CH-27: Interference and the Wave Nature of Light The interference of light waves is responsible for the lovely iridescent colors of the feathers of the bird and the colors in a CD. They are not caused by pigments.

Constructive Interference

Destructive Interference

Coherent Sources Two sources are coherent if the waves they emit maintain a constant phase relation. Effectively, this means that the waves do not shift relative to one another as time passes. Lasers are coherent sources of light, while incandescent light bulbs and fluorescent lamps are incoherent sources. Monochromatic light of wavelength 650 nm was provided by the diode laser used in our wave phenomena lab.

Young's Double-slit Experiment

Path Difference and Fringes

Conditions for Interference Path Difference = d Sin(θ) For Bright Fringes: d Sin(θ) = mλ; m = 0, 1,2,3,… For Dark Fringes: d Sin(θ) = (m+ 1/2)λ; m = 0, 1,2,3,…

Example Problem Red light (l = 664 nm in vacuum) is used in Young's experiment with the slits separated by a distance d = 1.20×10-4 m. The screen in Figure 27.8 is located at a distance from the slits given by L = 2.75 m. Find the distance y on the screen between the central bright fringe and the third-order bright fringe.

Thin-film Interference Consider a thin film of gasoline on water or soap film. A soap bubble is multicolored when viewed in sunlight because of the effects of thin-film interference.

Diffraction Diffraction is the bending of waves around obstacles or the edges of an opening.

The Amount of Diffraction

Diffraction Minima Dark fringes for single-slit diffraction                                    

Diffraction

Double Slit & Grating The bright fringes produced by a diffraction grating are much narrower than those produced by a double slit. Note the three small secondary bright fringes between the principal bright fringes of the grating. For a large number of slits, these secondary fringes become very small.

The Diffraction Grating Diffraction grating is an arrangement consisting of a large number of parallel, closely spaced slits. Gratings with as many as 40 000 slits per centimeter can be made, depending on the production method. In one method a diamond-tipped cutting tool is used to inscribe closely spaced parallel lines on a glass plate, the spaces between the lines serving as the slits.

When sunlight falls on a diffraction grating, a rainbow of colors is produced at each principal maximum (m = 1, 2, …). The central maximum (m = 0), however, is white, due to no diffraction.

A grating spectrometer is used to separate colors

A grating spectroscope

Grating in Nature Not all diffraction gratings are commercially made. Nature also creates diffraction gratings, although these gratings do not look like an array of closely spaced slits. Instead, nature’s gratings are the arrays of regularly spaced atoms that exist in crystalline solids.

Why X-rays? Typically, the atoms in a crystalline solid are separated by distances of about, 1 Å = 1x10-10 m. Crystalline array of atoms act like a grating with roughly this “slit” spacing. The appropriate wavelength for diffraction is found to be in the X-ray region of the EM spectrum.

X-Ray Diffraction of Crystals (a) (b) The X-ray diffraction patterns from (a) crystalline NaCl and (b) crystalline DNA. This image of DNA was obtained by Rosalind Franklin in 1953, the year in which Watson and Crick discovered DNA’s structure. (a: Courtesy Edwin Jones, University of South Carolina; b: © Omikron/Photo Researchers)