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Chapter 35: Q29P (page 1076)
Two waves of the same frequency have amplitudes 1.00 and 2.00. They interfere at a point where their phase difference is 60.0°. What is the resultant amplitude?
The resultant amplitude of wave is 2.65 .
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A thin film with index of refraction is placed in one arm of a Michelson interferometer, perpendicular to the optical path. If this causes a shift of 7.0 bright fringes of the pattern produced by light of wavelength , what is the film thickness?
57 through 68 64, 65 59 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 , the type.
Of interference, the thin-layer thickness in nanometres, and the wavelength in nanometres 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?
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.
Reflection by thin layers. In Fig. 35-42, 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.) The waves of rays 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- 2 refers to the indexes of refraction , localid="1663139751503" and , the type of interference, the thin-layer thickness in nanometres, and the wavelength in nanometres 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.
In Fig. 35-48, an airtight chamber of length is placed in one of the arms of a Michelson interferometer. (The glass window on each end of the chamber has negligible thickness.) Light of wavelength l is used. Evacuating the air from the chamber causes a shift of 60 bright fringes. From these data and to six significant figures, find the index of refraction of air at atmospheric pressure.
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