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Chapter 35: Q19P (page 1075)

Suppose that Young鈥檚 experiment is performed with blue-green light of wavelength 500 nm. The slits are 1.20 mm apart, and the viewing screen is 5.40 m from the slits. How far apart are the bright fringes near the center of the interference pattern?

Short Answer

Expert verified

The bright fringes near the center of the interference pattern are apart of 2.25 mm.

Step by step solution

01

Write the given data from the question

Blue-green light Wavelength, 位=500nm.

The slit separation, d=1.20mm.

The screen distance from the slit, D=5.4m.

02

Determine the formulas to calculate how far apart the bright fringes near the center of the interference pattern

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 how far apart the bright fringes near the center of the interference pattern

The maximum vertical distance from the center of the pattern is given by,

tan胃鈮�sin胃=ymD

Substitute ymDfor sin胃into equation (1).

dymD=m位ym=m位Dd

Substitute 1 for m, 54 m for D, 500 nm for 位and 1.20mmfor d into above equation.

ym=1脳500脳10-9脳5.41.2脳10-3=27脳10-71.2脳10-3=22.5脳10-4m=2.25mm.

Hence the bright fringes near the center of interference pattern are apart of 2.25 mm.

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Most popular questions from this chapter

Suppose that the two waves in Fig. 35-4 have a wavelength 位=500nmin air. What multiple of 位gives their phase difference when they emerge if (a) n1=1.50, n2=16and L=8.50渭m; (b) n1=1.62, n2=1.72, and L=8.50渭m; and (c) n1=1.59, n2=1.79, and L=3.25渭m? (d) Suppose that in each of these three situations, the waves arrive at a common point (with the same amplitude) after emerging. Rank the situations according to the brightness the waves produce at the common point.

In Fig. 35-4, assume that the two light waves, of wavelength 620nm in air, are initially out of phase by 蟺 rad. The indexes of refraction of the media are n1=1.45 andn2=1.65 . What are the (a) smallest and (b) second smallest value of Lthat will put the waves exactly in phase once they pass through the two media?

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?

Transmission through thin layers. In Fig. 35-43, 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.) Part of the light ends up in material 3 as ray r3 (the light does not reflect inside material 2) and r4(the light reflects twice inside material 2). The waves of r3 and r4 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refraction n1, n2, and n3, the type of interference, the thin-layer thickness L in nanometers, and the wavelength 位 in nanometers 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.

In Fig. 35-31, a light wave along ray r1reflects once from a mirror and a light wave along ray r2reflects twice from that same mirror and once from a tiny mirror at distance Lfrom the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength 位and are initially exactly out of phase. What are the (a) smallest (b) second smallest, and (c) third smallest values of L位that result in the final waves being exactly in phase?
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