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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 鈭�Lincrease or decrease and

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

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 位.

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 位 is

鈭�L=m位

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" 鈭�Lm=m位鈭�Lm+1=m+1位

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

鈭�Lm+1-鈭�Lm=m+1位-m位=位

The difference is 位.

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Most popular questions from this chapter

In Fig. 35-45, a broad beam of light of wavelength 620 nm is sent directly downward through the top plate of a pair of glass plates touching at the left end. The air between the plates acts as a thin film, and an interference pattern can be seen from above the plates. Initially, a dark fringe lies at the left end, a bright fringe lies at the right end, and nine dark fringes lie between those two end fringes. The plates are then very gradually squeezed together at a constant rate to decrease the angle between them. As a result, the fringe at the right side changes between being bright to being dark every 15.0 s.

(a) At what rate is the spacing between the plates at the right end being changed?

(b) By how much has the spacing there changed when both left and right ends have a dark fringe and there are five dark fringes between them?

Figure 35-30 shows three situations in which two rays of sunlight penetrate slightly into and then scatter out of lunar soil. Assume that the rays are initially in phase. In which situation are the associated waves most likely to end up in phase? (Just as the Moon becomes full, its brightness suddenly peaks, becoming 25% greater than its brightness on the nights before and after, because at full Moon we intercept light waves that are scattered by lunar soil back toward the Sun and undergo constructive interference at our eyes. Before astronauts first landed on the Moon, NASA was concerned that backscatter of sunlight from the soil might blind the lunar astronauts if they did not have proper viewing shields on their helmets.)

A thin film, with a thickness of272.7nmand with air on both sides, is illuminated with a beam of white light. The beam is perpendicular to the film and consists of the full range of wavelengths for the visible spectrum. In the light reflected by the film, light with a wavelength of600nmundergoes fully constructive interference. At what wavelength does the reflected light undergo fully destructive interference? (Hint: You must make a reasonable assumption about the index of refraction.

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?

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?
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