If a grating has 15,000 lines per inch and a ruled surface ex tending over two inches, the resolving power will be 6o,000 in the second order. Thus, at X6,000 the theoretical separating power would be o.IA, while at X3,000 it would be o•o5A. The resolving power increases towards the shorter wave-lengths because the diffraction bands become narrower.
The Concave Grating.—A very important contribution to the appliances for exact spectroscopy was made by Rowland in the introduction of concave gratings. These are ruled on concave speculum mirrors, which are generally of spherical form, but sometimes paraboloidal, and the rulings are intersections of equi distant parallel planes with the surface. The collimator and observing telescope are in this way dispensed with, because the ruled surface diffracts the rays from the slit to a focus. The in strument is equally good for the whole range of spectrum, since speculum metal is a good reflector for all wave-lengths and there are no lenses to produce absorption.
An important special case is that in which R=p cosi, for then r=p cos0 and the two curves coalesce in a circle of diameter p This is often called the Rowland circle, and (fig. 15a) if such a circle be drawn with the line joining the centre of the grat ing with the centre of curva ture as diameter, and the slit S be at any point on this circle, the spectra of various orders will be focussed on the circumference of the circle.
In Rowland's beautiful method of mounting, the slit is placed directly above the point of in tersection of two firmly supported rails GS and SF, at right angles to each other, while the grating, G, is supported on a girder GF equal in length to the radius of curvature. The ends of the girder rest on little carriages which run on the rails, and since G, S and F always lie on the Rowland circle, different parts of the spectrum are focussed at F as the girder is moved from one position to another. With this construction, 0=o and
mX= (a+b) sini; that is, the wave-length focussed at F is pro portional to SF. In other words, as observed with an eyepiece and cross-threads the spectrum is truly normal, and the rail SF may be graduated directly on a uniform scale of wave-length. When a photographic plate is substituted for the eyepiece, it is placed in a holder that will bend it to the curvature of the Row land circle, so that the whole of the spectrum is in focus. The spectrum is then only normal in so far as cos 0 can be considered equal to unity, because 0 is only zero for the centre of the plate.
Rowland's largest gratings have a radius of 21 ft. and a ruled surface 6 in. wide, the rulings being about 2 in. in length. These give a first order visible spectrum about 5 ft. long.
On account of the oblique incidence of the light falling on the grating, there is a considerable amount of astigmatism, so that even a point slit gives lines of considerable length, especially in the higher orders.
Numerous other constructions for concave grating spectro graphs have been devised.
The Eagle mounting utilizes the spectrum seen in the direc tion of incidence, being essentially a Littrow spectrograph with a concave grating in place of a prism and lens; to bring different parts of the spectra under observation, the grating can be rotated and moved towards or from the plate, and the plate holder can be tilted to fit the Rowland circle. This mounting greatly reduces the astigmatism as compared with Rowland's arrangement, and therefore gives brighter spectra, and has the advantage that it can be enclosed in a rectangular box; higher orders of spectra can also be photographed.
When a collimator is used, so that parallel light falls on a concave grating, there is no astigmatism, and the spectrum is consequently brighter. In this form, slit, grating and plate are no longer on the Rowland circle and good focus can only be obtained over a moderate range of spectrum. The linear dis persion is reduced to about one-half of that given by Rowland's arrangement.