is it within experimental uncertainty? If it is not, discuss possible -systematic errors which affected your results. - -\end{document} |