What affects DOF more...distance to subject or focal length?

Here is the standard Depth of Field formula for reference:

DOF = 2 u² N C / f²

N = aperture F-number
C = circle of confusion
u = distance to subject
f = focal length

• When aperture and subject size within the frame are constant, DOF will not change because changes to focal length (f) and distance (u) will be proportional to each other and cancel out.

• On most variable-aperture zooms shot wide open, DOF will be greatest when zoomed out because the focal length is shorter. The effect of focal length is greater than that of aperture because it is squared in the formula.

• At macro reproduction ratios, DOF is still controlled by aperture, but DOF can be so narrow, regardless of aperture, that it is worth considering techniques such as focus stacking.

  • Pat David: Focus Stacking Macro Photos (Enfuse)

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Although not very relevant to macro photography, people often refer to DOF when they want background blur. The amount of background blur does change with focal length, even when subject size and aperture are kept constant. Different focal length and aperture combinations can be compared by using f/N to estimate background blur.

On variable-aperture zooms, maximum background blur is usually at max focal length, rather than max aperture with minimum focal length, because zoom ratios are usually greater than 2, while the max-aperture ratio is usually less than 2.

• Does amount of background blur change with focal length given equal framing?
• How can I maximize the "blurry background, sharp subject" (bokeh) effect?

Tables an charts base the circle of confusion, the Case A 50mm lens focused @ 2 feet aperture f/8 circle of confusion 1/1000 of focal length = 0.05mm. Span of D of F = 0.39 feet. Case B 100mm lens focused @ 4 feet aperture f/8 circle of confusion same 0.05. Span of D of F same 0.39 feet = 4.7 inches Case C 100mm lens focused 4 feet criteria for D of F on1/1000 of the focal length sets circle size at 0.01mm. Span of D or F = 0.79 feet = 9.5 inches.

No need to apply this rule of thumb because the display magnification for both case A and B will be the same. Conclusion: Case C not applicable because images case A and B will be displayed at the same magnification so span f D of F for A & B are the same.

Focal length 50 mm Point focused upon 2.00 feet Distant point sharply defined 2.22 feet Near point sharply defined 1.82 feet Span 0.39 feet Diameter of circle of confusion 0.05 mm f/number 8.00

Focal length 100 mm Point focused upon 4.00 feet Distant point sharply defined 4.21 feet Near point sharply defined 3.81 feet Span 0.39 feet Diameter of circle of confusion 0.05 mm f/number 8.00

Focal length 100 mm Point focused upon 4.00 feet Distant point sharply defined 4.43 feet Near point sharply defined 3.64 feet Span 0.79 feet Diameter of circle of confusion 0.10 mm f/number 8.00

A lens collects light emitting from a point on the in-focus subject/plane to a point on the sensor. At a given aperture number, the light collected from a subject has a certain brightness, and when the subject has a certain size on the sensor, it does not really matter for the collection angle whether you achieve your size via changing distance or focal length. So disregarding the different perspective, depth of field is the same.

But you have tagged this question as "macro", so disregarding the different perspective may be uncalled for. The effect of a close-up perspective is to magnify parts closer to the lens and to shrink parts that are farther away. This will show more detail of the closer parts but with more blur, and less detail of the more distant parts but with less blur. The overall depth of field will be similar but the region of tolerable sharpness will extend more behind than in front of the focus plane than if the subject were placed at a longer distance while adjusting focal length.