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Chapter 36: Q113P (page 1115)

An acoustic double-slit system (of slit separation dand slit width ) is driven by two loudspeakers as shown in Fig. 36-51. By use of a variable delay line, the phase of one of the speakers may be varied relative to the other speaker. Describe in detail what changes occur in the double-slit diffraction pattern at large distances as the phase difference between the speakers is varied from zero to 2蟺. Take both interference and diffraction effects into account.

Short Answer

Expert verified

The peaks of the sine shift until splits from maximum central to smaller maxima.

Step by step solution

01

Write the given data from the question.

The slit separation isd .

The slit width isa .

02

Determine the changes occur in the double slit diffraction at large distance.

For the phase difference is 蟺, then the reverse of angle,

胃R=1.22位d

Here, 位is the wavelength andd is the slit separation.

For the phase difference is varied from 0to180掳 , and180掳 to360掳 the peaks of the sine shiftcontinuouslyuntil it spilt the maximum central into smaller maxima and located at the angle胃 , which is given by,

.

asin胃=卤位

Hence the peaks of the sine shift until splits from maximum central to smaller maxima.

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Most popular questions from this chapter

A grating has 600 rulings/mm and is 5.0 mm wide. (a) What is the smallest wavelength interval it can resolve in the third order at ? (b) How many higher orders of maxima can be seen?

(a) What is the angular separation of two stars if their images are barely resolved by the Thaw refracting telescope at the Allegheny Observatory in Pittsburgh? The lens diameter is 76 cm and its focal length is 14 m. Assume 位=550nm. (b) Find the distance between these barely resolved stars if each of them is 10 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens 鈥渆rrors.鈥�

A diffraction grating having is illuminated with a light signal containing only two wavelengths and . The signal in incident perpendicularly on the grating. (a) What is the angular separation between the second order maxima of these two wavelengths? (b) What is the smallest angle at which two of the resulting maxima are superimposed? (c) What is the highest order for which maxima of both wavelengths are present in the diffraction pattern?

Floaters. The floaters you see when viewing a bright, featureless background are diffraction patterns of defects in the vitreous humor that fills most of your eye. Sighting through a pinhole sharpens the diffraction pattern. If you also view a small circular dot, you can approximate the defect鈥檚 size. Assume that the defect diffracts light as a circular aperture does. Adjust the dot鈥檚 distance L from your eye (or eye lens) until the dot and the circle of the first minimum in the diffraction pattern appear to have the same size in your view. That is, until they have the same diameter D'on the retina at distance L'=2cmfrom the front of the eye, as suggested in Fig. 36-42a, where the angles on the two sides of the eye lens are equal. Assume that the wavelength of visible light is 位=550nm. If the dot has diameter D=2.0mmand is distance L=45.0cmfrom the eye and the defect is x=6.0mm in front of the retina (Fig. 36-42b), what is the diameter of the defect?

The D line in the spectrum of sodium is a doublet with wavelengths 589.0and589.6nm. Calculate the minimum number of lines needed in a grating that will resolve this doublet in the second-order spectrum.
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