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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° .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° phase difference at the detector.

Step by step solution

01

Given data

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

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

The initial phase difference of the two waves is ϕ0=90°.

02

Relation between path difference and phase difference

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

ϕ=2πλx ..... (1)

03

Determining the phase difference at the detector

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

ϕ=2π400m×100m=π2=90°

Thus, the net phase difference at the detector is

ϕD=ϕ0+ϕ=90°+90°=180°

Hence, the required phase difference is 180°.

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Most popular questions from this chapter

Figure 35-28 shows four situations in which light reflects perpendicularly from a thin film of thickness L sandwiched between much thicker materials. The indexes of refraction are given. In which situations does Eq. 35-36 correspond to the reflections yielding maxima (that is, a bright film).

In the double-slit experiment of Fig. 35-10, the electric fields of the waves arriving at point P are given by

E1=(2.00μV/m)sin[1.26×1015t]E2=(2.00μV/m)sin[1.26×1015t+39.6rad]

Where, timetis in seconds. (a) What is the amplitude of the resultant electric field at point P ? (b) What is the ratio of the intensity IPat point P to the intensity Icenat the center of the interference pattern? (c) Describe where point P is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies. In a phasor diagram of the electric fields, (d) at what rate would the phasors rotate around the origin and (e) what is the angle between the phasors?

In a phasor diagram for any point on the viewing screen for the two slit experiment in Fig 35-10, the resultant wave phasor rotates60.0°in 2.50×10-16 s. What is the wavelength?

A thin film of acetone n=1.25coats a thick glass platen=1.50White light is incident normal to the film. In the reflections, fully destructive interference occurs at 600nmand fully constructive interference at700nm. Calculate the thickness of the acetone film.

Figure 35-29 shows the transmission of light through a thin film in the air by a perpendicular beam (tilted in the figure for clarity). (a) Did rayr3undergo a phase shift due to reflection? (b) In wavelengths, what is the reflection phase shift for rayr4? (c) If the film thickness is L, what is the path length difference between raysr3andr4?
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