24 HANDBOOK OF PHOTOGRAPHY 



emulsions runs from 30 lines per millimeter for fast negative emulsions down to 

 80 lines per millimeter for process plates and lantern plates. Thus we may expect 

 that the minimum discernible circle of confusion over this range of emulsions will be 

 similarly from 0.03 to 0.01 mm. On the average, it is commonly stated that, for the 

 highest definition requirements, a circle of confusion of Hooo in- (0.025 mm.) is per- 

 missible, while 0.1 mm. is satisfactory in making direct-contact prints. 



Depth of Focus in the Image. — In Fig. 20 is shown the cone of rays from a lens in the 

 neighborhood of an image point. Assuming that the lens is perfectly corrected, this 



cone will shrink to a point at the best focus, and 

 expand uniformly within and beyond this focus. 

 Evidently, if the plate is situated anywhere in 

 the range for which the expanded beam has a 

 diameter less than that of the permissible circle 

 Fig. 20. Depth of focus in the of confusion c, the image will appear perfectly 

 image. sharp, whereas outside this range some diffusion 



will be observed. If this range extends to a distance R to each side of the perfect 

 focus, then R = cA, where A is the aperture number of the lens. The use of this 

 relationship is chiefly found in determining the precision of focusing necessary in a 

 camera, the permissible degree of nonflatness in films, etc. 



Depth of Focus in the Object.- — So far as the practical photographer is concerned, the 

 important aspect of depth of focus is the range of distances in the object which will 

 appear substantially in focus on the plate. This is more properly called "depth of field." 

 If the camera is focused accurately on a certain plane in the object, at a magnifica- 

 tion m, then the distance beyond the focused plane corresponding to a circle of con- 

 fusion c on the plate, is given by 



where d is the diameter of the entrance pupil of the lens, and s is the longitudinal 

 distance of the focused object plane from the entrance pupil. Similarly, the depth 

 of focus within the focused plane is 



R2=—^ (11) 



md + c 



If the object is fairly near the camera, md is large compared to c, and we can write 

 approximately 



«. = «' = £ (12) 



As an example in the use of these formulas, suppose we have an//4.5 lens of focal 

 length 100 mm. (4 in.). Then with an object at 10 ft. (3.28 m.) distance and assuming 

 a permissible circle of confusion of 0.1 mm. on the film, we have 



s = 3280 mm. 



, 100 „„„ 

 a = -T-p = 22.2 mm. 

 4.5 



c = 0.1 mm. 



- _JL _ J_ 



"^'s-f 31.8 

 md = 0.70 



i2„ = ^ = 410 mm. = 16.1 in. = 1 ft. 4 in. 



0.8 

 328 

 0.6 



iJi = ??§ = 546 mm. = 21.5 in. = 1 ft. 10 in. 



