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A diffraction grating is a group of uniformly spaced grooves or slits, from approximately 600 to 1000 slits per millimeter, that can be produced in a variety of ways. The following is one example of a diffraction grating:
The more uniform the slits or grooves are spaced, the higher the diffraction quality grating. Diffraction gratings are used to identify gases and other chemical substances using a spectrometer. A spectrometer is an instrument that disperses light into component colors of the scale for determining wavelength. A spectrograph is an instrument that can record all wavelengths simultaneously either on film or on an electronic photodetector.
In our lab we learned the principles of diffraction gratings, how they separate light into the separate constituent colors by their spectra, and how to use diffraction gratings to measure wavelengths. The following are pictures of various spectra:
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Hydrogen Spectra
Neon Specta
Helium Spectra
Diffraction gratings were originally made by a ruling machine that used a diamond to cut uniform, micro-graphic scratches into a master ruling. The master ruling was very expensive to make. Therefore, plastic or other materials are poured onto the master ruling creating a replica grating. The following is a schematic illustration of this process:
Since a waveform is a time-varying pattern, the amplitude of the signal at each frequency (cycles per time) can represent the Fourier transform. Since a slit is a spatially changing pattern, another phase for spatial frequency is cycles per length. If we have an array of slits with a square function of postion, the separation between each slit can be represented as d. Small d can be calculated by taking the inverse of the known pitch of the grating. If a wave not a simple sine wave, the wave will contain multiples of the fundamental spatial frequency. The diffraction angle is proportional to the spatial frequency of the slit pattern. The closer the spacing between the slits (the smaller d value is), the greater the spatial frequency (1/d), and the greater the diffraction angle (Sin theta = wavelength/d). The following is an illustration of these concepts:
The more complicated the slit pattern of the diffraction grating, the more spatial frequencies you will get, and each spatial frequency will have a corresponding peak.
We added a known grating of 600 lines per millimeter in front of a laser beam. We then used geometry to measure the angles of deflection of the beam. The following is a diagram of those measurements and the calculations and the formulas used:
Once we studied how diffraction gratings worked, we analyzed hydrogen spectra with a video spectrograph. We examined the different spectrograph of several gases. Through the grating each color appears at a different angle due to the different wavelengths. We measured the wavelength using the video spectrograph. The following is an illustration of the experimental setup:
After looking at the spectra of hydrogen through a diffraction grating, we looked through a grating (600lines/mm) aimed at the middle of the spectra and viewed the results through a color monitor. The zero order of the source was out of view (the hydrogen tube itself) to eliminate the chance for over exposure. The ruler was placed perpendicular to the optical axis of the camera with the zero end of the ruler even with the hydrogen discharge tube. We then measured the following quantities:
Then we measured the position of each spectral line using the video monitor. We then calculated the angles for diffraction for each colored line. The following is a diagram of the grating configuration and the angle of diffraction (theta r):
In order to calculate the wavelengths, we had to calculate the total path difference between the adjacent lines (PD= d(sin theta i + sin theta r)). The following is a chart of my findings and my calculations:
