This doubling of the original prism increases the angular dispersion of the assembly, and also has the useful property that the centre wavelength is refracted back into the direct line of the entrance beam.
12.
Where the first differential refers to the angular dispersion from the grating and the second differential refers to the overall dispersion from the multiple-prism beam expander ( given in the section above ).
13.
Since that refractive index varies with wavelength, it follows that the angle that the light is refracted by will also vary with wavelength, causing an angular separation of the colors known as " angular dispersion ".
14.
These equations can also be used to quantify the angular dispersion in prism arrays, as described in Isaac Newton's book " Opticks ", and as deployed in dispersive instrumentation such as multiple-prism spectrometers.
15.
The intensity pattern / distribution along the circumzenithal arc requires consideration of several effects : Fresnel's reflection & transmission amplitudes, atmospheric attenuation, chromatic dispersion ( i . e . the width of the arc ), azimuthal angular dispersion ( ray bundling ), and geometrical constraints.
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