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Chapter 35: Q17P (page 1075)

In Fig. 35-37, two radio frequency point sources S1and S2, separated by distance d=2.0m, are radiating in phase with 位=0.50m. A detector moves in a large circular path around the two sources in a plane containing them. How many maxima does it detect?

Short Answer

Expert verified

The total number of the maxima is 16.

Step by step solution

01

Write the given data from the question

The distance between the slits, d=2m.

The wavelength, 位=0.50m.

02

Determine the formulas to calculate the number of the maxima detect by the detector

The condition for the maxima in Young鈥檚 experiment is given as follows.

dsin胃=m位 鈥︹�� (1)

Here,d is the distance between the slits, 位is the wavelength, mis the order, and胃is the angular separation.

03

Calculate the number of the maxima detect by the detector

Calculate the number of the maxima.

Substitute 0.50mfor 位and 2m for d into equation (1).

2sin胃=m脳0.50sin胃=12脳m脳0.50sin胃=14脳m

Now,

sin胃猢�1m4猢�1.

The value of m can be negative as well as positive. Therefore, m will have -4,-3,-2,-1,0,+1,+2,+3,+4.

For each of the value there is two values of the 胃.

Therefore, one value for -900Cand other for +900C.

Hence, the total number of the maxima is 16.

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Most popular questions from this chapter

Two light rays, initially in phase and with a wavelength of 500 nm, go through different paths by reflecting from the various mirrors shown in Fig. 35-49. (Such a reflection does not itself produce a phase shift.) (a) What least value of distance will put the rays exactly out of phase when they emerge from the region? (Ignore the slight tilt of the path for ray 2.) (b) Repeat the question assuming that the entire apparatus is immersed in a protein solution with an index of refraction of 1.38.

Figure 35-57 shows an optical fiber in which a central platic core of index of refractionn1=1.58-is surrounded by a plastic sheath of index of refractionn2=1.53. Light can travel along different paths within the central core, leading to different travel times through the fiber, resulting in information loss. Consider light that travels directly along the central axis of the fiber and light that is repeatedly reflected at the critical angle along the core-sheath interface, reflecting from side to side as it travels down the central core. If the fiber length is 300 m, what is the difference in the travel times along these two routes?
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 Fig. 35-23, three pulses of light鈥� a, b, and c鈥攐f the same wavelength are sent through layers of plastic having the given indexes of refraction and along the paths indicated. Rank the pulses according to their travel time through the plastic layers, greatest first.

The reflection of perpendicularly incident white light by a soap film in the air has an interference maximum at 600nmand a minimum at role="math" localid="1663024492960" 450nm, with no minimum in between. If n=1.33for the film, what is the film thickness, assumed uniform?
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