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Chapter 35: Q8Q (page 1073)

Figure 35-26 shows two rays of light, of wavelength 600nm, that reflectfrom glass surfaces separated by 150nm. The rays are initially in phase.

(a) What is the path length difference of the rays?

(b) When they have cleared the reflection region, are the rays exactly in phase, exactly out of phase, or in some intermediate state?

Short Answer

Expert verified

(a) The path length difference between the two waves is 300nm.

(b) When the rays have cleared the region, they are exactly out of phase.

Step by step solution

01

Given data: 

The wavelength of the two rays is λ=600nm
.

The thickness of the glass surface is d=300nm.

02

Relation between phase difference and path difference:

The phase difference between two waves of a wavelength λ having the path difference x isϕ=2πλx

03

(a) Determining the path difference of the rays:

The upper wave travels a distance twice the thickness greater than the lower wave. Thus, the path difference isx=2×150nm=300

Therefore, the path difference is 300nm.

04

Determining the phase difference of the rays:

From equation (1), the phase difference between the two waves is,ϕ=2π600nm×300nm=2π2=π

Hence, the phase difference is π
.

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Most popular questions from this chapter

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, n2, and n3, the type of interference, the thin-layer thickness in nanometres, and the wavelength λ in 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.

Ocean waves moving at a speed of 4.0 m/s are approaching a beach at angle θ1=30°to the normal, as shown from above in Fig. 35-55. Suppose the water depth changes abruptly at a certain distance from the beach and the wave speed there drops to 3.0 m/s. (a) Close to the beach, what is the angle θ2between the direction of wave motion and the normal? (Assume the same law of refraction as for light.) (b) Explain why most waves come in normal to a shore even though at large distances they approach at a variety of angles.

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

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 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.

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.
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