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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 2π. 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 π, then the reverse of angle,

θR=1.22λd

Here, λis the wavelength andd is the slit separation.

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

.

asinθ=±λ

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 diffraction grating illuminated by monochromatic light normal to the grating produces a certain line at angle . (a) What is the product of that line’s half-width and the grating’s resolving power? (b) Evaluate that product for the first order of a grating of slit separation 900 nm in light of wavelength 600 nm.

A diffraction grating 3.00 cm wide produces the second order at 33.0° with light of wavelength 600 nm. What is the total number of lines on the grating?

A beam of light of a single wavelength is incident perpendicularly on a double-slit arrangement, as in Fig. 35-10. The slit widths are each 46μmand the slit separation is 0.30 mm. How many complete bright fringes appear between the two first-order minima of the diffraction pattern?

An x-ray beam of wavelength A undergoes first-order reflection (Bragg law diffraction) from a crystal when its angle of incidence to a crystal face is , and an x-ray beam of wavelength undergoes third-order reflection when its angle of incidence to that face is . Assuming that the two beams reflect from the same family of reflecting planes, find (a) the interplanar spacing and (b) the wavelength A.

A plane wave of wavelength is incident on a slit with a width of 590nm. A thin converging lens of focal length +70cm is placed between the slit and a viewing screen and focuses the light on the screen. (a) How far is the screen from the lens? (b) What is the distance on the screen from the center of the diffraction pattern to the first minimum?
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