GHOSTS AND OCULARS. 49 



nearly parallel to the transmitted ray incident on 3, and comes to 

 about the same focus. 



It is the ghost thus pi'oduced which is occasionally troublesome in 

 ordinary objectives, and frequently so in photographic doublets of the 

 Petzval construction. Under any conditions where two consecutive 

 surfaces are of substantially equal curvature the ghost should be looked 

 out for, whether the surfaces are those of an air space or are formed 

 by a lens element of very slight refraction. The exact position of this 

 ghost from the intermediate surfaces of an objective may be quickly 

 found graphically. From any point of sm-face 2 draw a line to the 

 focus of the front lens considered by itself. The intersection of this 

 line with surface 3 at once gi\'es the angle of incidence there from 

 which the reflected ray can be traced backward and then through the 

 rear lens to its new focal point. If one traces a ray in fact through 

 any combination an inspection of the angles of incidence at the vari- 

 ous surfaces will generally show at once where any possible danger 

 from ghosts lies. In dealing with a completed lens a very brief 

 inspection with a bright light in the field or the exposure of a photo- 

 graphic plate will tell the story. In a simple doublet all 6 reflections 

 can be photographed and in a triple or quadruple combination most 

 of the ghosts will show although some may be lost by overlapping. 



Effect of the Ghosts. 



In an ordinary objective the result of the 2nd order reflections is 

 slightly to brighten the field, except that the air space ghost may 

 appear as a spot. In the photographic case the effects are more con- 

 spicuous and where, as in uncemented 4-lens combinations, the total 

 intensity of the reflections may amount to something over 2% of the 

 total light, the clarity of the image may be materially impaired and 

 in photographing nebulae false images may appear. Such systems 

 give pictures distinctly less crisp and brilliant than does the single 

 cemented landscape lens. In the visual case a visible ghostly image 

 requires a surface brightness greater than the background of the 

 sky, in other words comparable with the star disc of the minimum 

 visibile in the instrument used. 



As the 2nd order ghost in focus is about 7-8 m. fainter than the 

 primary it must be thrown out of focus enough to dim it below prac- 

 tical visibility. In the objective the angle a between the ray incident 

 on surface 3 and its return after two reflections is 



a = 2 (i - i') 



