typos fix, thanks Jordan

1 files changed, 21 insertions, 4 deletions

diff --git a/interferometry.tex b/interferometry.tex
index d35f085..507a396 100644
--- a/interferometry.tex
+++ b/interferometry.tex
@@ -18,7 +18,18 @@ The \textbf{Michelson interferometer}, shown in Fig.~\ref{fig1mich.fig}, is base
 \end{figure}
 Such an interferometer was first used by Michelson and Morley in 1887 to determine that electromagnetic waves propagate in vacuum, giving the first strong evidence against the theory of a \textit{luminiferous aether} (a fictitious medium for light wave propagation) and providing insight into the true nature of electromagnetic radiation. Michelson interferometers are widely used in many areas of physics and engineering. At the end of this writeup we describe LIGO, the world's largest Michelson interferometer, designed to measure the gravitational waves and thus test general relativity.
 
-Figure~\ref{fig1mich.fig} shows the traditional setting for a Michelson interferometer. A beamsplitter (a glass plate which is partially silver-coated on the front surface and angled at 45 degrees) splits the laser beam into two parts of equal amplitude. One beam (that was initially transmitted by the beamsplitter) travels to a fixed mirror $M_1$ and back again. One-half of this amplitude is then reflected from the partially-silvered surface and directed at 90 degrees toward the observer (you will use a viewing screen). At the same time the second beam (reflected by the beamsplitter) travels at 90 degrees toward mirror $M_2$ and back. Since this beam never travels through the glass beamsplitter plate, its optical path length is shorter than for the first beam. To compensate for that, it passing twice through a clear glass plate called the compensator plate, that has the same thickness. At the beamsplitter one-half of this light is transmitted to an observer, overlapping with the first beam, and the total amplitude of the light at the screen is a combination of amplitude of  the two beams:
+Figure~\ref{fig1mich.fig} shows the traditional setting for a Michelson
+interferometer. A beamsplitter (a glass plate which is partially
+silver-coated on the front surface and angled at 45 degrees) splits the
+laser beam into two parts of equal amplitude. One beam (that was initially
+transmitted by the beamsplitter) travels to a fixed mirror $M_1$ and back
+again. One-half of this amplitude is then reflected from the
+partially-silvered surface and directed at 90 degrees toward the observer
+(you will use a viewing screen). At the same time the second beam
+(reflected by the beamsplitter) travels at 90 degrees toward mirror $M_2$
+and back. Since this beam never travels through the glass beamsplitter
+plate, its optical path length is shorter than for the first beam. To
+compensate for that, it passes twice through a clear glass plate called the compensator plate, that has the same thickness. At the beamsplitter one-half of this light is transmitted to an observer, overlapping with the first beam, and the total amplitude of the light at the screen is a combination of amplitude of  the two beams:
 \begin{equation}
 \mathbf{E}_{total} =  \mathbf{E}_1 + \mathbf{E}_2 = \frac12 \mathbf{E}_0 + \frac12 \mathbf{E}_0\cos(k\Delta l)
 \end{equation}
@@ -90,7 +101,8 @@ Recalling that  $\cos 2\theta = 2(\cos \theta)^2-1$, we obtain $ \Delta l=2d\cos
 constructively for any angle $\theta_c$ for which $ \Delta l=2d\cos\theta = m\lambda$ ($m$=integer); at the same
 time, two beams traveling at the angle $\theta_d$ interfere destructively when $ \Delta l=2d\cos\theta =
 (m+1/2)\lambda$ ($m$=integer). Because of the symmetry about the normal direction to the mirrors, this will mean
-that interference ( bright and dark fringes) appears in a circular shape. If fringes are not circular, it means
+that interference ( bright and dark fringes) appears in a circular shape.
+If the  fringes are not circular, it means
 simply that the mirrors are not parallel, and additional alignment of the interferometer is required.
 
 \begin{figure}
@@ -110,9 +122,14 @@ $\lambda$, is then given as:
 \lambda = 2(X_2-X_1)/\Delta m.
 \end{equation}
 
-Set up the interferometer as shown in Figure~\ref{fig1mich.fig} using components from the PASCO interferometry kit. A mirrors $M_{1,2}$ are, correspondingly, a movable and an adjustable mirror from the kit. Align the interferometer with a laser beam. Adjust the beam so that it is impinging on the beamsplitter and on the viewing screen. Try to make the beams to hit near the center of all the optics, including both mirrors, the compensator plate and beam splitter. The interferometer has leveling legs which can be adjusted. Align the beams such that they overlap on the viewing screen, and so that the reflected beam is directed back into the laser.  This can be tricky to get right the first time. Be patient, make small changes, think about what you are doing, and get some help from the instructor and TA. 
+Set up the interferometer as shown in Figure~\ref{fig1mich.fig} using
+components from the PASCO interferometry kit. The mirrors $M_{1,2}$ are, correspondingly, a movable and an adjustable mirror from the kit. Align the interferometer with a laser beam. Adjust the beam so that it is impinging on the beamsplitter and on the viewing screen. Try to make the beams to hit near the center of all the optics, including both mirrors, the compensator plate and beam splitter. The interferometer has leveling legs which can be adjusted. Align the beams such that they overlap on the viewing screen, and so that the reflected beam is directed back into the laser.  This can be tricky to get right the first time. Be patient, make small changes, think about what you are doing, and get some help from the instructor and TA. 
 
-Once the interferometer is aligned, insert a convex lens ($f=\unit[18]{mm}$ works well) after the laser to spread out the beam (ideally the laser beam should be pass through the center of the lens to preserve alignment). Adjust the adjustable mirror slightly until you see the interference fringes in the screen. Continue make small adjustments until you see a clear bull's eye circular pattern. \emph{A word of caution: sometimes dust on a mirror or imperfections on optical surfaces may produce similar intensity patterns. True interference disappears if you block one arm of the interferometer. Try it!}
+Once the interferometer is aligned, insert a convex lens ($f=\unit[18]{mm}$
+works well) after the laser to spread out the beam (ideally the laser beam
+should be pass through the center of the lens to preserve alignment).
+Adjust the adjustable mirror slightly until you see the interference
+fringes in the screen. Continue to make small adjustments until you see a clear bull's eye circular pattern. \emph{A word of caution: sometimes dust on a mirror or imperfections on optical surfaces may produce similar intensity patterns. True interference disappears if you block one arm of the interferometer. Try it!}
 
 \textbf{Note}: before starting the measurements, make sure you understand how to read the micrometer properly!
 \begin{figure}[h]