50 BELL. 



where i' is the angle of reflected incidence on surface 2. CalHng 

 this A i and noting that the deviation of a ray is for small refractions 

 constant, the variation of focal length A i^ is approximately 



. „ „ sin A i 



A / = / —, — - 

 sin ? 



The situation is just as if the original ray incident on 3 were tilted 

 through an angle A { swinging the line to focus along with it. 



It should be noted that where (i — i') is large, as for large values of 

 €•2 ?3, A F increases, so that for a given focal length high absolute 

 curvature, as in some flint-ahead combinations and objectives of 

 Fraunhofer form, gives larger variation of focus, while in Gaussian 

 objectives where Q-z Os are both large and widely difi'erent, the ghosts 

 are widespread and the field exceptionally dark, as m the Princeton 

 9".fi glass, designed by Professor Young. 



In actual practice, objectives of ordinary glasses computed to meet 

 the sine condition give Q2 and Qs difl'ering by 2-3% which is more 

 than enough to wipe out the A'isible ghost. 



Since, ractcris jxtribiis, {i — i') depends on the ratio between 6^ and 

 6*3, roughly, 



2 A P 



Whence a difference of 1% between Q-i and P3 will shift the focus about 

 2% back or forward according as 92 < 6*3 or the reverse. Thus is a 

 telescope of 100 cm. focus and 10 cm. aperture a ghost image of \" 

 radius has a diameter of 0.01 mm. The intersect of its cone of light at 

 2 cm. from focus would be 2 mm. and the surface intensity would be 

 400^00' i-C- 11 nig. below the original, or at least 18 mg. below the 

 primary, a negligible figure even allowing for the greater visibility of 

 an enlarged area. 



It is in oculars that troul)lesome ghosts are most frequently met, 

 sometimes distinctly \isible, often brightening the field. 



Consider a simple field-lens, A, Figure 2, of radii r, r' receiving sub- 

 stantially parallel light which is reflected from its rear surface. It is 

 subjected to 2 refractions and one reflection and comes to focus as if 

 the lens were replaced by a concave mirror of focus / defined by 



/ V' '• / 



For r = CO , the common form of field lens, and common crown glass, 

 / = \ F approximately, F being the 00 focus of the lens. This defines 



