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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

Figure 35-24a gives intensity lversus position x on the viewing screen for the central portion of a two-slit interference pattern. The other parts of the figure give phasor diagrams for the electric field components of the waves arriving at the screen from the two slits (as in Fig. 35-13a).Which numbered points on the screen bestcorrespond to which phasor diagram?

(a) Figure 1

(b) Figure 2

(c) Figure 3

(d) Figure 4

We wish to coat flat glass (n = 1.50) with a transparent material (n = 1.25) so that reflection of light at wavelength 600 nm is eliminated by interference. What minimum thickness can the coating have to do this?

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 r3 and r4 interfere, 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,n2andn3, the type.

Of interference, the thin-layer thickness L in 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?

A disabled tanker leaks kerosene n=1.20into the Persian Gulf, creating a large slick on top of the watern=1.30). (a) If you are looking straight down from an airplane, while the Sun is overhead, at a region of the slick where its thickness is460nm, for which wavelength(s) of visible light is the reflection brightest because of constructive interference? (b) If you are scuba diving directly under this same region of the slick, for which wavelength(s) of visible light is the transmitted intensity strongest?

A plane wave of monochromatic light is incident normally on a uniform thin film of oil that covers a glass plate. The wavelength of the source can be varied continuously. Fully destructive interference of the reflected light is observed for wavelengths of 500nmand 700nmand for no wavelengths in between. If the index of refraction of the oil is 1.30and that of the glass is 1.50, find the thickness of the oil film.
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