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Chapter 35: Q35P (page 1076)
We wish to coat flat glass (n = 1.50) with a transparent material (n = 1.25) so that reflection of light at wavelength 600 nm is eliminated by interference. What minimum thickness can the coating have to do this?
The minimum thickness of coating is
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The lens in a Newton’s rings experiment (see problem 75) has diameter 20 mm and radius of curvature . For in air, how many bright rings are produced with the setup (a) in air and
(b) immersed in water ?
In Fig. 35-37, two isotropic point sources S1 and S2 emit identical light waves in phase at wavelength. The sources lie at separation on an x axis, and a light detector is moved in a circle of large radius around the midpoint between them. It detects 30points of zero intensity, including two on the xaxis, one of them to the left of the sources and the other to the right of the sources. What is the value of ?
Figure 35-22 shows two light rays that are initially exactly in phase and that reflect from several glass surfaces. Neglect the slight slant in the path of the light inthe second arrangement.
(a) What is the path length difference of the rays?
In wavelengths,
(b) what should that path length difference equal if the rays are to be exactly out of phase when they emerge, and
(c) what is the smallest value of that will allow that final phase difference?
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.
A thin film of liquid is held in a horizontal circular ring, with air on both sides of the film. A beam of light at wavelength 550 nm is directed perpendicularly onto the film, and the intensity I of its reflection is monitored. Figure 35-47 gives intensity I as a function of time the horizontal scale is set by . The intensity changes because of evaporation from the two sides of the film. Assume that the film is flat and has parallel sides, a radius of , and an index of refraction of 1.40. Also assume that the film’s volume decreases at a constant rate. Find that rate.
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