General Announcements

(Posted Friday, November 19, 1999)

Pick up a Worksheet and a Lab Evaluation Form before you start the lab.  There is no report for Lab #7 and you do not have to turn in your notebooks either.  Simply fill out the Worksheet as you work through the lab and hand it in to your TA when you are finished. 

We would also appreciate your feedback on the course since we plan to make some significant changes over the next year.  So, before you leave, please fill out the Lab Evaluation Form and slip it into the envelope provided for your Lab Section/TA.  Do not write your name on this form since we want to insure that your comments are kept confidential.

MAKE-UP LABS  Make-up labs are available to students who had a legitimate excuse for missing a lab during the semester. All make-up labs are scheduled for Monday, December 6 from 9:00 AM – noon.  Diana Driscoll will be the TA for the make-ups.  All make-up reports are due the same day as the lab, Monday, Dec. 6 by 6:00 PM.   If you were entitled to a make-up, you were supposed to request it within 2 weeks of the missed lab.  To be certain we set up enough stations, please see Prof. Chottiner to confirm your appointment for a make-up lab.

IMPORTANT NOTICE:  If your lab meets in even weeks (Wednesday Nov. 10 and Thursday Nov. 11), then the due date for your Lab #6 is not 'one week before your next lab'  but is instead one week following your Lab #6 (Wednesday, Nov. 17 or Thursday Nov. 18) by the time that Rockefeller is locked.   There are no E&M  labs scheduled for the week of Thanksgiving vacation;  students scheduled for even weeks will work on Lab #7 the week after Thanksgiving.

 

Lab #7 : WAVES

WAVES-A is set up in Roc 402 while WAVES-B is set up in Roc 403.  You will switch labs roughly halfway through the period.

WAVES-A – Roc 402

 

Each laser is being used to operate two stations.  Don't touch the lasers, beam splitters or mirrors that make this possible.  The only part of the optics that you need to change are the 2"x2" slides mounted in a holder with a binder clip.  You should have three such slides at your station; single slit, double slit and diffraction grating.  When you mount these slides in the holder, angle them  10-20 degrees from vertical so that the reflected beam will not strike anyone in the face.  Be careful as you move around the lab.  Don't bend over a table or in any way let a beam strike you in the eye!

 

Section D.1.  You will need to consider Eq. 6,   wsinq = ml, as well as the approximation that for small angles, sinq » tanq = y/D, so that y = mlD/w.  To find l, simply plot y vs. m, with m = ±1, 2, 3, etc. for successive minima (values of y) and calculate l from the slope of this line.

Section D.2.  Note that the first questions posed on the worksheet are for the single slit aspect of the interference pattern and you should analyze this just as you did in section D.1.  For the second set of questions about the fine structure due to two slit interference, you will need to consider Eq. 5,   y/D  = ml/d.   You do not need to plot your data as a function of m or make a linear fit.  Simply plug your in value of Dy  for Dm = 1.  You know D and d so you can easily calculate l. 

Section D.3.  You are asked to take four measurements; first and second order maxima on the left and right sides (or + and - sides).  You must apply Eq. 3 separately to each of these measurements and then average your four values of l to obtain your best estimate of its value.  When Eq. 3 was derived, the term d referred to the spacing between slits.  To use this equation for the diffraction grating, you need to set d equal to the spacing between lines on the grating.  The number of lines per inch is given to you and the conversion factor to metric units is 2.54 cm/inch.  You should be able to calculate the metric spacing between lines from this information. 

Do not attempt to analyze errors for section D.3!  A proper error analysis is too difficult to carry out in class.  For example, you should start by finding the derivative of tanq  (it's sec2q) and the algebra is a bit messy.  You may just leave empty each of the blanks left for error estimates of l although you should go ahead and fill out the error estimates of the magnitude of y.

WAVES-B – Roc 403

There are several different experiments that must be done in this lab and there are not enough stations for everyone to do each part at the same time.  Start working on the experiment set up at the station where you are sitting and then move on to the other experiments as they become available.

There are 4 stations set up to do polarization with MPLI, Section C.  There are 3 stations set up for the Michelson Interferometer, Section E.  The Brewster's angle measurements of Section D are done in the hallway; 2 groups can work on this simultaneously.  The observations described in Sections F.1 and F.2 may be carried out at any time by any single group but are probably best done  before or after the Brewster's angle section.

Section C.3.  If MPLI has been turned off and you are restarting it, you may need to turn off Channels B and C and set the y-axis to autoscale.

Rather than using the cursor to read the values in each plateau, a better procedure is to use the mouse to define a region within each plateau and then use the MPLI ANALYSIS/STATISTICS capability to get an average value with error estimate.

Section C.4.  The equation that you need does not exist on the P-drive and in any case it is easier to type it in directly.  Type in the equation as:     P1 + P2*(cos(x + P3))^2 . (You can even cut it from here and paste it into Origin.) It should be obvious how  P1, P2 & P3 relate to the variables used in Equation 1. Before proceeding with your fit, it is important to decide whether you will use radians or degrees for your units of angle.  Most likely you will have taken and plotted your data in degrees. To force Origin to use a particular unit, go to TOOLS/OPTIONS/NUMERIC FORMAT and select DEGREES or RADIANS.

 If you don't remember how to carry out a least squares fit in Origin, the procedure is:

- Plot your data

- Select ANALYSIS/ NONLINEAR CURVE FIT

- Press the MORE button if necessary to see all the options

- Pick FUNCTION and NEW

- Set FORM = EXPRESSION, No. PARAMETERS = 3 and type it in.  P1 + P2*(cos(x + P3))^2

- Go to ACTION/FIT, answering YES to the question about using the ACTIVE DATASET and type in your initial estimates of the fitting variables.  These should be easy to estimate.  Note that the cos2 term just varies from 0 to 1.  So P1 describes the offset of the base of your curve from the x-axis while P2 describes the amplitude of the variations.  P3 is the phase which shifts the curve left or right.  P3 will be close to zero if your curve looks like a cos function.  However, we suggest that you never enter 0 as a parameter as this can lead to divide by zero errors.  Just enter a small number, say 0.01.

-  Press 1 or 10 ITER (iterations) and pray that Origin's fitting routine works.  If the initial fit is far off, the problem may be with the values you used for initializing the three variables.  You can check this by going to ACTION/SIMULATE, entering your values and telling the program to CREATE CURVE based on your values.  You may also notice that Origin draws a jagged line on the screen rather than a smooth curve.  This will usually, but not always, be corrected by the final step below.

- When you are satisfied with the fit, press DONE.  If the line plotted on the screen is still jagged, consult your TA for help or try the following.  Double-click on the line and replace the line option with a spline.  This is cheating a little to make the curve look good without fixing the underlying problem, but it doesn't effect the numerical results of the non-linear fit which are still fine.

Section D.3.  When you calculate n', be certain to use the angle with respect to the normal, as shown in Fig. 2, and not the angle with respect to the table. q = tan-1(L/H) and not (H/L).   n for vacuum is equal to 1 and n' for any material must be greater than 1.   

You may find it interesting that by measuring n' you are actually measuring the speed of light in the floor wax.  The speed of light in any media is equal to the speed in vacuum divided by the index of refraction.  So if you find that n' = 1.5, for example, then the speed of light =  c/1.5  or  2.0 x 108 m/sec.  If you find out that n' is less than 1, then you are saying that light moves faster in the floor wax than it does in vacuum; in other words, you made a mistake.   n' is also tells you the magnitude of the refraction or bending  that occurs as light moves across an interface; say from water into air. 

Section E.2.   DO NOT TOUCH ANY PART OF THE MICHELSON INTERFEROMETER APPARATUS other than the micrometer and DO NOT MOVE THE LASER OR INTERFEROMETER SUPPORT!  It is easy to screw up the instrument alignment and time-consuming to get it working again.  If it doesn't already have power, you can turn the laser on by turning on the Elenco power supply.  The laser works from the fixed 5 V output, so you don't have to adjust the voltage of the Elenco, just turn it on.

Section E.3  The equation that you need to calculate l from the Michelson Interferometer data is l = 2d/N where the 2 comes from the fact that the path is traveled by the light going and coming from the moving mirror, d is the distance you move the mirror with the micrometer and N is the number of fringes that you count, which should be about N = 50.