manual source dir properly named

1 files changed, 0 insertions, 298 deletions

diff --git a/manual/chapters/fabry-perot.tex b/manual/chapters/fabry-perot.tex
deleted file mode 100644
index d74745f..0000000
--- a/manual/chapters/fabry-perot.tex
+++ /dev/null
@@ -1,298 +0,0 @@
-%\chapter*{Fabry-Perot Interferometer and the  Sodium Doublet}
-%\addcontentsline{toc}{chapter}{Fabry-Perot Interferometer}
-\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{Fabry-Perot Interferometer and the  Sodium Doublet}
-\date {}
-\maketitle
-
-
-\noindent
- \textbf{Experiment objectives}: Assemble and align Fabry-Perot interferometer,
- and use it to measure differential wavelength for the Na doublet.
-
- \section*{Theory}
-
-\subsection*{The Fabry-Perot Interferometer}
-
-Any interferometer relies on interference between two or more light field. In a Fabry-Perot configuration input
-light field bounces between two closely spaced partially reflecting surfaces, creating a large number of
-reflections. Interference of these multiple beams produces sharp spikes in the transmission for certain light
-frequencies. Thanks to the large number of interfering rays, this type of interferometer has extremely high
-resolution, much better than, for example, a Michelson interferometer. For that reason Fabry-Perot
-interferometers are widely used in telecommunications, lasers and spectroscopy to control and measure the
-wavelengths of light. In this experiment we will take advantage of high spectral resolution of the Fabry-Perot
-interferometer to resolve two very closely-spaces emission lines in Na spectra by observing changes in a
-overlapping interference fringes from these two lines.
-\begin{figure}[h]
-\begin{center}
-\includegraphics[width=0.8\linewidth]{./pdf_figs/pfig1}
-\caption{\label{fpfig1}Sequence of Reflection and
-Transmission for a ray arriving at the treated inner surfaces $P_1 \& P_2$.}
-\end{figure}
-\end{figure}
-
-A Fabry-Perot interferometer consists of two parallel glass plates, flat to better than 1/4 of an optical
-wavelength $\lambda$, and coated on the inner surfaces with a partially transmitting metallic layer. Such
-two-mirror arrangement is normally called an {\it optical cavity}. The light in a cavity by definition bounces
-back and forth many time before escaping; the idea of such a cavity is crucial for the construction of a laser.
-Any light transmitted through such cavity is a product of interference between beams transmitted at each bounce
-as diagrammed in Figure~\ref{fpfig1}. When the incident ray arrives at interface point $A$, a fraction $t$ is
-transmitted and the remaining fraction $r$  is reflected, such that $t + r = 1$ ( this assumes no light is lost
-inside the cavity). The same thing happens at each of the points $A,B,C,D,E,F,G,H\ldots$, splitting the initial
-ray into parallel rays $AB,CD,EF,GH,$ etc. Between adjacent ray pairs, say $AB$ and $CD$, there is a path
-difference of :
-\begin{equation}
- \delta = BC+CK
-\end{equation}%eq1
-    where $BK$ is normal to $CD$.  In a development
-similar to that used for the Michelson interferometer, you can show
-that:
-\begin{equation}
- \delta = 2d\cos\theta
-\end{equation}%eq.2
-     If this path difference produces
-constructive interference, then  $\delta$  is some integer multiple of   ,
-$\lambda$ namely,
-\begin{equation}
-  m\lambda = 2d\cos\theta %eq.3
-\end{equation}%eq.3
-
-This applies equally to ray pairs $CD$ and $EF, EF$ and $GH$, etc, so that all parallel rays to the right of
-$P2$ will constructively interfere with one another when brought together.
-
-Issues of intensity of fringes \& contrast between fringes and dark background
-are addressed in Melissinos, {\it Experiments in Modern Physics}, pp.309-312.
-
-\subsection*{The Sodium Doublet}
-
-    In this lab you will measure the separation between the two
-    famous ``sodium doublet'' lines, the two closely spaced lines
-    which occur at 589 $nm$ and 589.59 $nm$, respectively. This ``doublet''
-    emission is evidence that the atomic electron has the property
-    of intrinsic angular momentum, or spin S.  As you are learning
-    in Modern Physics 201, the discrete spectral lines in atomic
-    emission are due to the quantization of electron energies in
-    the atom. As Niels Bohr postulated, electrons in atoms are
-    only allowed to absorb and emit energy in discrete
-    quantities. When an electron moves from one orbit to another
-    in an atom, a well-defined amount of energy is emitted as
-    light at a fixed wavelength. Later in this class we will
-    explore the spectra of various atomic gases.
-\begin{figure}[h]
-\centerline{\epsfig{height=5cm, file=fpfig2.eps}} \caption{\label{fpfig2.fig}Fine Structure Splitting in sodium
-giving rise to the sodium doublet lines}
-\end{figure}
-    For many
-     atoms, {\bf atomic levels are further split}, for example,
-    by interactions of electrons with each other (Russell-Saunders
-    coupling), external magnetic fields (Zeeman effect), and even
-    the interaction between the spin of an electron and the
-    magnetic field created by its orbital angular momentum
-    (spin-orbit coupling). This is known as fine structure
-    splitting (FSS). The fine structure splitting for the sodium
-    3P state is due to spin-orbit coupling, and is illustrated in
-    Figure \ref{fpfig2.fig}.  The "3P" state refers to sodium's
-valence electron
-    which has a principal quantum number of $n=3$ and an orbital
-    quantum number of $l=1$ (a P-state). Further, the electron has
-    an intrinsic spin (like a top), described by a spin quantum
-    number $S$, which is either +1/2 or -1/2. The electron has a
-    magnetic moment due to its intrinsic spin, given by $m_S$. Due to
-its orbital angular momentum around a charged nucleus, it
-    senses a magnetic field ${\mathbf H}$. The energy of interaction of a
-    magnetic moment in a field is given by $E = -\mu\cdot {\mathbf H}$.
-This gives
-    rise to the splitting and two spectral emission lines.
-
-
-\section*{Procedure}
-
-\subsection*{Set Up}
-\textbf{Equipment needed}: Pasco precision interferometry kit, Na lamp,
-adjustable-hight platform.
-
-\begin{figure}
-\centerline{\epsfig{width=0.7\linewidth,file=fpfig3new.eps}} \caption{\label{fpfig3.fig}The Fabry-Perot
-Interferometer}
-\end{figure}
-
-The interferometer layout is shown in Figure \ref{fpfig3.fig}. The inner spacing  $d$ between two
-partially-reflecting mirrors ($P1$ and $P2$) can be roughly adjusted by loosening the screw that mounts $P2$ to
-its base. It is important that the plates are as closely spaced as possible. Move the plates to within  $1.0 -
-1.5$~mm of each other, but make sure the mirrors do not touch!
-
-\subsection*{Data acquisition}
-
-\begin{enumerate}
-\item \textbf{Turn on the sodium lamp as soon as you arrive. It should warm up for about 20 minutes
-before starting}.
-\item Turn the micrometer close to or at 0.00.
-\item Remove the diffuser sheet from in front of the lamp. Look through
-plate $P2$ towards the lamp.  If the plates are not parallel, you will see
-multiple images of the lamp filament. Adjust the knobs on $P1$ until the images
-collapse into one. At this point, you should see faint circular interference
-fringes appear.
-\item Place the diffuser sheet in
-front of the lamp so you will now only see the fringes. Continue to adjust the
-knobs on one plate (not the knobs to move the plate back and forth, but the
-ones to bring it parallel) to get the best fringe pattern. It is the most
-convenient to view the interference picture directly.
-\item
-Seek the START condition illustrated in Fig.(\ref{fpfig4.fig}), in which all bright fringes are evenly spaced.
-You do this by moving the micrometer.  Note that alternate fringes may be of somewhat different intensities, one
-corresponding to fringes of  $\lambda_1$, the other to those for $\lambda_2$. If you do not see this condition,
-try moving the mirror $P2$ across the range of micrometer screw. If you still cannot find them, you can also
-move the whole plate by loosening one plate and sliding it a little.
-\item  Practice going through the fringe conditions as shown in Fig.(\ref{fpfig4.fig})
-by turning the micrometer and viewing the fringes. Do not be surprised if you
-have to move the micrometer quite a bit to go back to the original condition.
-\item Find a place on the micrometer ($d_1$) where you
-have the ``START'' condition for fringes shown in Fig.(\ref{fpfig4.fig}). Now
-advance the micrometer rapidly while viewing the fringe pattern ( NO COUNTING
-OF FRINGES IS REQUIRED ).  Note how the fringes of one intensity are moving to
-overtake those of the other intensity (in the manner of
-Fig.(\ref{fpfig4.fig})).  Keep turning until the ``STOP'' pattern is achieved
-(the same condition you started with).  Record the micrometer reading as $d_2$.
-\emph{Remember that 1 tick mark is 1 micrometer ($10^{-6}m$). That means if you
-read 1.24, your really move 124 $\mu m$.}
-\end{enumerate}
-
-\noindent \fbox{\parbox{\linewidth}{\textbf{Experimental tip:} You may have to
-``home in'' on the best START and STOP conditions. Let's say that the even
-fringe spacing for the START condition ($d_1$) is not exactly in view. Now move
-the micrometer, looking to see if the pattern moves toward even spacing. If so,
-stop and read the micrometer for $d_1$. Move a bit more. If this second fringe
-spacing looks better than the first, then accept this for $d_1$. The same
-``homing in'' procedure should be used to select the reading for $d_2$. In
-other words as you approach the even spacing condition of the STOP pattern,
-start writing down the micrometer positions. Eventually you will favor one
-reading over all the others.}}
-
-\section*{Analysis}
-
-    Since the condition we are seeking above for ``START'' places
-    the bright fringes of   $\lambda_1$ at the point of destructive
-    interference for  $\lambda_2$, we can express this for the bull's eye
-    center ($\theta= 0 $) as:
-\begin{equation}
-2d_1=m_1\lambda_1=\left(m_1+n+\frac{1}{2}\right)\lambda_2
-\end{equation}
-
-  Here the integer n accounts for the
-    fact that   $\lambda_1 >  \lambda_2$ ,  and the  $1/2$  for the
-condition of
-    destructive interference for   $\lambda_2$  at the center. Since the
-    net action of advancing by many fringes has been to increment
-    the fringe count of   $\lambda_2$ by one more than that of
-$\lambda_1$  ,
-    then we express the ``STOP'' condition as:
-\begin{equation}
-2d_2=m_2\lambda_1=\left(m_2+n+\frac{3}{2}\right)\lambda_2
-\end{equation}
-   Subtracting the
-    two interference equations gives us:
-\begin{equation}
-2(d_2-d_1)=(m_2-m_1)\lambda_1=(m_2-m_1)\lambda_2+\lambda_2
-\end{equation}
- Eliminating  $(m_2-m_1)$
-    in this equation we obtain:
-
-\begin{equation}
-2(d_2-d_1)=\frac{\lambda_1\lambda_2}{(\lambda_1-\lambda_2)}
-\end{equation}
-
- Solving this for $\Delta \lambda = \lambda_1-\lambda_2$, and
-    accepting as valid the approximation that  $\lambda_1\lambda_2\approx
-\lambda^2$   ( where $\lambda$ is the
-    average of $\lambda_1$  and $\lambda_2 \approx 589.26 nm$ ), we obtain:
-\begin{equation}
-\boxed{\Delta\lambda=\frac{\lambda^2}{2(d_2-d_1)}}
-\end{equation}
-
-Each lab partner should independently align the interferometer and make at least \textit{two} measurements of
-``START'' and ``STOP'' positions. A sample table to record the data is shown below. \\{\large
-\begin{tabular}{|p{27mm}|p{27mm}|p{27mm}|p{27mm}|}
-\hline
- $d_1$ $\pm \dots$ & $d _2$ $\pm \dots$& $(d_1-d_2)$ $\pm \dots$&
-$\Delta \lambda(nm) $ $\pm \dots$\\
-\hline
-&&&\\
-\hline &&&\\ \hline &&&\\ \hline &&&\\ \hline &&&\\ \hline
-\end{tabular}
-}
-
-\vspace{1cm} Calculate average value of Na doublet splitting and its standard deviation. Compare your result
-with the established value of $\Delta \lambda_{Na}=0.598$~nm.
-
-
-\begin{figure}[h]
-\centerline{\epsfig{width=0.8\linewidth,file=fpfig4.eps}} \caption{\label{fpfig4.fig}The Sequence of fringe
-patterns encountered in the course of the FSS measurements. Note false colors: in your experiment the background
-is black, and both sets of rings are bright yellow.}
-\end{figure}
-
-\end{document}
-
-\newpage
-\noindent
-Physics 251 Section:\\
-\hskip 4.5in Name:\\
-\hskip 4.5in Partners:\\
-\vskip 0.5in
-\subsection*{The Fabry-Perot Interferometer}
-1. Briefly describe how the Fabry-Perot interferometer gives and interference
-pattern (in one or two sentences):\\
-\vskip 1.2in
-2. How does the interferometer's resolving power of the fringes depend on the
-reflectivity of plates, r ? That is, does the sharpness of the fringes increase
-or decrease with r ? Consult Melissinos or Professor Kane's Mathview program.
-(The reflectivity of the plates defines the {\it finess} of the cavity).\\
-\vskip 1in.
-
-
-{\large
-\noindent
-Fill in:
-
-The sodium doublet lines arise because an atomic$\underline{\hskip 1.in}$
-is split into two by$\underline{\hskip 1.in}$ coupling.
-The electron has
-intrinsic $\underline{\hskip 1.in}$, like a top, with values of
-$\underline{\hskip 1.in}$ or$\underline{\hskip 1.in}$. Because of
-this, the electron has in intrinsic magnetic$\underline{\hskip 1.in}$  and
-has magnetic
-energy in a magnetic field given by E=$\underline{\hskip 1.in}$
-case comes from the electron's $\underline{\hskip 1.in}$ motion.
-
-}
-
-\subsection*{DATA:}
-{\large
-\begin{tabular}{|p{27mm}|p{27mm}|p{27mm}|p{27mm}|}
-\hline
- $d_1$ $\pm \dots$ & $D _2$ $\pm \dots$& $(d_1-d_2)$ $\pm \dots$&
-$\Delta \lambda(nm) $ $\pm \dots$\\
-\hline
-&&&\\
-\hline
-&&&\\ \hline
-&&&\\ \hline
-&&&\\ \hline
-&&&\\ \hline
-\end{tabular}
-}
-\vskip .2in
-$\Delta \lambda=$\hskip 1.5in nm\\
-\vskip .2in
-Standard deviation= \hskip 1.5in nm
-\newpage
-\end{document}