Physics II Lab

Diffraction Grating and Hydrogen Spectra

Text:HRW pp 1006-1011 Gratings
Any other textbook - Bohr Atom
 
OBJECTIVE
  • Use a diffraction grating to measure laser wavelength
  • Use laser to determine the grating pitch of another grating
  • View several spectra using eyeball and video spectrograph (H, Hg, Na,... Filament, Sun)
  •  Derive the equation relating angle and wavelength
  • Fit the hydrogen wavelengths to the Quantum model for the Balmer series

    •
    INTRODUCTION A diffraction grating is an array of uniformly spaced slits, or grooves (~600 to 1000 groovs/mm).  A grating is made by a variety of processes.  The uniformity of groove spacing is a measure of the quality of the grating.  Diffraction gratings are extremely valuable tools for physicists, astronomers, chemists, and biologists as components of spectrometers.  The object of this exercise is to learn the principle of diffraction gratings, to use them to measure wavelengths, and to resolve light into component colors or spectra and analyze the spectra.

    THE PHENOMENON. (Monday)

    1. Predict what happens to a laser beam when the beam is shined through the diffraction grating of about 700 grooves/mm
    2. Take a diffraction grating and shine a laser beam through it and note the results.
    MEASUREMENT OF LASER WAVELENGTH  - Note: 2011, the He-Ne wavelength is given as 633 nm.  Use laser to measure pitch of holographic grating and calaculate uncertainty.

    MEASUREMENT OF WAVELENGTH OF DIODE LASER.
    Use the holographic grating and the pitch measured above to determine the wavelength of a diode laser. Propagate the uncertainties.

    Make a table showing the laser, wavelength, and uncertainty as well as the pitch of the unknown grating and its uncertainty in simple tables.

    HYDROGEN SPECTRA WITH VIDEO SPECTROGRAPH (Tuesday)

    As we learned from the use of the diffraction grating the major use of a diffraction grating is to disperse light into spectra so that the material emitting the light may be analyzed. From the angle of diffraction and the pitch of the grating the wavelength is determined. Any instrument which disperses the light into component colors along a scale for determining wavelength is called a spectrometer. An instrument in which all wavelengths are recorded simultaneously on a film or an electronic photodetector is called a spectrograph. The simplest spectrograph is the "eyeball" spectrograph. The grating is held close to the eye, and the focusing of the eye focuses the image of each wavelength on the retina.

     
    A common type of spectrometer uses a monochromator. Such a device uses an entrance slit, collimator, grating, focuser, exit slit, and a detector. See Figure 2. The gears rotating the grating are connected to a dial which indicates the wavelength. The signal at the detector is a measure of the brightness at the appropriate wavelength. If the grating is connected to a motor, and the detector connected to a chart recorder (or data acquisition system) a spectrum can be obtained.
    A scanning spectrometer is employed in many analytical instruments and has proved invaluable to modern science: chemistry, biology, physics, medicine.... The scanning process is often very slow. Some reactions proceed at a rapid rate so another method is needed. Modern electronic cameras permit recording the whole spectrum at once - a return to the spectrograph of Figure 1, with a camera (complete with lens) replacing the eye.
    PROCEDURE

    1.  Eyeball spectrograph. Examine and sketch the emission spectra from a variety of elements including hydrogen and mercury and two others.

    2.  Video spectrograph. With the video camera, webcam, or digital camera "looking" through a grating (Holographic) aimed at the middle of the spectrum, connect the camera to a color monitor.  See Fig. 1

    .
    Figure 1.  The configuration for a video spectrograph.

    The spectrograph should be set-up so that the 0-order image of the source is outside the field-of-view. Otherwise it over exposes the image. The ruler should be perpendicular to the optical axis of the camera with the 0-end of the ruler even with the discharge tube.   You do not need to digitize images, just use the monitor or the computer screen as a live monitor.
     

    3.  Calibrate for wavelength. In order for the wavelength to be determined, it is essential that the appropriate geometric quantities be measured:

    4.   Measure the positions of each spectral line. Using the video monitor, record the position of each line for the hydrogen spectrum.  This is the effective distance from the source.
    5.    Calculate angles of diffraction.  Calculate the diffraction angle for each colored line.  Use trigonometry with the line's position, xcen, D.  If the angle is on the same side xcen as the source, the angle is to be negative.  See the figure below:

    Figure 2.  The grating configuration.  qr is the angle of diffraction.  Positive in this case.

    6. Calculate the wavelengths.  For each of the diffraction images, calculate the total path difference between adjacent lines

    and compare with the values given by the Balmer series in the textbook.