THE OPTICS OF PHOTOGRAPHIC LENSES 23 



some softening of the contrast. Indeed, some "diffusion attachments" operate on 

 this principle. 



Optical Density. — While on the subject of light transmission, it is convenient to 

 introduce the frequently occurring concept of optical density. "Light transmission" 

 is defined as the ratio of the amount of light leaving the system to the amount entering 

 it in the same time. This is a ratio which is never greater than 0.9, since that is the 

 transmission of a single lens or plate of glass. 



Since the transmissions of plates or other elements passed in succession by a beam 

 of light must be multiplied together to yield the over-all transmission, it is more con- 

 venient to adopt a logarithmic unit which can be directly added for successive trans- 

 missions. Such a unit is "optical density," which is defined as log (1/transmission). 

 Thus transmissions of 1, 10, and 50 per cent have densities, respectively, 2.0, 1.0, 

 and 0.301. A transparent clear-glass plate transmitting 90 per cent of the light, has a 

 density of 0.046. 



The term "opacity" is sometimes used for the reciprocal of the transmission. 

 Thus a transmission of 50 per cent has an opacity of 2 and a density of logio 2, or 

 0.301. If several plates are used in succession, their opacities must be multiplied 

 together to get the over-all opacity. 



Cleaning a Lens. — Dirt or finger marks on a lens act both as obstructions to 

 light and as diffracting agents which soften definition and contrast. A lens should 

 not be cleaned more than necessary as grit is likely to be harder than glass and indis- 

 criminate wiping maj^ scratch the lens surfaces. Clean chamois leather moistened 

 with alcohol is a good cleanser, followed by the minimum of polishing with a dry 

 chamois leather. Soft tissue paper or specially made lens paper may also be used. 

 A lens should not be taken apart unless absolutely necessary as this will admit dust 

 and dirt which will settle eventually on the inner lens surfaces. Slight decentration 

 may also arise from casual disassembly of a lens. 



If a lens has been dropped, it may be found that one of the balsam layers between 

 the elements of a cemented component has started to break apart. In this case the 

 lens should be returned to the makers to be recemented; this is not a job for the user to 

 undertake himself. 



Depth of Field. — We have so far supposed that the whole of our object lies in a 

 plane at a fixed distance from the camera and that the image is sharply focused on the 

 plate. If either of these conditions is not fulfilled, we shall, of course, obtain a 

 blurred image. In practice it is found that a certain slight amount of blur is tolerable 

 because it cannot be detected in the final picture, and thus we have a certain deter- 

 minable "depth of field" for our camera, which is the range over which the object or 

 the photographic plate may be moved along the axis of the lens before the consequent 

 blurring of the picture becomes noticeable. To obtain a quantitative measure of this 

 effect, we consider the passage of the beam of light from a single object point to the 

 corresponding image point. If this image point is out of focus, a "circle of confusion " 

 will be seen on the plate instead of a point of light, and if the diameter of this circle of 

 confusion subtends an angle of a minute of arc or less at the observer's eye, he will be 

 unable to say whether the image is in sharp focus or not. 



Now a minute of arc is an angle of 1 in 3400, so that a circle of 0.1-mm. diameter 

 should just be distinguishable as such when viewed at a distance of about 12 in. As 

 this is the normal viewing distance for direct contact prints, a circle of confusion of 

 0.1-mm. diameter provides the limit of our depth of focus for such cases. 



However, when the photographic picture is subsequently enlarged, as occurs in 

 motion pictures for example, it is necessary to adopt a much more stringent criterion 

 of sharpness than 0.1 mm.; indeed, the limit is then fixed by the coarseness of the grain 

 structure in the photographic emulsion. The measured "resolving power" of 



