Some preliminary notes on diffraction gratings

In ? 1 a simple test, using polarized light, for the best setting of a diffraction grating is described. When used under the best conditions for brightness, a grating should show little or no polarizing effect. The reason for this depends upon the fact that the Huygens-Kirchhoff integrals for the electric and magnetic vectors have different cosine factors which have the same value only in the case of ordinary reflection. In ? 2 an extension of the Huygens-Kirchhoff integrals bringing in a second approximation is given. This second approximation becomes important if either the radius of curvature is comparable to the wave-length of light or the angle of incidence is very nearly 90?, as it may be in soft X-ray experiments. In ? 3 a new curve for the effect of slit-width upon the resolving-power of a spectroscope is given and compared with Schuster's curve also. Schuster's curve is based on the assumption that the slit is filled with incoherent light; the author's, with coherent light. These two curves are probably upper and lower limits. In ? 4 a new method of ruling concave gratings, namely radial ruling, is suggested. In this method the diamond is given a uniform chordal displacement, from line to line, as in the present method of ruling, but during its displacement from line to line it is constrained to rotate about an axis parallel to the ruled lines and passing through the centre of curvature of the face of the grating. For the metal concave grating of more than 20,000 lines per inch this method of ruling would do what figuring does for an astronomical mirror, though not to so high an order of accuracy.