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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 46渭尘and the slit separation is 0.30 mm. How many complete bright fringes appear between the two first-order minima of the diffraction pattern?

Short Answer

Expert verified

The number of complete bright fringes appear between the two first-order minima is 13.

Step by step solution

01

Concept/Significance of double slit experiment

For the first minima in the diffraction pattern,

asin=m1

The angular locations of the bright fringes of the double-slit interference pattern is given by,

dsin=m2 鈥︹ (1)

Here, d is the slit separation, and a is single slit width.

02

Find the number of complete bright fringes appear between the two first-order minima of the diffraction pattern

For the 1st minimam1=1, then rewrite the equation (1) as follows.

localid="1664273954467" asin= 鈥.. (2)

From the equations (2) and (3),

localid="1664273961623" m2=da=0.3010-3m4610-6m=6.52

The seventh maximum occurs at localid="1664273966471" m2=7, this means there are only 6 maximums in each side with a central maximum atlocalid="1664273971604" m2=0.

The number of complete bright fringes will be as follows.

localid="1664273976726" n=7+6+0=13

Therefore, the number of complete bright fringes appear between the two first-order minima is 13.

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Most popular questions from this chapter

A circular obstacle produces the same diffraction pattern as a circular hole of the same diameter (except very near u 0).Airborne water drops are examples of such obstacles. When you see the Moon through suspended water drops, such as in a fog, you intercept the diffraction pattern from many drops. The composite of the central diffraction maxima of those drops forms a white region that surrounds the Moon and may obscure it. Figure 36-43 is a photograph in which the Moon is obscured. There are two faint, colored rings around the Moon (the larger one may be too faint to be seen in your copy of the photograph). The smaller ring is on the outer edge of the central maxima from the drops; the somewhat larger ring is on the outer edge of the smallest of the secondary maxima from the drops (see Fig. 36-10).The color is visible because the rings are adjacent to the diffraction minima (dark rings) in the patterns. (Colors in other parts of the pattern overlap too much to be visible.) (a) What is the color of these rings on the outer edges of the diffraction maxima? (b) The colored ring around the central maxima in Fig. 36-43 has an angular diameter that is 1.35 times the angular diameter of the Moon, which is 0.50掳. Assume that the drops all have about the same diameter. Approximately what is that diameter?

Figure shows a red line and a green line of the same order in the pattern produced by a diffraction grating. If we increased the number of rulings in the grating 鈥 say, by removing tape that had covered the outer half of the rulings 鈥 would (a) the half-widhts of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place

Two emission lines have wavelengths and +, respectively, where< . Show that their angular separation in a grating spectrometer is given approximately by

=(d/m)2-2

where dis the slit separation andm is the order at which the lines are observed? Note that the angular separation is greater in the higher orders than the lower orders.

Visible light is incident perpendicularly on a diffraction grating of 200 rulings/mm. What are the (a) longest, (b) second longest, and (c) third longest wavelengths that can be associated with an intensity maximum at 胃 = 30.0掳?

In conventional television, signals are broadcast from towers to home receivers. Even when a receiver is not in direct view of a tower because of a hill or building, it can still intercept a signal if the signal diffracts enough around the obstacle, into the obstacle鈥檚 鈥渟hadow region.鈥 Previously, television signals had a wavelength of about 50cm, but digital television signals that are transmitted from towers have a wavelength of about 10mm. (a) Did this change in wavelength increase or decrease the diffraction of the signals into the shadow regions of obstacles? Assume that a signal passes through an opening of 5mwidth between two adjacent buildings. What is the angular spread of the central diffraction maximum (out to the first minima) for wavelengths of (b)localid="1664270683913" 50cmand (c) localid="1664270678997" 10mm?

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