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Chapter 27: Q14PE (page 997)
Find the largest wavelength of light falling on double slits separated by 1.20 µm for which there is a first-order maximum. Is this in the visible part of the spectrum?
The largest wavelength of light falls on double slits separated and this is beyond the visible spectrum.
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The limit to the eye’s acuity is actually related to difdfraction by the pupil.
(a) What is the angle between two just-resolvable points of light for a \(3.00 - mm\)-diameter pupil, assuming an average wavelength of \(550{\rm{ }}nm\)?
(b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are \(1.30{\rm{ }}m\) apart?
(c) What is the distance between two just-resolvable points held at an arm’s length \(\left( {0.800{\rm{ }}m} \right)\) from your eye?
(d) How does your answer to (c) compare to details you normally observe in everyday circumstances?
(a) What visible wavelength has its fourth-order maximum at an angle ofwhen projected on a 25,000 -line-per-centimeter diffraction grating? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
The analysis shown in the figure below also applies to diffraction gratings with lines separated by a distance . What is the distance between fringes produced by a diffraction grating having 125 lines per centimeter for light, if the screen is away?
The distance between adjacent fringes is, assuming the slit separation d is large compared with.
Consider difdfraction limits for an electromagnetic wave interacting with a circular object. Construct a problem in which you calculate the limit of angular resolution with a device, using this circular object (such as a lens, mirror, or antenna) to make observations. Also calculate the limit to spatial resolution (such as the size of features observable on the Moon) for observations at a specific distance from the device. Among the things to be considered are the wavelength of electromagnetic radiation used, the size of the circular object, and the distance to the system or phenomenon being observed
(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm when they fall upon a single slit of width 2.00 µm. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.
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