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Chapter 36: Q60P (page 1113)
The D line in the spectrum of sodium is a doublet with wavelengths . Calculate the minimum number of lines needed in a grating that will resolve this doublet in the second-order spectrum.
The minimum number of lines needed in the grating, to resolve the douplet, is 491.
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The two headlights of an approaching automobile are apart. At what (a) angular separation and (b) maximum distance will the eye resolve them? Assume that the pupil diameter is , and use a wavelength of for the light. Also assume that diffraction effects alone limit the resolution so that Rayleigh’s criterion can be applied.
In Fig. 36-48, let a beam of x-rays of wavelength 0.125 nm be incident on an NaCl crystal at angle θ = 45.0° to the top face of the crystal and a family of reflecting planes. Let the reflecting planes have separation d = 0.252 nm. The crystal is turned through angle ϕ around an axis perpendicular to the plane of the page until these reflecting planes give diffraction maxima. What are the (a) smaller and (b) larger value of ϕ if the crystal is turned clockwise and the (c) smaller and (d) larger value of ϕ if it is turned counter-clockwise
For three experiments, Fig. 36-31 gives versus angle in one-slit diffraction using light of wavelength 500 nm. Rank the experiments according to (a) the slit widths and (b) the total number of diffraction minima in the pattern, greatest first.
The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as across (see Google Earth), and the telescopes on military surveillance satellites reportedly can resolve objects as small as across. Assume first that object resolution is determined entirely by Rayleigh’s criterion and is not degraded by turbulence in the atmosphere. Also assume that the satellites are at a typical altitude of and that the wavelength of visible light is role="math" localid="1663028559183" . What would be the required diameter of the telescope aperture for (a) role="math" localid="1663028596951" resolution and (b) role="math" localid="1663028635287" resolution? (c) Now, considering that turbulence is certain to degrade resolution and that the aperture diameter of the Hubble Space Telescope is role="math" localid="1663028673584" , what can you say about the answer to (b) and about how the military surveillance resolutions are accomplished?
A source containing a mixture of hydrogen and deuterium atoms emits red light at two wavelengths whose mean is 656.3 nm and whose separation is 0.180 nm. Find the minimum number of lines needed in a diffraction grating that can resolve these lines in the first order.
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