808 HANDBOOK OF PHOTOGRAPHY 



swinging the engraved transparent scale up into position before the plate and mak- 

 ing a brief exposure to a small incandescent lamp provided for the purpose in the 

 spectrograph. 



Prisms. — Dispersing prisms are almost always cut with 60° refracting angles. 

 This angle is a compromise between smaller angles which give less dispersion and 

 larger angles which require more material, produce a greater loss of light by reflection, 

 and give a decreased aperture. 



A dispersing prism should be used in such a way that the ray of mean wavelength 

 passes through it at the angle of minimum deviation, this ray then passing through 

 the prism parallel to its base. Under these conditions the effective free aperture 

 of the prism is a maximum, and the light loss by reflection is a minimum. The 

 resolving power of a prism is proportional to the difference in thickness between the 

 prism base and its refracting edge. The exact calculation for the resolving power of a 

 prism as used in a given spectroscope is exceedingly complex since it depends on many 

 factors, including the method of illumination of the slit. 



A prism is usually shaped so that it will transmit a beam of circular cross section 

 falling on its front face at the proper angle for minimum deviation. This condition 

 leads to a standard set of dimension ratios for anj'- material, the length of a face being 

 for most substances roughly 1.6 times the height. For good definition the prism 

 height should be at least three times as great as the maximum length of slit which 

 is to be used with it, and preferably the ratio should be even greater. Spectrum lines 

 produced with prisms are curved, and definition may be lost when the prism slit-height 

 ratio is too small. 



Prisms made of crystalline quartz show double refraction, and produce doubled 

 spectra even when cut with their optic axis parallel to the crystalline axis. Cornu 

 showed how to overcome this defect by making a 60° prism of two 30° prisms in 

 optical contact, one of left-handed and the other of right-handed quartz, the second 

 thus serving to offset the optical rotation produced bj'- the first. When a reflection 

 prism is used, only one type of quartz is required, since the beam passes through it 

 both ways. 



Gratings. — Diffraction gratings consist essentially of a large number (sometimes 

 as many as 180,000) of close equidistant slits, which are usually made by ruling lines 

 with a diamond on a smooth surface. The greater the number of these slits, the 

 greater the resolving power of the grating. Light which falls on a grating is thrown 

 into several orders of spectra, and the resolving power P of the grating is given by 

 the formula P = nm, where n is the total number of lines on the grating and m is the 

 order being considered. Theoretically, resolving powers of 500,000 can be realized 

 in the higher orders of some gratings which have been produced, but actuallj^ values of 

 P greater than 300,000 are seldom found. 



The angular dispersion of a grating depends on the distance between successive 

 rulings (the grating space d) and can be derived by differentiating the grating formula 

 toX = d (sin 6 ± sin i) where d is the angle of emergence, i is the angle of incidence, 

 and 771 is the order. The dispersion can also be written dO/dX = A/nni, where A is the 

 linear aperture of the grating. 



Small gratings are sometimes ruled on glass, successive lines being ruled as closely 

 as 500 per inch for a very coarse grating or 15,000 per inch for a fine grating of high 

 dispersion. Glass gratings can be used onlj' in the visible and infrared regions to 

 which the glass is transparent, and require collimator and camera lenses to make the 

 light parallel and refocus to it. For larger instruments and for those suited to all 

 spectnun regions, gratings are commonlj^ ruled on highly polished reflecting surfaces. 

 either plane or concave. Gratings up to 7 in. in diameter have been successfully 

 ruled with 20.000 and even 30,000 lines per inch. 



