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Chapter 35: Q22P (page 1075)

In Fig. 35-37, two isotropic point sources S1 and S2 emit identical light waves in phase at wavelengthλ. The sources lie at separation on an x axis, and a light detector is moved in a circle of large radius around the midpoint between them. It detects 30points of zero intensity, including two on the xaxis, one of them to the left of the sources and the other to the right of the sources. What is the value of dλ?

Short Answer

Expert verified

The value dλ is m+12 where m=0,1,2,3...

Step by step solution

01

Given data

The wavelength the waves emitted from the sources isλ .

The separation between the two sources is d.

02

Path difference for destructive interference

The path difference for destructive interference of two waves having wavelength λ∆L=m+12λm=0,1,2,3... ..... (1)

03

Determining the ratio dλ

At any point on the x axis the path difference between the two waves is

ΔL=x+d-x=d

From equation (1), for destructive interference

d=m+12λdλ=m+12

Hence, the ratio is m+12 where m=0,1,2,3....

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Most popular questions from this chapter

In two experiments, light is to be sent along the two paths shown in Fig. 35-35 by reflecting it from the various flat surfaces shown. In the first experiment, rays 1 and2 are initially in phase and have a wavelength of 620.0nm. In the second experiment, rays 1 and2 are initially in phase and have a wavelength of 496.0nm . What least value of distance L is required such that the 620.0nmwaves emerge from the region exactly in phase but the 496.0nmwaves emerge exactly out of phase?

In Fig. 35-33, two light pulses are sent through layers of plastic with thicknesses of either Lor 2Las shown and indexes of refraction n1=1.55, n2=1.70, n3=1.60, n4=1.45,n5=1.59 , n6=1.65 and n7=1.50. (a) Which pulse travels through the plastic in less time? (b) What multiple of Lcgives the difference in the traversal times of the pulses?


Does the spacing between fringes in a two-slit interference pattern increase, decrease, or stay the same if

(a) the slit separation is increased,

(b) the color of the light is switched from red to blue, and

(c) the whole apparatus is submerged in cooking sherry?

(d) If the slits are illuminated with white light, then at any side maximum, does the blue component or the red component peak closer to the central maximum?

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 λ in nanometers of the light as measured in air. Where λ 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.

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,n2andn3, the type.

Of interference, the thin-layer thickness L in nanometres, and the wavelength λ in nanometres of the light as measured in air.

Where λ 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?
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