Apertia · Library
Why does this model stop at a sensor-to-subject distance of four focal lengths?
Find the four-focal-length boundary of the thin-lens model: a 60 mm lens reaches 1:1 at 240 mm from the sensor, and 300 mm gives u = 217.082 mm and m = 0.382.
Where the boundary comes from
Apertia finds the lens-side distance from the sensor-plane distance d by solving u² − d·u + d·f = 0. The square root in u = (d + √(d² − 4df)) ÷ 2 is real only when d ≥ 4f. At exactly d = 4f both roots meet at u = v = 2f, which is one-to-one magnification; no thin-lens arrangement of that focal length can focus closer.
The app handles the boundary in two ways. In the depth-of-field calculation a distance at or inside 4f is held at the one-to-one point, u = 2f. The shot planner returns no plan when the nearest sharp point is at or inside 4f and shows its invalid-range message instead. The library calculator linked on this page rejects any distance shorter than 4f.
Worked example
At a 400 mm combined distance with a 100 mm thin lens, the object and image distances are both 200 mm. A smaller combined distance is not silently substituted with this boundary.
- Object-side distance at the model boundary (mm)
- 200
Check a macro target against the boundary
- Multiply the real focal length by four to get the closest sensor-to-subject distance the model accepts.
- Measure your intended distance from the sensor-plane mark, not from the lens front.
- If the distance is larger, compute u and v and the magnification v ÷ u.
- If it is equal or smaller, the setup is beyond one-to-one in this model; use the lens maker's macro data.
Worked example: a 60 mm macro lens
For f = 60 mm the boundary is 240 mm, where u = v = 120 mm and m = 1. At d = 300 mm, d² − 4df = 90000 − 72000 = 18000, √18000 = 134.164, so u = 217.082 mm and v = 82.918 mm; m = 0.382, a little more than one-third life size. At d = 230 mm the discriminant is negative and the model has no solution.
- 60 mm · boundary distance
- 240 mm
- d = 300 mm · u / v
- 217.082 / 82.918 mm
- d = 300 mm · magnification
- 0.382
Common mistakes
- Entering a lens's published minimum focus distance as if it were the 4f boundary; the two are measured differently and rarely agree.
- Confusing a 400 mm sensor distance with a 400 mm object distance for a 100 mm lens.
- Reading a depth result at or inside 4f as valid even though the app has clamped it to the one-to-one point.
Boundary of the method
The four-focal-length limit belongs to one ideal thin lens. Real macro lenses, extension tubes and reversed lenses use other geometry and can exceed one-to-one. The DOFMaster equations listed below describe the thin-lens relations this boundary comes from.