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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.
A thin film of acetone coats a thick glass plateWhite light is incident normal to the film. In the reflections, fully destructive interference occurs at and fully constructive interference at. Calculate the thickness of the acetone film.
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.
In Fig, monochromatic light of wavelength diffracts through narrow slit S in an otherwise opaque screen. On the other side, a plane mirror is perpendicular to the screen and a distance h from the slit. A viewing screen A is a distance much greater than h. (Because it sits in a plane through the focal point of the lens, screen A is effectively very distant. The lens plays no other role in the experiment and can otherwise be neglected.) Light travels from the slit directly to A interferes with light from the slit that reflects from the mirror to A. The reflection causes a half-wavelength phase shift. (a) Is the fringe that corresponds to a zero path length difference bright or dark? Find expressions (like Eqs. 35-14 and 35-16) that locate (b) the bright fringes and (c) the dark fringes in the interference pattern. (Hint: Consider the image of S produced by the minor as seen from a point on the viewing screen, and then consider Young’s two-slit interference.)
Figure 35-26 shows two rays of light, of wavelength 600nm, that reflectfrom glass surfaces separated by 150nm. The rays are initially in phase.
(a) What is the path length difference of the rays?
(b) When they have cleared the reflection region, are the rays exactly in phase, exactly out of phase, or in some intermediate state?
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