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Chapter 35: Q22P (page 1075)

In Fig. 35-37, two isotropic point sources S1 and S2 emit identical light waves in phase at wavelength位. 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 d位?

Short Answer

Expert verified

The value d位 is m+12 where m=0,1,2,3...

Step by step solution

01

Given data

The wavelength the waves emitted from the sources is位 .

The separation between the two sources is d.

02

Path difference for destructive interference

The path difference for destructive interference of two waves having wavelength 位鈭�L=m+12位m=0,1,2,3... ..... (1)

03

Determining the ratio dλ

At any point on the x axis the path difference between the two waves is

螖L=x+d-x=d

From equation (1), for destructive interference

d=m+12位d位=m+12

Hence, the ratio is m+12 where m=0,1,2,3....

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Most popular questions from this chapter

In Fig. 35-31, a light wave along ray r1reflects once from a mirror and a light wave along ray r2reflects twice from that same mirror and once from a tiny mirror at distance Lfrom the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength 位and are initially exactly out of phase. What are the (a) smallest (b) second smallest, and (c) third smallest values of L位that result in the final waves being exactly in phase?

A 600nm-thick soap film n=1.40in air is illuminated with white light in a direction perpendicular to the film. For how many different wavelengths in the 300to 700nm range is there (a) fully constructive interference and (b) fully destructive interference in the reflected light?

Light of wavelength 624 nm is incident perpendicularly on a soap film (n = 1.33) suspended in air. What are the (a) least and (b) second least thicknesses of the film for which the reflections from the film undergo fully constructive interference?

In Fig 35-59, an oil drop (n=1.20) floats on the surface of water (n=1.33) and is viewed from overhead when illuminated by sunlight shinning vertically downward and reflected vertically upward. (a) Are the outer (thinnest) regions of the drop bright or dark? The oil film displays several spectra of colors. (b) Move from the rim inward to the third blue band and using a wavelength of 475 nm for blue light, determine the film thickness there. (c) If the oil thickness increases, why do the colors gradually fade and then disappear?

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 r1and r2interfere, 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 n1, n2andn3, the type of interference, the thin-layer thickness Lin nanometres, and the wavelength 位in nanometres of the light as measured in air. Where 位is missing, give the wavelength that is in the visible range. Where Lis missing, give the second least thickness or the third least thickness as indicated.
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