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Chapter 35: Q23P (page 1075)

In Fig. 35-38, sourcesand emit long-range radio waves of wavelength400m , with the phase of the emission from ahead of that from source Bby 90掳 .The distance rA from Ato detector Dis greater than the corresponding distance localid="1663043743889" rBby 100m .What is the phase difference of the waves at D ?

Short Answer

Expert verified

The two waves have a 180掳 phase difference at the detector.

Step by step solution

01

Given data

The wavelength of the radio waves is 位=400m.

The path difference of the two waves to the detector is x=100m.

The initial phase difference of the two waves is 蠒0=90掳.

02

Relation between path difference and phase difference

The phase difference of two waves of a wavelength 位 having path difference x is

蠒=2蟺位x ..... (1)

03

Determining the phase difference at the detector

From equation (I) the phase difference introduced in the path to the detector is,

蠒=2蟺400m脳100m=蟺2=90掳

Thus, the net phase difference at the detector is

蠒D=蠒0+蠒=90掳+90掳=180掳

Hence, the required phase difference is 180掳.

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Most popular questions from this chapter

Two waves of light in air, of wavelength 位=600.0nm, are initially in phase. They then both travel through a layer of plastic as shown in Fig. 35-36, with L1=4.00渭m, L2=3.50渭m, n1=1.40, n2=1.60and. (a) What multiple of 位gives their phase difference after they both have emerged from the layers? (b) If the waves later arrive at some common point with the same amplitude, is their interference fully constructive, fully destructive, intermediate but closer to fully constructive,or intermediate but closer to fully destructive?

Two waves of the same frequency have amplitudes 1.00 and 2.00. They interfere at a point where their phase difference is 60.0掳. What is the resultant amplitude?

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 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.

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 ?

Figure 35-40 shows two isotropic point sources of light (S1and S2) that emit in phase at wavelength 400 nm and at the same amplitude. A detection point P is shown on an x-axis that extends through source S1. The phase difference 蠒between the light arriving at point P from the two sources is to be measured as P is moved along the x axis from x=0 out to x=+鈭�.The results out to xs=10脳10-7m are given in Fig. 35-41. On the way out to +鈭� , what is the greatest value of x at which the light arriving at from S1is exactly out of phase with the light arriving at P from S2?
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