Apertia · Library
Why does the lens-to-sensor distance change in a thin-lens close-up model?
See how the thin-lens image distance v = u·f ÷ (u − f) grows from 50 mm at infinity to 62.5 mm at a 250 mm object distance, and why Apertia keeps v and u apart.
Why the image side moves
In the thin-lens model Apertia uses, an object at distance u from the lens forms a sharp image at v = u × f ÷ (u − f). Only for an object at infinity does v equal the focal length. As the subject comes closer, v grows, which is the extension a real lens provides by moving its focusing group or the whole optical block.
The app needs v twice. It converts the sensor-plane distance you enter into u, and after computing the near and far limits on the lens side it adds the matching image distance back, so every displayed distance is again measured from the sensor plane. The same function returns f itself when the far limit or focus distance is infinite.
Worked example
A subject 1000 mm from a 50 mm thin lens produces an image distance of about 52.632 mm. The combined model distance is about 1052.632 mm, rather than 1000 mm.
- Model image distance (mm)
- 52.631579
Follow the extension as focus gets closer
- Keep the focal length fixed; the examples here use 50 mm.
- Choose an object distance u measured from the lens, not from the sensor.
- Compute v = u × f ÷ (u − f).
- Subtract f to see the extra image-side distance compared with infinity focus.
- Add u and v to recover the sensor-to-subject distance the app would display.
Worked example: three object distances
At u = 1000 mm, v = 50000 ÷ 950 = 52.632 mm, so the image side is 2.632 mm longer than the focal length. At u = 500 mm, v = 25000 ÷ 450 = 55.556 mm, an extension of 5.556 mm. At u = 250 mm, v = 12500 ÷ 200 = 62.5 mm. Halving the object distance from 500 to 250 mm more than doubles the extension, from 5.556 to 12.5 mm.
- u = 1000 mm
- v = 52.632 mm · d = 1052.632 mm
- u = 500 mm
- v = 55.556 mm · d = 555.556 mm
- u = 250 mm
- v = 62.5 mm · d = 312.5 mm
Common mistakes
- Assuming v stays at 50 mm for a close subject, which understates both the total distance and the magnification.
- Treating u ≤ f as a very close subject: in this model such an object forms no real image, and the function rejects it.
- Reading the computed extension as the travel of a specific lens barrel; internally focusing lenses change their focal length instead.
- Adding v to a distance that was already measured from the sensor plane.
Model boundary
The image distance belongs to an ideal single thin lens. It does not describe flange distance, a real lens's principal planes or how its focusing mechanism moves. The DOFMaster equations listed below use the same lens-side quantities; check the manufacturer's close-focus data when real extension matters.