Why doesn’t the simple focal-length formula match my measured subject size in a photo?
Asked 9/27/2015
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I tested the geometry with a Sony A7 (full-frame 36×24 mm sensor) and a Canon FD 50mm lens. I photographed an A4 sheet and adjusted the setup so the paper filled the frame width/height, with the sensor and paper planes parallel.
Using the common similar-triangles formula, I expected the subject distance to be about:
- focal length: 50 mm
- A4 dimension used: 297 mm
- sensor dimension used: 36 mm
- expected distance ≈ 50 × 297 / 36 = 412 mm
But my measured distance was closer to 485–525 mm depending on focus setting.
Why doesn’t the calculation match the real-world measurement?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
10y ago
2 Answers
5
I think that you have, in fact, successfully answered this inverse question: How to test actual focal length?. It's not just infinity focus, but that lens focal lengths are generally rounded to familiar even numbers. Two different nominally-50mm lenses won't always give the same field of view even when focused at infinity. (And as a side note, be aware that turning the lens as far as it will go will usually focus past infinity.)
You'll also find that some pixels from the edge of the frame aren't included in the actual image, and 36mm may not be precisely the correct value to use.
Altogether, this demonstrates another basic fact: equipment made for photography is made for photography, not for photometry. You can use a hammer to drive in screws, but you won't get ideal results.
Originally by user1943. Source · Licensed CC BY-SA 4.0
user1943
10y ago
0
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Because the simple formula assumes an ideal thin lens focused at infinity, and your real setup is not that.
Key points:
- A lens’s marked focal length is nominal and specified at infinity focus. Actual focal length can differ slightly, and many “50mm” lenses are not exactly 50.
- When focusing on closer subjects, the effective image distance changes, so the infinity-focus geometry no longer applies exactly.
- Measuring subject distance from the sensor plane is not the same as measuring from the lens’s optical center/nodal point. In the simple geometry, using the sensor-plane distance overstates the distance by roughly the focal length.
- Real photographic lenses are complex, not ideal thin lenses, so small discrepancies are normal.
- Also, the usable imaged sensor width may not be exactly 36 mm edge-to-edge in practice.
So nothing is necessarily “wrong” with your camera. The mismatch comes from applying an idealized formula to a real lens at close focus, plus measuring distance from the sensor plane instead of the lens’s optical center.
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