6 Prof. Petzval on the Camera Obscura. 



refrangible violet rays the focal length is less than that corre- 

 sponding to red raj^s by f in. nearly. If the latter combine in 

 a point R, the former will converge to a point V nearer the lens, 

 and the foci of all the other rays of the spectrum will lie between 

 R and V. The rays which, on account of their number or colour, 



exercise the strongest action on the retina, will be congregated 

 about a determinate point 0. Strictly speaking, the optical focus 

 here referred to is not a fixed point, since all eyes are not affected 

 in the same manner by diiferently-coloured rays, nevertheless it 

 is in the neighbourhood of that most observers obtain the best 

 image. In another fixed point C, nearer to V than to R, will be 

 collected the rays which exert the greatest chemical action ; and 

 at this chemical focus, which may also vary a little with the 

 material exposed to the action of light, the best photographic 

 image will be obtained. Lastly, about midway between V and 

 R, there is a third point P at which the screen intersects the cone 

 of rays in its narrowest part, the diameter of the circular section 

 being 



D 



= ^1^ =0-036 p, 

 P 



where, as before, p is the semi-aperture of the lens, p its focal 

 length for red rays, and djj the so-called linear chromatic aber- 

 ration*. 



To this diameter of the circle of chromatic aberration must be 

 added that of the circle of aberration due to difii'actiou, with 

 which we are already acquainted, so that the total aberration 

 will amount to 



D = 0-036 p+^. 

 P 



If we seek, as before, the value of p which corresponds to a mi- 



* The above formula expresses an important theorem in the theory of 

 the camera as well as in that of the telescope, inasmuch as it shows that 

 the diameter of the smallest circle of chromatic aberration is dependent 

 solely upon the aperture of the lens, and not upon its focal length. 



