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Review: Two speakers, one placed at some distance behind the other, are each generating a 245-Hz sound wave (and these two waves are exactly out of phase with one another when they emerge from their respective speakers). Assuming vsound is 343 m/s, which of these separation distances will produce perfectly destructive interference for a listener standing in front of them? 1. 0.700 m 2. 2.10 m 3. 4.20 m 4. 7.70 m 5. More than one of the above. 6. None of the above OSU PH 212, Before Class #24
Review: Two speakers, one placed at some distance behind the other, are each generating a 245-Hz sound wave (and these two waves are exactly out of phase with one another when they emerge from their respective speakers). Assuming vsound is 343 m/s, which of these separation distances will produce perfectly destructive interference for a listener standing in front of them? 1. 0.700 m 2. 2.10 m 3.4.20 m 4. 7.70 m 5. More than one of the above. 6. None of the above (See After class 24 for the full solution.) OSU PH 212, Before Class #24
Thin-Film Interference Everyone has seen the colorful sheens in soap bubbles or layers of oil on water. This, too, is a consequence of the wave nature of light and interference. In this case, the interference is due not only to dif-ferent distances traveled but also to phase (timing) changes that may occur during reflection at the boundaries between different materials (e.g. oil and water). What’s happening? (Read or review pages 472-474, also.) Knowing the wavelengths of the incident light, we can deduce the thickness of thin films by observing the colors that are enhanced or obscured. (We can also use this phenomenon to protect and enhance the optics of lenses.) OSU PH 212, Before Class #24
Key points about thin-film interference: The number of wavelengths that fit into a path length difference depends on the wavelength of the light in that medium. (Recall that light slows down in more refractive materials. It maintains its frequency but decreases its speed—and therefore decreases its wavelength.) When light is incident from a faster medium onto a slower one (i.e. from a lower to a higher index of refraction), any reflection that happens at the boundary will cause a timing delay of half a period—and therefore a phase delay of p radians. There is no such phase change (no timing delay) when the light reflects at a boundary while incident from a slower medium onto a faster one. OSU PH 212, Before Class #24
Here is a summary of what happens when light whose wavelength in a vacuum is lvacuum is incident normally (at an incidence angle of 0°), from a refractive index noriginal onto a film of thickness (t > 0) and refractive index nfilm, a film which covers another material of refractive index nsubstrate: # of Phase ShiftsCondition for C.I.Condition for D.I. 0 or 2 2t = mlfilm 2t = (m+1/2)lfilm 1 2t = (m+1/2)lfilm 2t = mlfilm _______________________________________________________ m is a non-negative integer value—which may be 0 so long as t > 0. lfilm = lvacuum/nfilm A phase shift occurs whenever light refracts from a faster into a slower material. OSU PH 212, Before Class #24
Try an example: What is the thinnest film of MgF2 (n = 1.39) that you could coat onto glass (n = 1.50) that results in a strong reflection of normally incident orange light with a wavelength of 600 nm? (see After class 24 for the solution.) OSU PH 212, Before Class #24
