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					Physics Lab                                         Grating Spectrometer                                                         1

Introduction
In this lab, we will familiarize ourselves with a spectrometer: a device for making very precise
measurements of wavelengths of spectral lines. The earliest spectrometers used prisms: by using
Snell’s Law (n1sinθ1 = n2sinθ2), and measuring the angle of incidence and angle of refraction, we
could determine the index of refraction n of our prism, for each colored line. In order to determine
the wavelength of the spectral line, we would need an excellent understanding of the dispersion
characteristics of the glass our prism is made from.
                                                                             Why bother measuring spectral lines?
Instead, we will use a diffraction grating. With this, it is                   Each atom or molecule, when given energy
possible to use the relatively simple grating equation d                      to excite its electrons, is only able to release
sinθ = mλ to determine the wavelength, as long as the                          that energy in certain ways. This produces
                                                                              emission spectra with specific wavelengths,
light hitting the grating is normal to the slits. If the light                 that serve as a “fingerprint” for each type of
hitting the grating is not normal to the slits, we must use a                     molecule. Likewise, if light is passing
more general method, outlined in Appendix A.                                  through a sample of that material, it will tend
                                                                               to absorb light at those same wavelengths,
Procedure                                                                           producing an absorption spectrum.

Part I: Familiarizing yourself with the spectrometer
The spectrometer has many different parts, but one main function:
measuring angles very precisely.
                                                                                             Emission Spectrum of Helium
1.     Review the main parts, as shown in the photograph. Below,
                                                                                           The absorption spectrum of the
       there’s the name of each item, and a brief description of its                       Sun may be found in Figure
       function.                                                                           38.12 in the text.

    Slit: provides a narrow opening through which light can pass, to form sharp
     lines, and provides an opaque surface for our optics to focus on. It is mounted on a fixed arm, to provide a stable
     reference point.
    Collimator: assures that the light from the slit travels parallel to the collimator axis, when it reaches the grating.
    Stage: a place for the grating, which can be adjusted independently of all other parts of the spectrometer.
    Telescope: gathers the light from the grating. It is mounted on a rotating arm, to allow you to measure angles.
    Eyepiece: lenses you look through, to observe the spectral lines. Includes crosshairs for more precise positioning.
    Divided Circle: the inner black circle and/or the outer ring may be free to rotate, independently of other parts. Once
     the grating is properly placed, we will lock the inner circle in place with the stage, while allowing the telescope to
     rotate, locked with the outer ring. Note the two Vernier scales for measuring angle.
Physics Lab                                        Grating Spectrometer                                                   2


2.     Familiarize yourself with the adjustment screws.
    (1) The black screw attached to the Slit adjusts the slit width. A wider slit allows more light through, for brighter
     lines. A narrower slit allows for sharper lines, for more precise angle measurements.
    (2) The screw just below the rear of the Collimator allows you to adjust the Collimator and Slit vertically, so that it
     can be viewed in the Eyepiece.
    (3) The screw just behind the Collimator arm allows you to lock the inner black portion of the Divided Circle to the
     rigid base. This will usually be locked.
    (4) The screw just to the right of the prior screw allows you to make fine adjustments to the inner black portion of
     the Divided Circle. We will not use this screw.
    (5) Just below the Stage are three screws that allow you to keep the Stage level.
    (6) The screw further below the Stage allows you to lock the Stage to the inner black portion of the Divided Circle.
     This will usually remain locked.
    (7) Similar to the Collimator, the Telescope has two adjustment screws on the upper portion of the Telescope arm,
     for small horizontal and vertical adjustments. These may be adjusted during the initial setup, but should not be used
     after that point.
    (8) The end of the Eyepiece itself may be turned, to allow the Slit to be brought into focus.
    (9) Below the Divided Circle are two screws attached to the Telescope arm. The one on the right (when looking
     through the Telescope) allows you to lock the Telescope to the base. You should do this whenever taking a
     measurement. The one on the left allows you to lock the Telescope to the outer ring of the Divided Circle. This
     should remain locked, except during the initial setup.
    (10) At the bottom right of the Telescope arm, nearest the Eyepiece, is a fine adjustment screw that you can use
     when making your final measurements of angle.
3.     Prepare the Stage. First, use the three screws below the Stage (5), to ensure that the Stage is
       roughly level, relative to the Divided Circle. Next, loosen screw (3), and rotate the inner black
       portion of the Divided Circle until both Vernier scales are easily accessible. Tighten screw (3)
       to lock it in place in this position (you should not need to use screw (3) again). Loosen screw
       (6) and rotate the Stage until one of the radial grooves is nearly perpendicular to the Collimator
       axis, then lock the Stage in place.
4.     Prepare the Telescope, Eyepiece, and Slit. Look through the Eyepiece, and adjust the end (8),
       until the crosshairs are in sharp focus. Aim the Telescope at the Slit, and look through the
       Eyepiece. You should see a bright line from the Slit, although it may be out of focus. If you
       can’t, then turn the Telescope a bit to either side, until you can see it. Then, without touching
       the adjustment on the Eyepiece, slide the Eyepiece in and out of the Telescope tube, until both
       the crosshairs and Slit are in sharp focus. Align the crosshairs as well as possible with the Slit.
       If necessary, rotate the Slit to make sure it is vertical. You may choose to use a relatively
       narrow slit, for more precise positioning. Once this is done, lock everything in place, using
       both of the screws on the Telescope (9).
5.     Set the Vernier. Loosen the left screw (9), and rotate the outer ring of the Divided Circle, until
       the Vernier reads exactly zero. Then, lock that screw in place. You should not need to touch
       the left screw (9), through the rest of this lab. You have now set zero to be straight through
       from the Slit to the Eyepiece. To see how to read this type of Vernier, see Appendix B.
Physics Lab                               Grating Spectrometer                                         3

     Note 1: if you have trouble setting the Vernier to exactly zero, you can leave it at any arbitrary
     angle instead, and simply subtract that amount from all of your data values. This is the
     “reference angle” in the data table.
     Note 2: we will not be as precise with the Vernier scale as we can be. A discussion of this is
     explained in Appendix C.
6.   Place the grating on the Stage. Do not touch the surface of the grating: the grating can be
     damaged easily. You want the lines of the grating to be as close to the center of the Stage as
     possible; you can use the three radial grooves to help you align it. Note that, because the stand
     for our gratings cannot be locked in place, and because the grating sits loosely in its stand, it is
     hard to place the grating precisely. So, we will do a much rougher version of the alignment.
     This should still give us rather good agreement with theory, though it is possible to use these
     spectrometers to measure wavelengths with far more precision than we will.
You are now ready to take data with the spectrometer. No screws should be loosened or adjusted
after this point, except for the right screw (9), and the Telescope fine-adjustment screw (10).
Part II: Familiarizing yourself with the light source
1.   Unpack the light source, and Helium tube. DO NOT PLUG THE LIGHT SOURCE IN, until
     you are ready. IMPORTANT: The tubes run on high voltage, which can be extremely
     dangerous. Do not touch the electrodes, and do not touch the lamp while it is in operation.
2.   Insert the Helium tube in the light source (the terminals of the light source are springs, to make
     this process reasonable).
3.   Plug in the light source into a wall outlet, and briefly turn it on, to make sure it is operating
     properly. If so, turn it off. NOTE: The instructions for the spectrum tubes note that they will
     work best and last longest when they are not allowed to get overheated. Therefore, try to leave
     the tubes on for a relatively short amount of time, allowing for a cooldown period in between
     uses. As it says, "Tube life is extended if operation is cyclic for no more than 30 seconds 'on',
     30 seconds 'off', etc.” You may work with longer times, but try to keep them to a minimum.
4.   Place the light source just beyond the Slit. Make sure that the light from the light source
     appears centered in the crosshairs through the Eyepiece.
Part III: Collecting Data
1.   Your first piece of data is straight from the manufacturer. According to them, the gratings
     included with the spectrometer have 300 lines per millimeter. If we were seeking higher
     precision, we would use a reference light source to determine the true grating spacing for each
     grating, but this will be close enough for our purposes.
2.   Loosen the right screw (9), and rotate the Telescope arm to the right until you can see a
     spectral line in the Eyepiece. Nothing on the apparatus should rotate except for the telescope
     arm and the outer ring of the Divided Circle. Continue rotating, so you can see the range of
     spectral lines that you will record. You should see a set for m=1, and m=2. Also rote it to the
     left, to see the m=1 and m=2 lines on the left.
3.   Return to the first spectral line on the right. Get it nearly centered on the crosshairs, and lock
     right screw (9). If any fine adjustment is necessary to align the spectral line with the
     crosshairs, use the Telescope fine-adjustment screw (10). Use the Vernier scale to read the
Physics Lab                                Grating Spectrometer                                      4

     angle of this line. For this line, record the angle, the color, and its brightness in comparison
     with the other lines you see.
4.   Repeat step 3, for as many lines as you can clearly identify on the right (at least 3 from each of
     m=1 and m=2, but no more than 6 from each).
5.   Repeat step 4, for those lines on the left.
Data Table
Reference Angle (if necessary):___________
                                                                Difference Angle
      Color, Side            Order (m)      Measured Angle       (if necessary)      Average Angle

              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
              , Right
              , Left
Physics Lab                              Grating Spectrometer                                       5

Analysis
1.   Calculate the average of your left and right angles for each line (a column for this is included
     in the data table above).
2.   Use the average angle, the order, and the grating spacing in the grating equation, to calculate
     the wavelength in each case. (Note that you only have to show one such calculation, just show
     results for the rest.)
3.   Average the wavelength that you found for that line in the first order, and the same line in the
     second order.
4.   Compare your wavelengths with those in the table at
     right. Try to match your spectral lines with those in the
     table (those with a low relative intensity may have been
     too dim to see).
5.   Calculate the % error in your wavelength values,
     assuming you chose the correct corresponding values
     from the table at right.

Results
Give a table listing your calculated wavelengths from Analysis
step 2 above, the average wavelength from step 3, and the %
error from step 5.
                                                                       Spectral Lines of Helium

Sources of Error
In your sources of error section, be sure you explain which parts of the setup process were most
likely to introduce significant errors, and why.

Conclusions
Be sure to include a fair amount of description in your conclusions. The usual sorts of things in a
conclusion include what you learned, what you’d do differently if you were to do it again, surprises,
comparisons with theory, etc. Since you will be using this apparatus for next week’s lab, it would
also be very helpful for you to explain what you found confusing, and what needs to be addressed
before jumping into data taking next week.

Appendix A: A More General Approach
The following Appendix is copied entirely from
“Memorial University of Newfoundland Department of Physics and Physical Oceanography Physics 3900
Laboratory: The Diffraction Grating”
http://www.physics.mun.ca/~cdeacon/labs/3900/grating_nolaser.pdf
Physics Lab                             Grating Spectrometer                       6




Appendix B: Reading a spectrometer Vernier scale
The following figure is taken from “Visible Spectrometer”
http://www.phys.ufl.edu/courses/phy4803L/group_III/optical_spectroscopy/Spec.pdf
Physics Lab                                 Grating Spectrometer                                             7

Appendix C: Obtaining precise measurements from a spectrometer Vernier scale
In “Use of the AO Spectrometer,” American Optical Corporation, p. 12:
   The heart of the spectrometer is the divided circle from which all angular measurements are obtained.
   The circle is graduated with such accuracy that the error in the position of the various scale marks is much
   less than one minute of arc (the smallest interval readable on the verniers). In spite of years of
   experience, instrument makers have never found it possible to assemble the circle and verniers onto the
   instrument bearings with as great accuracy as can be obtained in the engraving of the scales themselves.
   This minute departure from exact alignment produces small errors which are of opposite sign on opposite
   sides of the circle and are completely eliminated from the average of two opposite vernier readings.
   Recognizing this, Martin says, [1] “It is as well always to take opposite vernier readings for any work
   (students’ experiments or the like). No student should be encouraged to think that two verniers are
   provided on a spectrometer because one may sometimes get too close to the collimator to be conveniently
   readable.”
     [1] L.C. Martin, “Optical Measuring Instruments,” pg. 57.

				
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