Lab15_Slides Diffraction Grating

Diffraction Grating A diffraction grating consists of a large number of equally spaced narrow slits or lines. A transmission grating has slits, while a reflection grating has lines that reflect light. The more lines or slits there are, the narrower the peaks. Figure 35-18. Intensity as a function of viewing angle θ (or position on the screen) for (a) two slits, (b) six slits. For a diffraction grating, the number of slits is very large (≈104) and the peaks are narrower still.

Diffraction Grating The maxima of the diffraction pattern are defined by Figure 35-19. Spectra produced by a grating: (a) two wavelengths, 400 nm and 700 nm; (b) white light. The second order will normally be dimmer than the first order. (Higher orders are not shown.) If grating spacing is small enough, the second and higher orders will be missing.

Diffraction Grating Example 35-8: Diffraction grating: lines. Determine the angular positions of the first- and second-order maxima for light of wavelength 400 nm and 700 nm incident on a grating containing 10,000 lines/cm. Solution: The distance between the lines is 1.0 μm. For m = 1, the angles are 23.6° and 44.4°. For m = 2, the angle for 400 nm is 53.1°; the equation for sin θ gives a result greater than 1 for 700 nm, so the second order will not appear.

Diffraction Grating Example 35-9: Spectra overlap. White light containing wavelengths from 400 nm to 750 nm strikes a grating containing 4000 lines/cm. Show that the blue at λ = 450 nm of the third-order spectrum overlaps the red at 700 nm of the second order. Solution: The third-order blue maximum is at sin θ = 0.540; the second-order red maximum is at sin θ = 0.560 (a greater angle), so the spectra will overlap.

Diffraction Grating Conceptual Example 35-10: Compact disk. When you look at the surface of a music CD, you see the colors of a rainbow. (a) Estimate the distance between the curved lines (to be read by the laser). (b) Estimate the distance between lines, noting that a CD contains at most 80 min of music, that it rotates at speeds from 200 to 500 rev/min, and that 2/3 of its 6-cm radius contains the lines. Solution: a. The CD acts as a reflection diffraction grating. In order to see rainbow colors, the distance between the lines must be one or a few optical wavelengths, or 0.5 – 1.5 μm. b. If the CD rotates at an average rate of 350 rev/min, and plays for 80 min, it must contain about 28,000 lines. If these are contained within 4 cm, the spacing between them must be about 1.4 μm, in agreement with the estimate in part (a).

The Spectrometer and Spectroscopy A spectrometer makes accurate measurements of wavelengths using a diffraction grating or prism. Figure 35-21. Spectrometer or spectroscope.

The Spectrometer and Spectroscopy The wavelength can be determined to high accuracy by measuring the angle at which the light is diffracted:

The Spectrometer and Spectroscopy Atoms and molecules can be identified when they are in a thin gas through their characteristic emission lines. Figure 35-22. Line spectra for the gases indicated, and the spectrum from the Sun showing absorption lines

The Spectrometer and Spectroscopy Example 35-11: Hydrogen spectrum. Light emitted by hot hydrogen gas is observed with a spectroscope using a diffraction grating having 1.00 x 104 lines/cm. The spectral lines nearest to the center (0°) are a violet line at 24.2°, a blue line at 25.7°, a blue-green line at 29.1°, and a red line at 41.0° from the center. What are the wavelengths of these spectral lines of hydrogen? Since these are the lines nearest the center, m = 1. Then the wavelengths are 410 nm, 434 nm, 486 nm, and 656 nm.