Ox CONCAVE GRATINGS FOR OPTICAL PURPOSES 



497 



Whence the focal length is 





pR cos' 



COS a COS p COb v 



For the transmitted beam, change the sign of R. Supposing p, R and v 

 to remain constant and r and // to vary, this equation will then give the 

 line on which all the spectra and the central image are brought to a 

 focus. 



By far the most interesting case is obtained by making 



since these values satisfy the equation. The line of foci is then a 

 circle with a radius equal to one-half p. Hence if a source of light 



FIG. i. 



exists on this circle, the reflected image and all the spectra will be 

 brought to a focus on the same circle. Thus if we attach the slit, the 

 eye-piece and the grating to the three radii of the circle, however we 

 move them, we shall always have some spectrum in the focus of the 

 eye-piece. But in some positions the line of foci is so oblique to the 

 direction of the light that only one line of the spectrum can be seen 

 well at any one time. The best position of the eye-piece as far as we 

 consider this fact is thus the one opposite to the grating and at its 

 centre of curvature. In this position the line of foci is perpendicular 

 to the direction of the light, and we shall show presently that the 

 spectrum is normal at this point whatever the position of the slit, pro- 

 vided it is on the circle. 



Fig. 1 represents this case; A is the slit, C is the eye-piece, and B is 

 the grating with its centre of curvature at C. In this case all the con- 

 ditions are satisfied by fixing the grating and eye-piece to the bar BC 

 32 



