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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

Figure 35-29 shows the transmission of light through a thin film in the air by a perpendicular beam (tilted in the figure for clarity). (a) Did rayr3undergo a phase shift due to reflection? (b) In wavelengths, what is the reflection phase shift for rayr4? (c) If the film thickness is L, what is the path length difference between raysr3andr4?

In Fig. 35-33, two light pulses are sent through layers of plastic with thicknesses of either Lor 2Las shown and indexes of refraction n1=1.55, n2=1.70, n3=1.60, n4=1.45,n5=1.59 , n6=1.65 and n7=1.50. (a) Which pulse travels through the plastic in less time? (b) What multiple of Lcgives the difference in the traversal times of the pulses?

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 r3(the light does not reflect inside material 2) and r4(the light reflects twice inside material 2). The waves of and interfere, r3and r4here 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 n1,n2and n3the type of interference, the thin-layer thickness Lin nanometers, and the wavelength in nanometers 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.

A thin film with index of refraction n=1.40 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 589nm, what is the film thickness?

A thin film of acetone n=1.25coats a thick glass platen=1.50White light is incident normal to the film. In the reflections, fully destructive interference occurs at 600nmand fully constructive interference at700nm. Calculate the thickness of the acetone film.
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