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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 wings of tiger beetles (Fig. 36-41) are coloured by interference due to thin cuticle-like layers. In addition, these layers are arranged in patches that are across and produce different colours. The colour you see is a pointillistic mixture of thin-film interference colours that varies with perspective. Approximately what viewing distance from a wing puts you at the limit of resolving the different coloured patches according to Rayleigh’s criterion? Use as the wavelength of light and as the diameter of your pupil.
What is the smallest Bragg angle for x rays of wavelength 30 pm to reflect from reflecting planes spaced 0.30 nm apart in a calcite crystal?
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.
(a) What is the angular separation of two stars if their images are barely resolved by the Thaw refracting telescope at the Allegheny Observatory in Pittsburgh? The lens diameter is 76 cm and its focal length is 14 m. Assume . (b) Find the distance between these barely resolved stars if each of them is 10 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens “errors.”
Assume that the limits of the visible spectrum are arbitrarily chosen as and. Calculate the number of rulings per millimeter of a grating that will spread the first-order spectrum through an angle of
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