Question

An object is photographed at a large distance. The same object is again photographed at a small distance, but under the same conditions of illumination. How will the illumination on the photographic film in the camera differ under these two conditions? Which case requires a greater exposure?

Answer 1

The illumination of the film in the camera depends on the amount of light energy passing throught the objective glass and on the ratio of the area of the photographed object to the area of its image on the film. The amount of light energy Q passing through the objective is proportional to the size of the solid angle subtended by the objective when viewed from points on the object, i.e., it is directly proportional to the area of the objective aperture S and inversely proportional to the square of the distance a₁ from the camera to the object (Fig. 324), or QαS/a1₂. The ratio of the linear dimensions of the object to the linear dimensions of the image is equal to the ratio of the distances of the object and image to the objective of the camera (Fig. 325).

Consequently, the ratio of the area of the object σ₁, to the area of the image σ₂ should be equal to the ratio of the squares of the distances of the object and image to the objective, i.e.,

i.e., the illumination of the image in a camera turns out to be proportional to the square of the distance from the objective to the image.

The image of the more distant object lies closer to the objective than the image of the closer object. Consequently, the illumination of the image of the more distant object will always be greater than the illumination of the image of the closer object. The second, case (closer object) requires a greater exposure than the first.