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Chapter 35: Q30P (page 1076)
Find the sum y of the following quantities: and
The sum of wave is .
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Transmission through thin layers. In Fig. 35-43, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray (the light does not reflect inside material 2) and (the light reflects twice inside material 2). The waves of and interfere,and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refraction and the type of interference, the thin-layer thickness in nanometers, and the wavelength in nanometers of the light as measured in air. Where is missing, give the wavelength that is in the visible range. Where is missing, give the second least thickness or the third least thickness as indicated.
Transmission through thin layers. In Fig. 35-43, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray (the light does not reflect inside material 2) and (the light reflects twice inside material 2). The waves of andinterfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refractionandthe type of interference, the thin-layer thicknessin nanometers, and the wavelengthin nanometers of the light as measured in air. Whereis missing, give the wavelength that is in the visible range. Whereis missing, give the second least thickness or the third least thickness as indicated.
A thin film, with a thickness ofand with air on both sides, is illuminated with a beam of white light. The beam is perpendicular to the film and consists of the full range of wavelengths for the visible spectrum. In the light reflected by the film, light with a wavelength ofundergoes fully constructive interference. At what wavelength does the reflected light undergo fully destructive interference? (Hint: You must make a reasonable assumption about the index of refraction.
A double-slit arrangement produces interference fringes for sodium light that have an angular separation of . For what wavelength would the angular separation be 10% greater?
Suppose that the two waves in Fig. 35-4 have a wavelength in air. What multiple of gives their phase difference when they emerge if (a) , and ; (b) , , and ; and (c) , , and ? (d) Suppose that in each of these three situations, the waves arrive at a common point (with the same amplitude) after emerging. Rank the situations according to the brightness the waves produce at the common point.
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