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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 位=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 位 having the path difference x is蠒=2蟺位x

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脳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,蠒=2蟺600nm脳300nm=2蟺2=蟺

Hence, the phase difference is 蟺
.

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Most popular questions from this chapter

In Fig. 35-35, two light rays go through different paths by reflecting from the various flat surfaces shown.The light waves have a wavelength of 420.0 nm and are initially in phase. What are the (a) smallest and (b) second smallest value of distance L that will put the waves exactly out of phase as they emerge from the region?
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).

If mirror M2in a Michelson interferometer (fig 35-21) is moved through 0.233mm, a shift of 792 bright fringes occurs. What is the wavelength of the light producing the fringe pattern?

A 600nm-thick soap film n=1.40in air is illuminated with white light in a direction perpendicular to the film. For how many different wavelengths in the 300to 700nm range is there (a) fully constructive interference and (b) fully destructive interference in the reflected light?

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
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