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Unformatted text preview: Experiment 5
Diffraction Gratings Procedure Outline Introduction This week’s lab covers diffraction gratings. 1 Grating Equation [J 85 W Chap. 17] Procedure In the ﬁrst section, you will align the spectrometer. The spectrometer has
three major components: (1) A collimator, with a slit at the focal point of a convex lens;
the lens will produce a beam of parallel light i.e. collimate the light passed by the slit. (2)
A table on which the grating is located. (3) A telescope which can be rotated about the central axis. It has a vernier scale marked in degrees and minutes. The telescope is aligned
ﬁrst. 0 Check to make sure that the cross—hairs in the telescope are in focus. If they are not,
move the eyepiece until they are. Once set, the eyepiece should not be moved. 0 Now you can focus the telescope for inﬁnity using auto-collimation. Take the small
metal mirror and place it on the spectrometer table. a The eyepiece has an illuminator on it. Make sure that this is on and that light is
shining into the telescope. o Rotate the mirror until the light is reﬂected back into the telescope. You should be
able to see the light in the telescope. If the telescope is still in focus, you will see an
image of the cross-hairs. If not, you will need to adjust the telescope. Do not move
the eyepiece to do this; if you do, the cross—hairs will be out of focus. There is a screw
on the side of the teleseope which locks the objective into place. Loosen the screw
and move the eyepiece tube until the reﬂected image of the cross-hairs is in focus,
then tighten the screw again. 0 Next check the adjustment of the collimator. Remove the mirror and point the tele—
scope directly at the collimator. 0 Place a hydrogen lamp directly behind the slits. Move it around a little until you ﬁnd
the spot where the most light comes through the slit. 0 The slit should be in focus. If it is not, adjust the distance between the slit and the
collimating lens. 0 Set the telescope at 180 degrees. Do this by setting the cross-hair on the image of the
slit. Record the spectrometer reading. You need this number as a correction since
the collimator is not guaranteed to be at 180 degrees. Optics 350/450 Laboratory Procedure Outline 5 — September 18, 2007 2 0 Turn the hydrogen lamp off and turn the eyepiece illuminator on. Place the grating
on the spectrometer table and rotate until you can see the cross—hairs reflected from
the grating. a Set the image so that the cross—hairs are aligned. This is to insure that the grating is
perpendicular to the axis (zero angle of incidence). 0 Now set the scale below the grating to read zero and turn the hydrogen lamp back
on. 0 Next ﬁnd the spectral lines of hydrogen and measure the angle of diffraction with the
telescope. Do this on both sides of the spectrometer. 0 Don’t forget to check the accuracy of your angle measurements. How repeatable are
your settings? 0 Next ﬁnd the spectral lines of helium and the measure them.
0 Measure the third order lines on one side. 0 Now rotate the grating to 15 degrees and measure the ﬁrst order lines on both sides.
How accurately can you set this angle? 0 Measure the second order lines on one side. 0 Now rotate the grating to 30 degrees and measure the ﬁrst order lines on both sides.
0 Finally rotate the grating to 45 degrees and measure the first order lines on one side.
0 Record the number of lines per centimeter of the grating. 0 Calculate the wavelengths for each observation. Sign Convention: Negative diffraction orders are to the left and positive diffraction
orders are to the right. Negative angles of incidence are clockwise on the prism table scale
(eg. a 350 reading corresponds to a —-10 angle of incidence). Positive angles of incidence
are counter-clockwise on the scale. Analysis Compare the angles measured to theory. The grating equation is: d,[sin(z') + sin(9)] = mA, where d is the spacing of the grating (inverse of lines/cm), i is the angle of incidence, 6 is
the diffraction angle, m is the diffraction order, and A is the wavelength. 2 Resolving Power Procedure
0 Replace the hydrogen lamp with the sodium lamp. 0 Reset the grating for i = 0. Optics 350/450 Laboratory Procedure Outline 5 —— September 18, 2007 3 0 Observe the yellow sodium line in several orders. Is the doublet resolved? Remember you can also change the incident angle 1' to see higher orders. 0 Record the diameter of the lens on the collimator. Analysis Calculate the resolving power of the grating using A
m—mN where m is the diﬁraction order, and N is the total number of slits illuminated. Calculate
N from the diameter of the collimator lens and the number of lines per centimeter of the
grating. Should the sodium doublet be resolved for a given order? Is it resolved? What is the doublet splitting in mm for each order? What is the average splitting? What is the
standard deviation? 3 Observation 0 Replace the grating that you have been using with a 500 lines per cm grating. This
grating will show many diffraction orders. 0 Place the hydrogen lamp back in front of the spectrometer. 0 Record the ﬁrst ﬁve or more orders. Record the order of the lines (ie. blue, green,
red, blue, etc.) and plot spectrum vs. wavelength. 0 Match each spectrum with a diffraction order. 0 Match your recorded wavelengths with tabulated wavelengths. Calculate the stan-
dard deviation for a given order. Plot the standard deviation vs. the order number.
Comment on how the graph behaves. ...
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- Fall '08