H = 100F2/12f ft.
Now the distance of the farthest sharp plane from the lens when sharp focus is secured on a plane distant u feet can be shown to be uH/H-u approximately and the distance of the near plane uH/H+u approximately.
A knowledge of the distance of these planes is invaluable to the hand-camera user, and many cameras are now fitted with an index which enables them to be very easily read off from a scale. It is also possible to buy scales calculated for lenses of four common focal lengths.
The solution of an example will perhaps help to an understanding of the use of these formulae.
A 6 in. lens is sharply focussed on an object 20 ft. away. What will be the Depth of Field at f8?
We must first calculate H.
Now H = 100F2/12f ft.
Here F = 6,f= 8, so that H =100x6x6/12x8 ft. = 300/8 ft.
Distance of far plane is uH/H-u = (20 x 300/8)/(300/8-20) ft. = 43 ft. (approximately).
Distance of near plane is uH/H+u = 13 ft.
So that Depth of Field is (43 - 13) ft., i.e. 30 ft.
With respect to fixed-focus cameras it will now be obvious that the lens should be set for sharp focus on an object at the Hyperfocal Distance for the largest aperture of the lens.
Again referring to Fig. 14, it will be understood that the plane AB will not only be sharply reproduced on the plane 6a, but also on planes lying on either side of it. The distance apart of the extreme planes on which sharp focus is obtained is called the Depth of Focus for the aperture in use. Depth of Focus is not a large quantity unless very minute apertures are used; and when that is so, Diffraction is very likely to occur, and the fine definition is accordingly destroyed. It is periodically pointed out by writers in the photographic press that by using a very small stop any ordinary lens can be used as a so-called wide-angle lens. Suppose the depth of focus of a 6 in. lens at F 300 is 4 inches. Then this lens could be used as a lens of 4 in. focal length, which would include a much larger field of view. It could also be used as a lens of focal length 8 inches, which would include a much smaller field of view. The reader can try the effect of placing a piece of very finely perforated card against the ordinary diaphragm, and then making a series of exposures with the lens at varying distances from the plate. The results will probably not be satisfactory. As a guide it may be mentioned that when the screen is v inches from the lens, and the aperture is a inches, the depth of focus is approximately v/50a.
The screen can therefore be moved v/100a inches on either side of the position in which the sharpest definition is obtained.
A lens is said to equally illuminate a plate when the same amount of light is incident on unit areas at the centre and margin of the plate. No lens does this. With many lenses it is found that the plate is not uniformly illuminated at large apertures, but that the illumination apparently becomes uniform when the aperture is decreased. The reason for this can be understood from Fig. 13, in which a good part of the oblique cylinder of rays is cut off by the lens mount. When the aperture is reduced sufficiently, all the rays of the oblique cylinder enter the lens, and take part in the formation of the image. It will be seen that even then the cross-sectional areas of the axial and oblique cylinders are unequal, but it is found in practice that the equality of illumination is not influenced very much by this, unless the lens is used as a wide-angle lens. With wide-angle lenses the illumination will always fall off towards the edges of the plate.