Depth of Field When Image Size is Constant

A rule of thumb for depth of field is:

This rule of thumb is approximately true when the focus distance for the shortest lens is less than about 1/4 of the hyperfocal distance for that lens.

The hyperfocal distance for telephoto lenses is always large, so this rule works well for telephoto lenses. For example, it would work well for a 100mm lens and a 200mm lens on a 35mm camera. It can be shown mathematically that the rule is not exactly correct for any situation. This article explains when the rule yields a reasonable result.

The size of an image on film remains constant as the focal length increases when the object distance (distance from the lens to the object) increases by the same factor as the increase in focal length. For example, a 50mm lens focused on an object at 10 feet produces an image that is the same size as the image produced by a 100 mm (2 * 50 mm) lens focused on the object from 20 feet ( 2 * 10 feet). (Note 2 explains why this statement is true.)

The graphs below show how the depth of field changes as the lens focal length changes. It can be seen from the graphs that the rule of thumb is true only when the object distance is small compared to the hyperfocal distance of the shortest lens. It appears that the depth of field is the approximately the same for two lenses when the object distance for the shortest lens is less than about 1/4 of its hyperfocal distance. (Note 1 explains how to read the graphs.)

From Figure 1, it is seen that:

• The hyperfocal distance for the 50mm lens, set to f/8, is about 41 feet. (Circle of confusion = 0.025 mm for 35mm format)

• The depth of field is approximately the same for both lenses when the object distance is less than 10 feet (40 feet for the 200mm lens). 10 feet is about 1/4 the hyperfocal distance of the 50mm lens.

• The depth of field is significantly different for each lens for object distances greater than 10 feet (40 feet for the 200mm lens).

Figure 1

From Figure 2, it is seen that:

• The hyperfocal distance for the 50mm lens, set to f/8, is about 41 feet. (Circle of confusion = 0.025 mm for 35mm format)

• The depth of field is approximately the same for both lenses when the object distance is less than 10 feet (80 feet for the 400mm lens). 10 feet is about 1/4 the hyperfocal distance of the 50mm lens.

• The depth of field is significantly different for each lens for object distances greater than 10 feet (80 feet for the 400mm lens).

Figure 2

From Figure 3, it is seen that:

• The hyperfocal distance for the 200mm lens, set to f/8, is about 660 feet. (Circle of confusion = 0.025 mm for 35mm format)

• The depth of field is approximately the same for both lenses when the object distance is less than 130 feet (260 feet for the 400mm lens). 130 feet is a little less than 1/5 the hyperfocal distance of the 200mm lens.

• The depth of field is significantly different for each lens for object distances greater than 130 feet (260 feet for the 400mm lens).

Figure 3

From Figure 4, it is seen that:

• The hyperfocal distance for the 28mm lens, set to f/8, is about 13 feet. (Circle of confusion = 0.025 mm for 35mm format)

• The depth of field is approximately the same for both lenses when the object distance is less than 4 feet (12 feet for the 85mm lens). 4 feet is about 1/3 the hyperfocal distance of the 28mm lens.

• The depth of field is significantly different for each lens for object distances greater than 4 feet (12 feet for the 85mm lens).

Figure 4

From these results, it can be seen that the rule of thumb is reasonable when the object distance for the shorter lens is less than about 1/4 the hyperfocal distance of the shorter lens.

• Rear depth of field is the distance behind the object that will be acceptably sharp in the photograph. For example, if the focus distance is 9 feet and the rear depth of field is 6 feet, objects up to 15 feet (9 + 6) will be acceptably sharp in the photograph.

• Front depth of field is the distance in front the object that will be acceptably sharp in the photograph. For example, if the focus distance is 9 feet and the front depth of field is -4 feet, objects beyond 5 feet (9 - 4) will be acceptably sharp in the photograph.

• Total depth of field is calculated as: rear depth of field - front depth of field. For example, if the rear depth of field is 6 feet and the front depth of field is 4 feet, the total depth of field is 10 feet ( 6 - (-4)). If the focus distance is 9 feet, the depth of field for this example ranges from 5 feet (9-4) to 15 feet (9 + 6).

• The X-axis of a graph shows the focus distance of the shorter focal length lens. The focus distance for the longer lens will be the distance on the axis times the lens multiplier. For example, if the shorter lens is a 50mm lens and the longer lens is a 200mm lens, the multiplier is 4 (200/50). The focus distance for the longer lens in this example would be 4 times the value shown on the X-axis.

The equation for scale of reproduction, R, of an object is:

or,

The scale of reproduction R is also:

If you increase the focal length by a factor N, and increase the object distance by the same factor, the scale of reproduction doesn't change:

Thus, the image size remains constant when the object distance is increased by the same factor as the increase in focal length.