The relation between the density and the exposure of the plate can easily be represented as a curve, and for most of this curve the density is increased proportionally as the exposure is doubled (See Fig. 53). This condition is that which produces a correct rendering of the original in the print, and for that reason the parts of the curve for which it is true is known as the region of correct exposure. But at the beginning and the end, the curve is not straight; at the beginning, the density increases more rapidly; this is known as the region of under-exposure, and at the top of the curve the density falls off and finally fails to increase at all when the exposure is increased; this is the region of over-exposure. We may note that in the example taken the under-exposure region persists while the exposure increases from unity to three and one-half units; then we have correct exposure until the exposure becomes about one hundred and twenty-eight units, and then the over-exposure region appears, differences in exposure failing to grow in density after about five hundred units of exposure. For a rapid film, the point marked unity on this curve represents an exposure of about l/50th of a candle-foot-second; that is, this film requires an exposure of l/50th of a second to a candle at one foot distance in order to give the first visible trace of deposit.

When photographing a landscape, we want to obtain in our negative just a trace of deposit for the shadows, and we have already seen that the image of the shadows on the film will have a brightness of one foot-candle, so that the correct exposure time to give for such a landscape will be l/50th of a second with the lens working at an aperture of f.8. The exposure given for such a landscape will therefore vary from l/50th candle-foot-second in the shadows to 30/50th or 3/5th of a candle-foot-second for the sky.

This reasoning applies to an ordinary film, but photographic materials are of various speeds, and we can clearly define the speed according to the exposure required to give an impression upon it. The shorter the exposure required, the "faster" the film; and from the exposure which we find to be required, we may calculate a number which will represent the "speed" of the film.

A film might be said to have a speed of unity which requires the exposure of l/50th of a second to give a deposit equal to that given by the light of an intensity of 1 foot-candle, such as is reflected from the darkest shadows of a landscape. But it would be inconvenient to choose unity as the speed of our film, because the speeds of all slower materials would have to be expressed in fractions, and in practice such a film is said to have a speed of 250 in the units generally used by photographic workers.

We see, therefore, that for a film of speed 250 at f.8 which reduces the light by about 100 times, we shall require an exposure of l/50th of a second if the light reflected from the darkest portion is about 100 foot-candles. If the light reflected from the darkest shadow of the object is one foot-candle, we shall require an exposure of 1 second on a film of speed 500, or 500 seconds with a film of speed one. Or, generally, if L is the light intensity from the darkest part of the subject, P is the speed of the film or plate, and E is the exposure at f.8, then

500

E = ----------

L x P

E being exposed in seconds, L in foot-candles, and P in the usual speed units.

It will be seen that this method of calculating exposures assumes that the exposure is made for the shadows, and in practical photography this is almost always true; one exposes to get shadow detail and trusts to the latitude of the emulsion being sufficient to render the whole scale of gradation of the subject.

If, instead of a landscape with foreground, we photograph a quite open landscape with sea or open country in the distance, then the darkest part of the picture will reflect perhaps 1/5th of the sky light or about 500 foot-candles. Using a film of speed 250, we should have to give an exposure of only 1/250th second atf.8 or about l/60th of a second atf. 16.

Using this line of reasoning, let us consider what the shortest exposures practicable for figures in rapid motion are likely to be. The range of contrast when taking a photograph of an athlete jumping, for instance, will be much smaller than in our typical landscape, and probably 1 to 10 would be a fair approximation; if the scene is in sunlight, the shadow detail may be represented by 250 foot-candles. Using the most rapid lenses available for such work, we may reckon on having 3 times as much light as a lens at f.8 will give, and we can use a Seed Graflex plate of speed 500; the exposure required will therefore be 500/250 x 3 x 500 or 1/750th of a second. We see, therefore, that unless the light conditions are of the very best, the use of such high shutter speeds will involve some degree of under-exposure, and this fact illustrates the advantage well-known in practice of taking very rapidly moving objects as silhouettes against the sky.

When photographing in the streets of cities, a considerably greater exposure is permissible than in landscape work, because there are always deep shadows outside the main range of contrast, in which an increase of exposure will give detail at the expense of the highlights, and an increase of exposure therefore means a shifting of the center of the scale of gradation from the highlights to the shadows. In practice topographical views are usually made at the shorter exposures, while the pictorial photographer prefers the longer exposures which concentrate interest on the lower-toned portions of the picture.

When using color filters, their factors must be allowed for in considering exposure; thus, taking the speed of film as 250, the use of the color filter requires an increase of five times in the exposure, so that for our typical landscape when using a color filter at f.8 we shall need an exposure of l/10th of a second.