PHY 242 Laboratory for 12/02/99

Spectroscopy

Analysis of the Continuous Visible Spectrum

The spectroscope attachments for the force tables will be used with a diffraction grating to determine some of the details of our perceptions of the continuous visible spectrum produced by an incandescent source.

The spectroscope consists of a slit which allows a narrow beam of white light to pass through a diffraction grating at the center of the table. The grating will spread the light into a spectrum which can be seen through the pivoting telescope on the opposite side. The wavelength (l ) can be determined from

d sin q = ml

where d is the spacing between the lines of the grating, q is the angle between the perpendicular to the grating and the telescope, and m = 1,2,3, ... (You will have to calculate the spacing from the grating specification giving in lines per inch or lines per mm, etc)

  1. From the first order (m = 1) diffraction, each member of the group will determine the wavelength of their visual threshold at both the violet and the red end of the spectrum. Determine the wavelength at the center of the red/green (yellow), and the blue/violet (cyan) transition bands. Measure the angle for the second order diffraction (m = 2) of the yellow band and verify that it yields the same wavelength as the calculations for first order. In both cases, measure the angle on both sides of the perpendicular and average the results. This will compensate for any misalignment of the apparatus.

  2. Some students may see a wide yellow band while others will see a very narrow band. Some may see a sharp division between green and blue while others will not.

    Color vision starts with the retina, which has three "cone" cells sensitive to a range of frequencies centered on the red, green, and blue regions respectively. The response curves (plots of cell response vs. wavelength) are roughly bell-shaped and overlap to varying extents. Sketch the three response curves for your eyes based upon your calculations above. While the sketches are quantitative, the tails of the red and blue curves and the overlap regions should reflect your data.

The Hydrogen Spectrum

In this section, you will calculate the wavelengths of the three most visible spectral lines in hydrogen. They will be red, green and blue or cyan in appearance. (There may also be a fourth violet line visible.)
  1. Determine the wavelengths of each spectral line using the same technique as in the first section. You need only to use the first order diffraction, but be sure to take angles from both sides to compensate for any misaligment. Estimate an error in your calculation of l from an estimate of the error of the measured angle. Be sure to explain your assumptions and show all calculations.

  2. Using Balmer's technique, find the Balmer constant (R) to fit the equation

    1 / l = R ( 1 / n12 - 1 / n22 )

    First, assume n1 has the value of 1 and calculate R for n2 = 2, 3 and 4 corresponding to each of the three wavelengths you have measured. Do you get the same value for R for each of the three wavelengths? (You may also wish to check n2 = 3, 4 and 5.)

    Repeat the procedure above assuming n2 = 2 and n2 = 3, 4, and 5. Finally, Repeat the procedure assuming n1 = 3 and n2 = 4, 5, and 6.

  3. Which, if any, of the three assumptions for n1 yields a consistent value for R? Is the value consistent within your error?