Experiment IX

Diffraction Grating

Objective

(1) To learn to use a diffraction grating spectroscope.

(2) To measure characteristic emission lines of certain elements and identify the source.

Equipment

Spectrometer, replica grating, high voltage source, four spectral emission tubes, connecting wires, handy lamp.

Preliminary Discussion

Interference refers to the interaction of two or more wave trains of light having the same frequency and having a phase difference which remains constant with time, so that they may combine with the result that the energy is not distributed uniformly in space but is a maximum at certain points and a minimum (perhaps zero) at others.

Diffraction is a term applied to problems in which one is concerned with the resultant effect produced by a limited portion of a wave surface. It is also an interference phenomenon. Since in most diffraction problems some light is found within the region of the geometrical shadow, diffraction is sometimes defined as "the bending of light around an obstacle". It should be emphasized, however, that the process by which diffraction effects are produced is going on continuously in the propagation of every wave. Only if a part of the wave is cut off by some obstacle are the effects commonly called "diffraction effects" observed. But, of course, this occurs for every optical instrument.

Suppose that instead of a single slit (used for diffraction studies), or two narrow slits side by side (as used for interference studies), we have a very large number of parallel slits all of the same width, and spaced at regular intervals. Such an arrangement is known as a diffraction grating. The problem of finding the intensity of the light transmitted by the grating then combines the principles of interference and diffraction.

When light from a single source is observed through a single slit, the image which the eye forms is not absolutely sharp; the light bends, or "diffracts" around the slit edges, softening the shadows and often producing maxima and minima of intensity within the geometrical shadow. (When the slit is very small, the pattern of light intensity widens as the slit is narrowed!)

If the light from a single source is observed through two parallel slits, the relative phase of the waves coming from the slits varies with the angle of observation relative to the plane of the slits, since the waves from the slits in general travel different - distances to reach the eye. Indeed, along certain directions in space, the waves will be out of phase and will interfere destructive and zero intensity results along these nodal planes. In between the nodal planes, there will be other directions along which the light waves will interfere constructively and intensity maxima will occur. If many slits are used the conditions for intense maxima (waves from all slits in phase) become more critical, and the maxima sharpen. The distance between maxima, however, is still determined by the distance between slits.

Thus, the distance between maxima depends on the distance between slits and the resolution, the relative sharpness of the maxima, depends on the total number of slits. (Often a grating is characterized by the number of slits per unit length. From this information one can, of course, deduce the distance between the slits.)

Light Source

Atoms when isolated and excited, such as in a low pressure gas discharge, emit light only of characteristic sharply defined wavelengths. You will be supplied with four discharge tubes each containing a gas at low pressure.

The high voltage source used with these tubes can cause an uncomfortable or even dangerous shock so keep your hands away when the power is on. Do not turn on the high voltage without a discharge tube inserted in the power supply socket.

Spectrometer

The spectrometer (See Figure 9.1) consists of three parts: 1. The collimator which consists of a slit of adjustable width together with a lens. The slit is located in the focal plane of the lens, so that the light from the slit is rendered parallel by the lens. 2. The center disk upon which the grating is mounted. 3. The telescope for viewing light from the grating.

Experimental work using the grating spectroscope

I. As with many optical instruments, the spectroscope requires some initial adjustments before the desired measurements can be performed.

1. Focusing the eyepiece. Place a discharge lamp in front of the spectroscope and turn the telescope until it is in line with and pointing directly at the collimator. In this instrument the angular scale will read about 180° in this position. Now slide the eyepiece in and out until a sharp image of the entrance slit is seen. You should at the same time also see an image of a cross-hair with one hair vertical, the other horizontal. If the cross hair and slit are not quite simultaneously in focus, set the eyepiece so the cross hair is sharp. During the course of the experiment you may well find that the eye piece has moved out of adjustment. Simply slide the eyepiece back and forth until the cross hair is sharp again should this problem occur. (Note that if you or your partner wear eyeglasses and these are removed during the observations, then the focus adjustment will be different for the two of you. This is no problem as each observer can quickly adjust the focus for their own eyes.)

2. Aligning the diffraction grating. Place the grating on the center disk so that the long dimension of the glass backing is horizontal and the grating is held erect by the spring clip. The grating slits are located in the plastic film glued to the glass backing and this film should be on the telescope side. Try to get the grating reasonably centered behind the collimator.

Check to make sure that the grating is not too high or low relative to the collimator. If it is, look for the 2 horizontal screws below the disk projecting out from the vertical center post. Loosen the lower screw and slide the ring down. Hold the vertical assembly with one hand and loosen the upper horizontal screw. Move the assembly up or down until the grating is at the proper height. Tighten the upper horizontal screw. Slide the ring up as far as it will go and tighten its screw.

Now the goal is to get the slits on the grating vertical, i.e., parallel with the axis of rotation of the telescope so that the spectral lines you observe later will be properly centered in the telescope. This will require some care and perseverance on your part and possibly some help from your lab instructor. As the first step, try to adjust the disk that holds the grating so that the grating looks vertical and the bottom edge looks horizontal. This adjustment is made with the 3 vertical adjusting screws located under the mounting disk. Now loosen the upper of the two horizontal screws below the disk projecting out from the center post. When this upper screw is loosened you will be able to rotate the whole central assembly until the grating face also looks perpendicular to the collimator. Do this and retighten the screw. You must now be careful not to bump the grating out of position during the rest of the experiment.

II. Calibration of the grating

When the condition ml = d sin q is satisfied for a grating used at normal incidence, the wavelength l will give a maximum in intensity at the angle q as measured from the normal to the grating. In the equation above, d is the spacing between the grating slits and m is an integer called the order number. m = 0 is called the central maximum or zeroth order and corresponds to q = 0 for all values of l. In order to measure the wavelengths of emission lines of several elements, you need to determine the spacing d. This will be done by observing several emission lines of known wavelength from the element Mercury. In particular you should observe 1) a purple line at 4358.3 Angstroms, 2) a green line at 5460.7 Angstroms, 3) two yellow lines, one at 5769.6 Angstroms and the other at 5790.7 Angstroms. (The Angstrom is a common unit of wavelength used in spectroscopy, 1 Angstrom = 0.10 nm.).

Set up the mercury discharge lamp with its slit as close as possible to the slit of the collimator. Observe the central maximum and adjust the collimator slit to a moderate width. Center the vertical cross hair on the slit image and focus the eyepiece. (If you do not get a bright image, move your source back and forth sideways until you do.) The zeroth order angle should be close to 180°. Test your ability to read the angle scale by reading this angle.

Note on reading the angle scale. Each degree on the main scale is divided in half. The upper or Vernier scale is labeled over a range of 30 divisions. Convince yourself that the grating angle is read in degrees plus minutes of arc. When you think you know how to read the scale, ask your lab instructor to check you on this.

Now observe in first order the four mercury lines listed above. Do this on both sides of the central maximum. Before recording any angles on one side be sure that the lines are observable on both sides. If the lines do not fairly well fill the field of view on both sides of the central maximum, i.e., if they are too high or low on one or both sides you have not adjusted the grating well enough and you will have to repeat that adjustment.

When you can observe the lines well on both sides of the central maximum, record the angles of the lines in first order on both sides. If the yellow lines are not resolved (separated) you will need to close the slit more. If when viewing a low intensity line the vertical cross hair cannot be seen, shine light on the grating using the small light bulb.

Unless your grating is poorly adjusted about its vertical axis, i.e., the grating face is not perpendicular to the collimator, you should find that the same wavelength observed on both sides is nearly equidistant in angle from the central maximum. If there is more than about 2 degrees difference, you should rotate your grating about its vertical axis until it is more nearly perpendicular to the collimator.

For each line (wavelength) of Mercury take the difference in the two angles of observation and divide by 2. This gives you the angle to be used in ml = d sin q. Obtain a value for d from your measurements of each of the 4 lines. Decide on a best value for d and estimate its uncertainty.

III. Measurement of l for Unknown Sources

You are now to determine the wavelengths or light generated by three other sources and to identify the sources. Given below are the brightest lines for several elements. Use these to identify your sources. You may see more or fewer lines than listed.

Wavelengths in Angstroms (1 Angstrom = 10-10 m = 0.10 nm)

 Barium Cadmium Calcium Helium Sodium 4554.0 4934.1 5519.1 5535.5 5777.5 5853.7 6063.2 6110.8 6141.7 6498.8 4678.2 4799.9 5085.8 6099.1 6438.5 4226.7 4434.9 4454.8 4527.0 4878.2 6122.2 6439.1 6462.6 6499.6 4387.9 4471.5 4685.8 4921.9 5015.7 5875.6 6678.2 4665.0 4669.0 4979.0 4983.2 5682.8 5688.3 5890.0 5895.9 6154.4 6160.8
 Hydrogen Lithium Mercury Neon Strontium 4102.0 4340.5 4861.3 6562.8 4602.0 4971.9 6103.6 6707.9 4358.3 4916.0 5460.7 5769.6 5790.7 6234.4 6907.5 5341.1 5400.6 5852.5 5881.9 6029.0 6163.6 6266.5 6383.0 6402.3 6506.5 6598.9 4077.7 4215.5 4607.3 4832.1 4872.5 4962.3 6617.3 6878.4
 Wavelength Range Central Color 6100 - 6700 5900 - 6100 5700 - 5900 5000 - 5700 4500 - 5000 4000 - 4500 red orange yellow green blue purple

Balmer Series of Hydrogen

Of all the atoms, Hydrogen has by far the simplest spectrum. Observations of its spectrum prior to the development of quantum theory showed that the wavelengths of the emission (or absorptions) lines of hydrogen could be represented by the formula, l/l = 1.097x107 m-1 (1/n - 1/n) where n1 and n2 are integers with n2 > n1. When n1 is taken as 1 the resulting l for n2 = 2, 3, 4, etc., are in the ultraviolet. However, when n1 = 2 and n2 = 3, 4, 5, etc., some of these lines are in the visible and are members of what is called the Balmer series.

Calculate the wavelengths of the lines in the Balmer series for n2 = 3, 4, 5, and 6. Compare these values with your measurements and with the values given in the table.

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