## L-8 WAVELENGTH OF LIGHT
To determine the grating space of a plane transmission grating and to use this information to measure wavelengths of spectral lines.
Replica grating, electrical discharge tubes (sodium, mercury, hydrogen, helium, argon, neon), grating holder, power supply and mount for discharge tubes, 2 to 4 K-ohm rheostat. METHOD 1 requires: spectrometer (same kind as used in L-4). METHOD 2 requires: optical bench, scale with slit, light shield.
The experiment consists of two parts: (A) determination of the grating constant (the number of lines per unit length), and (B) use of this grating constant to determine the wavelengths of "unknown" spectral lines. Well-known spectral lines may be used to calculate the grating space, d, from the grating equation:
where λ is the wavelength, θ is the angle of deviation of the spectral line, and d is the grating space, in the units cm/line. The grating constant is defined as 1/d in the units lines/cm. Well-known lines which are reasonably bright and easy to identify are found in the spectra of sodium, mercury, and helium:
These may be taken as "known" or standard lines. Tabulations of wavelengths of other lines of these and other sources will be found in the appendix of this lab manual, and also in the Handbook of Chemistry and Physics. Such tables often list relative brightness of lines for particular types of sources. Relative line brightness depends on the source excitation method, and the temperature, pressure and other conditions in the source, so do not expect the brightness you observe to agree with those in tables.
The spectral orders are then observed with the telescope, and the angular deviation of each spectral line from the zeroth order is directly measured, both left and right. The deviation of a given line in a given order should be the same on the left as it is on the right. If it is not, the grating is not perpendicular to the incident beam, and readjustment is necessary. Small differences are tolerable, and may be treated by finding the difference between the left and right readings and dividing it by two.
(1) (2) (3) (4)
(1) Devise a valid and efficient weighted averaging procedure for using the data for (2) Devise an averaging procedure for calculating one "best" wavelength for each "unknown" line, from the data of each line's deviations in the several orders, left and right. Compare these results with tabulated values.
If you cannot "puzzle" out the answers to these questions by yourself, a little digging in optics books in the library may give you some clues. (1) What would happen if the grating were (2) A grating may be thought of as a regular array of transmitting "slits" with opaque space
between them. Sometimes gratings are made in which the opaque space between the slits is
exactly equal to the slit width. What effect does this have on the observed spectrum? In
particular, which "orders" will be seen and which will not be seen? You must consider the
fact that diffraction and interference are (3) The instructions stated: "If you are using a grating which is mounted on glass, be sure that the side on which the grating is mounted faces (4) It is obviously important to have the grating perpendicular to the collimated light. But what about the placement of the grating on the spectrometer table. What if the grating were, say 1 cm displaced from the center of the table, toward the collimator? How much error would this introduce into your measurements? Be quantitative. Remember that the telescope rotates around the center of the table, and this is also the center of the scale with which you measure angles. (5) Why are the higher orders less bright? Before you answer, consider the fact that some gratings are made in which the second order is brighter than the first order spectrum. How could this be accomplished? (6) Suppose the effective area of the grating were reduced, say by covering all but the center with opaque paper. How would this affect your measurements? Would they be as precise? As accurate? (7) Figure 2 is schematic and simplified. It doesn't show the details of all of the light rays from the slit to the retina. In particular, there's a cone of rays which reaches the eyelens, its diameter limited by the eye's pupil. As you noticed, one must look in a different direction for each of the spectral lines. Show a picture with these details, and discuss how this can introduce both indeterminate and determinate error into the results. (8) If a grating with smaller grating space (larger grating constant) is used, how are the observed angles or spread of the spectra affected? (9) Did you observe any difference in the accuracy of the determination of the wavelengths of the mercury lines for the different order spectra? If so, give an explanation. (10) Is it possible for part of the first-order spectrum to overlap the second-order spectrum? Explain, assuming a continuous spectrum. (11) What is the highest order of the spectrum one can observe from a particular diffraction grating? Justify your answer mathematically. Wave lengths of prominent spectral lines may be found in experiment L-7. Text and line drawings © 1996, 2004 by Donald E. Simanek |