Prof. Petzval on the Camera Obscura, 5 



curvature of the image, &c., so that ultimately the fine black 

 lines of the original would in the copy be either undistinguish- 

 able, or at most mere pale shadows ; at all events the picture, if 

 it bore examination with the naked eye, would suffer no mag- 

 nifying. 



In order to advance step by step, let us now return to the 

 natural camera, and seek to improve it by introducing into the 

 hole in the shutter a small, simple, and therefore unachromatic 

 lens of crown glass, which, for the sake of comparison, we will 

 suppose to have a focal length of 11 inches. Let us examine 

 what good properties are lost and gained by this certainly cheap 

 alteration. 



As long as the aperture of the lens is small in comparison 

 with its focal length, we may safely assume that, apart from dif- 

 fraction, the equally refrangible rays in any incident cylinder are 

 made to converge to a point, — in other words, that on placing the 

 screen properly, the image of a point in homogeneous light is 

 itself a point. This condition of placing the screen exactly in 

 the focus of the lens at once constitutes an inconvenience, inse- 

 parable from the new camera, which did not exist in the natural 

 one. There are, however, graver complications to notice. Glass 

 does not refract all rays of the spectrum alike ; each differently 

 coloured ray has a different focus, and the screen cannot of course 

 accommodate all. To examine the consequences here involved, 

 let n be the index of refraction for red rays, and p the distance 

 of the corresponding focus from the centre of the lens, whose 

 anterior and posterior surfaces we will suppose to have the radii 

 r and r' respectively ; then by a well-known formula, 



l = („-l)(i-i,); (3) 



and n + dn being the index of refraction for violet rays, whilst 

 p-\-dp\s the corresponding focal distance, we have on differen- 

 tiating (3), 



p'i. \^ ,.'/ ^n — \.)p 



whence 



For crown glass, 



consequently 



(jp= _ 0-036 .p, or (fp= - 0-396 in. . . (4) 



sinccby hypothesis ;j = 11 in.; that is to say, for the most 



, pdn 

 ^ l—n 



-^=0-036, 

 n — 1 



