Lecture Notes (When Light Waves Interfere) Intro: - starting in the 1600's there was a debate among scientists as to whether light was made up of waves or particles - Newton (1642-1727) believed that light was composed of fast-moving, tiny particles which he called corpuscles - a Dutch scientist named Christiaan Huygens (1629-1695) proposed a wave model to explain diffraction - by the early 1900's Einstein and other scientists discovered that light has both particle and wave qualities Wave Theory of Light: - Huygens' model is described below
- although the wave model of diffraction was easy to see for water waves, it was not at all intuitive as an explanation for the nature of light - light does not seem to bend around corners as water does around a barrier; furthermore, it was argued that if light was a wave, then we should also be able to see around corners just as we hear around corners - we now know that light does indeed bend around corners, but it is not easy to observe because the wavelength of light is so small - an English physician/physicist named Thomas Young (1773-1829) also believed that many properties of light could be explained in terms of wave theory - Young devised a "double-slit" experiment, which is considered one of the most important experiments ever performed
Young's Double-Slit Experiment: - Young cut a hole in a window shutter, covered it with a thick piece of paper punctured with a tiny pinhole and used a mirror to divert the thin beam that came shining through (the pinhole was used to allow only a small portion of light into the experiment; this ensured that all the light waves were in phase; this is called coherent light) - then he took "a slip of a card, about one-thirtieth of an inch in breadth" and held it edgewise in the path of the beam, dividing it in two (Young split the coherent light beam in two in order to let the light waves interact with one another) - the result was a shadow of alternating light and dark bands, a phenomenon that could be explained if the two beams were interacting like waves
- bright bands appeared where two crests overlapped (constructive interference), reinforcing each other; dark bands marked where a crest lined up with a trough (destructive interference), neutralizing each other; he called the series of alternating light and dark bands interference fringes
- the demonstration was often repeated over the years using a card with two holes to divide the beam; these so-called double-slit experiments became the standard for determining wavelike motion, a fact that was to become especially important a century later when quantum theory began - Young used monochromatic light in this experiment; light of only one color or wavelength, instead of white light; Young used monochromatic light because it produced a diffraction effect of light and dark bands whereas white light would produce the effect of colored bands - Young used the double-slit experiment to make the first precise measurement of the wavelength of light - the diagram below illustrates the analysis of the angles of light formed by double-slit interference S 2 x S 1 L - areas of constructive interference will show up on the screen as bright bands; the areas of destructive interference will appear as dark regions between the bright bands - constructive interference occurs at the red points on the screen, starting with the central band (n = 0) - the first bright band on either side of the central band is called the first-order line and falls at points (n = 1) and (n = -1) - the distance from the point (n = 0) to the point (n = 1) is given the symbol x
- the distance between the slits and the screen is given the symbol L - the distance between the centers of the two slits, S 1 and S 2, is given the symbol d - due to geometrically similar triangles, Young devised the following mathematical relationship: λ xd L - this allows an accurate measurement of the wavelength of light Thin-Film Interference: - colors seen in soap bubbles or due to oily films on water puddles are not caused by dispersion (like a prism) or by absorption (like in a pigment) - instead, colors on a soap bubble are produced by thin-film interference When an incoming ray of light strikes the outer surface of a bubble, part of the light ray is reflected immediately, while the other part is transmitted into the soap film. After reaching the inner surface of the film, this transmitted light ray is reflected back toward the outer surface. When it leaves the bubble, it travels in the same direction as the ray that was immediately reflected and is, therefore, parallel to that ray.
- thin-film interference occurs when light is reflected from two closely spaced surfaces; the colors result from the interference of waves reflected from opposite sides of the film - the specific color is dependent upon the thickness of the film, ranging from black, where the film is thinnest, to red where it is thickest - when the film's thickness is one-quarter the wavelength of the wave in the film, the wave reflected from the back surface returns to the front surface in sync with the first reflected wave - reinforcement occurs at any thickness equal to an odd multiple of the quarter wavelengths Ex. λ/4, 3λ/4, 5λ/4, etc... - different colors have different wavelengths; therefore, as the film thickness changes, the one-quarter wavelength reinforcement will be met at different locations for different colors - thin-film interference also generates the colorful patterns found in the wings of moths and butterflies; the wings themselves don't have much color; it is the presence of scales on the wings that produce the patterns
Butterfly wing magnified about 75 times. - each wing may have hundreds or thousands of scales that contribute to the wing color pattern - when you catch a butterfly or moth you may notice a powder that rubs off of them; this powder is a bunch of tiny scales - colors generated by thin-film interference seem to change depending on our point of view; this is called iridescence (from the Latin word, "iris," meaning rainbow) - iridescent objects include pearls, the transparent wings of houseflies and dragonflies, the scales on butterflies, the feathers of hummingbirds and peacocks, and the eyes of certain animals The eyes of many nocturnal animals contain multilayer structures that improve night vision and produce iridescent metallic like reflections. The metallic like reflection of a photographic flash from the eyes of deer, caused by multiple thin film interference. - iridescence can be caused by interference of light as described above, and also by diffraction of light which will be discussed later