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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

Figure 35-22 shows two light rays that are initially exactly in phase and that reflect from several glass surfaces. Neglect the slight slant in the path of the light inthe second arrangement.

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

In wavelengthsλ,

(b) what should that path length difference equal if the rays are to be exactly out of phase when they emerge, and

(c) what is the smallest value of that will allow that final phase difference?

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