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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

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 r3and r4interfere, 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 n1,n2and n3the type of interference, the thin-layer thickness Lin nanometers, and the wavelength λin nanometers 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.

Figure 35-27a shows the cross-section of a vertical thin film whose width increases downward because gravitation causes slumping. Figure 35-27b is a face-on view of the film, showing four bright (red) interference fringes that result when the film is illuminated with a perpendicular beam of red light. Points in the cross section corresponding to the bright fringes are labeled. In terms of the wavelength of the light inside the film, what is the difference in film thickness between (a) points a and b and (b) points b and d?

In Fig. 35-32a, a beam of light in material 1 is incident on a boundary at an angle of 30o. The extent to which the light is bent due to refraction depends, in part, on the index of refraction n2of material 2. Figure 35-32b gives the angle of refraction θ2versus n2for a range of possible n2values, from na=1.30to nb=1.90. What is the speed of light in material 1?

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 λand are initially exactly out of phase. What are the (a) smallest (b) second smallest, and (c) third smallest values of Lλthat result in the final waves being exactly in phase?

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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