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diff --git a/interferometry.tex b/interferometry.tex index 186b4fa..d3ed02b 100644 --- a/interferometry.tex +++ b/interferometry.tex @@ -177,7 +177,18 @@ sodium might be a better calibration source than a HeNe laser, since it has well Without changing the alignment of the interferometer (i.e. without touching any mirrors), remove the focusing lens and carefully place the -interferometer assembly on top of an adjustable-height platform such that it is at the same level as the output of the lamp. Since the light power in this case is much weaker than for a laser, you won't be able to use the viewing screen. You will have to observe the interference looking directly to the output beam - unlike laser radiation, the spontaneous emission of a discharge is not dangerous\footnote{In the ``old days'' beams in high energy physics were aligned using a similar technique. An experimenter would close his eyes and then put his head in a collimated particle beam. Cerenkov radiation caused by particles traversing the experimenter's eyeball is visible as a blue glow or flashes. This is dangerous but various people claim to have done it... when a radiation safety officer isn't around.} However, your eyes will get tired quickly! Placing a diffuser plate in front of the lamp will make the observations easier. Since the interferometer is already aligned, you should see the interference picture. Make small adjustments to the adjustable mirror to make sure you see the center of the bull's eye. +interferometer assembly on top of an adjustable-height platform such that +it is at the same level as the output of the lamp. Since the light power in +this case is much weaker than for a laser, you won't be able to use the +viewing screen. You will have to observe the interference looking directly +to the output beam - unlike laser radiation, the spontaneous emission of a +discharge is not dangerous\footnote{In the ``old days'' beams in high +energy physics were aligned using a similar technique. An experimenter +would close his eyes and then put his head in a collimated particle beam. +Cerenkov radiation caused by particles traversing the experimenter's +eyeball is visible as a blue glow or flashes. This is dangerous but various +people claim to have done it... when a radiation safety officer isn't +around.}. However, your eyes will get tired quickly! Placing a diffuser plate in front of the lamp will make the observations easier. Since the interferometer is already aligned, you should see the interference picture. Make small adjustments to the adjustable mirror to make sure you see the center of the bull's eye. Repeat the same measurements as in the previous part by moving the mirror and counting the number of fringes. Each lab partner should make at least two independent measurements, recording initial and final position of the micrometer, and you should do at least five trials. Calculate the wavelength of the Na light for each trial. Then calculate the average value and its experimental uncertainty. Compare with the expected value of \unit[589]{nm}. @@ -190,22 +201,32 @@ In reality, the Na discharge lamp produces a doublet - two spectral lines that a \includegraphics[width=0.8\linewidth]{./pdf_figs/fpfig3} \caption{\label{fpfig3.fig}The Fabry-Perot Interferometer. For initial alignment the laser and the convex lens are used instead of the Na lamp.} \end{figure} Disassemble the Michelson Interferometer, and assemble the Fabry-Perot interferometer as shown in -Figure~\ref{fpfig3.fig}. First, place the viewing screen behind the two partially-reflecting mirrors ($P1$ and $P2$), and adjust the mirrors such that the multiple reflections on the screen overlap. Then place a convex lens after the laser to spread out the beam, and make small adjustments until you see the concentric circles. Is there any difference between the thickness of the bright lines for two different interferometers? Why? +Figure~\ref{fpfig3.fig}. First, place the viewing screen behind the two +partially-reflecting mirrors ($P1$ and $P2$), and adjust the mirrors such +that the multiple reflections on the screen overlap. Then place a convex +lens after the laser to spread out the beam, and make small adjustments +until you see the concentric circles. Is there any difference between the +thickness of the bright lines for the two different interferometers? Why? Loosen the screw that mounts the movable mirror and change the distance between the mirrors. Realign the interferometer again, and comment on the difference in the interference picture. Can you explain it? -Align the interferometer one more time such that the distance between two mirrors is $1.0 - \unit[1.5]{mm}$, but make sure the mirrors do not touch! +Align the interferometer one more time such that the distance between the two mirrors is $1.0 - \unit[1.5]{mm}$, but make sure the mirrors do not touch! \subsection*{Sodium doublet measurements} \begin{enumerate} -\item Turn off the laser, remove the viewing screen and the lens, and place the interferometer on the adjustable-height platform, or alternatively place the Na lamp on it's side and plan to adjust it's height with books or magazines. With the diffuser sheet in front of the lamp, check that you see the interference fringes when you look directly to the lamp through the interferometer. If necessary, adjust the knobs on the adjustable mirror to get the best fringe pattern. +\item Turn off the laser, remove the viewing screen and the lens, and place + the interferometer on the adjustable-height platform, or + alternatively place the Na lamp on its side and plan to adjust it's + height with books or magazines. With the diffuser sheet in front of + the lamp, check that you see the interference fringes when you look + directly at the lamp through the interferometer. If necessary, adjust the knobs on the adjustable mirror to get the best fringe pattern. \item Because the Na emission consists of two lights at two close wavelengths, the interference picture consists of two sets of rings, one corresponding to fringes of $\lambda_1$, the other to those for $\lambda_2$. Move the mirror back and forth (by rotating - the micrometer) to identify two sets of ring. Notice that they move + the micrometer) to identify two sets of rings. Notice that they move at slightly different rates (due to the wavelength difference). \item Seek the START condition illustrated in Fig.(\ref{fpfig4.fig}), such that all bright fringes are evenly spaced. Note that alternate fringes may be of somewhat different intensities. Practice going through the fringe conditions as shown in Fig.(\ref{fpfig4.fig}) by turning the micrometer and viewing the relative movement of fringes. Do not be surprised if you have to move the micrometer quite a bit to return to the original condition again. @@ -218,7 +239,8 @@ Align the interferometer one more time such that the distance between two mirror \end{enumerate} -We chose the ``START'' condition (the equally spaced two sets of rings) such that for the given distance between two mirrors, $d_1$, the bright fringes of $\lambda_1$ occur at the points of destructive interference for $\lambda_2$. Thus, the bull's eye center ($\theta= 0 $) we can write this down as: +We chose the ``START'' condition (the equally spaced two sets of rings) +such that for the given distance between the two mirrors, $d_1$, the bright fringes of $\lambda_1$ occur at the points of destructive interference for $\lambda_2$. Thus, the bull's eye center ($\theta= 0 $) we can write this down as: \begin{equation} 2d_1=m_1\lambda_1=\left(m_1+n+\frac{1}{2}\right)\lambda_2 @@ -238,17 +260,20 @@ Subtracting the two interference equations, and solving for the distance travele 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: +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)}} +\boxed{\Delta\lambda \approx \frac{\lambda^2}{2(d_2-d_1)}} \end{equation} Use this equation and your experimental measurements to 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] \centering -\includegraphics[width=0.7\linewidth]{./pdf_figs/fpfig4} \caption{\label{fpfig4.fig}The Sequence of fringe patterns encountered in the course of the measurements. Note false colors: in your experiment the background is black, and both sets of rings are bright yellow.} +\includegraphics[width=0.7\linewidth]{./pdf_figs/fpfig4} \caption{\label{fpfig4.fig}The sequence of fringe patterns encountered in the course of the measurements. Note false colors: in your experiment the background is black, and both sets of rings are bright yellow.} \end{figure} \newpage @@ -269,9 +294,9 @@ has been in the observation of the rotation of a binary pulsar (for which the \includegraphics{./pdf_figs/LIGO} \caption{\label{LIGO.fig}For more details see http://www.ligo.caltech.edu/} \end{figure} Laser Interferometry Gravitational-wave Observatory (LIGO) sets the ambitious -goal to direct detection of gravitational wave. The measuring tool in this +goal of the direct detection of a gravitational wave. The measuring tool in this project is a giant Michelson interferometer. Two mirrors hang $2.5$~mi apart, -forming one "arm" of the interferometer, and two more mirrors make a second arm +forming one ``arm'' of the interferometer, and two more mirrors make a second arm perpendicular to the first. Laser light enters the arms through a beam splitter located at the corner of the L, dividing the light between the arms. The light is allowed to bounce between the mirrors repeatedly before it returns to the |