From b7c42566a899b479f86ba215e3e79ac5a7c13a21 Mon Sep 17 00:00:00 2001
From: Eugeniy Mikhailov <evgmik@gmail.com>
Date: Tue, 27 Aug 2013 10:17:12 -0400
Subject: added lab manual as it was prepared by Mike with better structured
 directories

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+%\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}
-- 
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