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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

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?

With a particular grating the sodium doublet (589.00 nm and 589.59 nm) is viewed in the third order at 10掳 to the normal and is barely resolved. Find (a) the grating spacing and (b) the total width of the rulings.

Monochromatic light of wavelength 441nmis incident on a narrow slit. On a screen 2.00maway, the distance between the second diffraction minimum and the central maximum is 1.50cm. (a) Calculate the angle of diffraction role="math" localid="1663145961694" 胃of the second minimum. (b) Find the width of the slit.

Consider a two-dimensional square crystal structure, such as one side of the structure shown in Fig. 36-28a.The largest interplanar spacing of reflecting planes is the unit cell size ao. Calculate and sketch the (a) second largest, (b) third largest, (c) fourth largest, (d) fifth largest, and (e) sixth largest interplanar spacing. (f) Show that your results in (a) through (e) are consistent with the general formula

d=aoh2+k2

where h and k are relatively prime integers (they have no common factor other than unity).

The two headlights of an approaching automobile are 1.4m apart. At what (a) angular separation and (b) maximum distance will the eye resolve them? Assume that the pupil diameter is 5.0mm, and use a wavelength of 550nm for the light. Also assume that diffraction effects alone limit the resolution so that Rayleigh鈥檚 criterion can be applied.
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