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Chapter 36: Q2Q (page 1107)

In a single-slit diffraction experiment, the top and bottom rays through the slit arrive at a certain point on the viewing screen with a path length difference of 4.0 wavelengths. In a phasor representation like those in Fig 36-7, how many overlapping circles does the chain of phasors make?

Short Answer

Expert verified

4 overlapping circles are made.

Step by step solution

01

The given data

Given that in a single-slit diffraction experiment, the top and bottom rays through the slit arrive at a certain point on the viewing screen with a path length difference of 4.0 wavelengths.

02

Concept and Formula used

The dark fringes can be located with the general equation

asinθ=mλfor m=1, 2, 3,...

a is path length difference of slit , andλ is wavelength.

03

Take path length difference to be 4λ

Using the above equation, path length difference is4λ

So role="math" localid="1663147887994" asinθ=4λ

Here, role="math" localid="1663147935739" m=4

This is a point of minimum.

A complete circle for each minima will appear.

Thus, chain of phasors will make 4 overlapping circles.

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Most popular questions from this chapter

The wings of tiger beetles (Fig. 36-41) are coloured by interference due to thin cuticle-like layers. In addition, these layers are arranged in patches that are 60μm across and produce different colours. The colour you see is a pointillistic mixture of thin-film interference colours that varies with perspective. Approximately what viewing distance from a wing puts you at the limit of resolving the different coloured patches according to Rayleigh’s criterion? Use 550nm as the wavelength of light and 3.00nm as the diameter of your pupil.

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.

Figure 36-46 is a graph of intensity versus angular positionfor the diffraction of an x-ray beam by a crystal. The horizontal scale is set byθs=2.00°.The beam consists of two wavelengths, and the spacing between the reflecting planes is0.94nm. What are the (a) shorter and (b) longer wavelengths in the beam?

Figure 36–35 shows the bright fringes that lie within the central diffraction envelope in two double-slit diffraction experiments using the same wavelength of light. Is (a) the slit width a, (b) the slit separation d, and (c) the ratio d/ain experiment B greater than, less than, or the same as those quantities in experiment A?

In an experiment to monitor the Moon’s surface with a light beam, pulsed radiation from a ruby laser (λ= 0.69 µm) was directed to the Moon through a reflecting telescope with a mirror radius of 1.3 m. A reflector on the Moon behaved like a circular flat mirror with radius 10 cm, reflecting the light directly back toward the telescope on Earth. The reflected light was then detected after being brought to a focus by this telescope. Approximately what fraction of the original light energy was picked up by the detector? Assume that for each direction of travel all the energy is in the central diffraction peak.
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