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Chapter 35: Q2Q (page 1072)

If you move from one bright fringe in a two-slit interference pattern to the next one farther out,

(a) does the path length difference ∆Lincrease or decrease and

(b) by how much does it change, in wavelengths λ ?

Short Answer

Expert verified

(a) The path length difference increases if one moves from one bright fringe in a two-slit interference pattern to the next one farther out.

(b) The path length difference is equal to wavelength λ.

Step by step solution

01

Path difference for double slit interference maxima

The path difference of two rays creating a bright fringe of order m for slit separation d, screen distance D and wavelength λ is

∆L=mλ

02

(a) Determining path length difference for two consecutive fringes

From equation (i) the path difference for the mthbright fringe and the m+1th bright fringes are

role="math" localid="1663149650272" ∆Lm=mλ∆Lm+1=m+1λ

Thus the path difference increases.

03

(b) Determining the difference in path length difference for two consecutive fringes

The difference in path length difference of themth bright fringe and the m+1th bright fringes is

∆Lm+1-∆Lm=m+1λ-mλ=λ

The difference is λ.

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Most popular questions from this chapter

In Fig. 35-48, an airtight chamber of length d=5.0cm 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 λ=500nm 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.

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 λin nanometres of the light as measured in air. Where λis 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.

In Fig. 35-45, a broad beam of light of wavelength 683 nm is sent directly downward through the top plate of a pair of glass plates. The plates are 120 mm long, touch at the left end, and are separated by 48.0μm at the right end. The air between the plates acts as a thin film. How many bright fringes will be seen by an observer looking down through the top plate?

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, n2and n3, the type of interference, the thin-layer thickness Lin nanometres, and the wavelength λin nanometres of the light as measured in air. Where λis missing, give the wavelength that is in the visible range. Where localid="1663142040666" Lis missing, give the second least thickness or the third least thickness as indicated

Figure 35-25 shows two sources s1 and s2 that emit radio waves of wavelengthλin all directions. The sources are exactly in phase and are separated by a distance equal to 1.5λ . The vertical broken line is the perpendicular bisector of the distance between the sources.

(a) If we start at the indicated start point and travel along path 1, does the interference produce a maximum all along the path, a minimum all along the path, or alternating maxima and minima? Repeat for

(b) path 2 (along an axis through the sources) and

(c) path 3 (along a perpendicular to that axis).
See all solutions

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