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Chapter 36: Q24P (page 1110)

Question:If someone looks at a bright outdoor lamp in otherwise dark surroundings, the lamp appears to be surrounded by bright and dark rings (hence halos) that are actually a circular diffraction pattern as in Fig. 36-10, with the central maximum overlapping the direct light from the lamp. The diffraction is produced by structures within the cornea or lens of the eye (hence entoptic). If the lamp is monochromatic at wavelength 550nm and the first dark ring subtends angular diameter 2.5o in the observer鈥檚 view, what is the (linear) diameter of the structure producing the diffraction?

Short Answer

Expert verified

The diameter of the structure producing the diffraction is 31.0渭m.

Step by step solution

01

Given data

The wavelength of monochromatic light 位=550nm

The angular diameter '蠒'=1.25掳

02

Definition of diffraction effect

When a wave hits a barrier or aperture, numerous events are referred to as diffraction. It is described as the interference or bending of waves through an aperture or around the corners of an obstruction into the geometric shadow of the obstruction or aperture.

03

Determining the diameter of the structure producing the diffraction

So the angle '胃'=2.5/2=1.25掳

The linear diameter 'd'

sin胃=1.22位dd=1.22脳550脳10-9msin1.25掳d=3.07588脳10-5m=31.0渭m

Hence, the diameter is 31.0渭m.

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Most popular questions from this chapter

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.

Light of wavelength 440 nm passes through a double slit, yielding a diffraction pattern whose graph of intensity I versus angular position is shown in Fig. 36-44. Calculate (a) the slit width and (b) the slit separation. (c) Verify the displayed intensities of the m=1and m=2 interference fringes.

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?

Suppose that the central diffraction envelope of a double-slit diffraction pattern contains 11 bright fringes and the first diffraction minima eliminate (are coincident with) bright fringes. How many bright fringes lie between the first and second minima of the diffraction envelope?

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?
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