Can a 50mm lens image a 3mm object full-frame on a 5.2×3.9mm sensor, and are my distance calculations correct?

Asked 11/3/2023

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I want to photograph a 3 × 3 mm object so it fills the frame on a 5.2 × 3.9 mm sensor. I have a machine-vision camera and a single 50 mm bi-convex lens mounted in a tube. Using the thin-lens formula, I calculated the required magnification as 3.9 / 3 = 1.3, then solved for the object and image distances:

  • object distance a ≈ 88.5 mm
  • image distance b ≈ 115 mm
  • total object-to-image distance ≈ 203.5 mm

Is this the right approach, and would it work in practice with my setup?

Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0

Photography Stack Exchange contributor

2y ago

2 Answers

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I checked your math using a different approach. More years ago, than I care to remember, I needed to calculate the focal length needed to yield a specific magnification with a specific Object to Image distance. I calculated based on 1.3 magnification. Lens 50mm magnification 1.3 Object to Image 203.5mm Lens to Image 115mm Lens to Object 88.5mm

Originally by user44949. Source · Licensed CC BY-SA 4.0

user44949

2y ago

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AI Answer

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Yes—your math is correct for a single 50mm lens forming an image directly on a bare sensor. With magnification m = 1.3, the thin-lens relations give:

  • a = f(1 + 1/m) ≈ 88.5 mm
  • b = f(1 + m) ≈ 115 mm

So the total object-to-image distance is about 203.5 mm.

A few practical caveats:

  • This is a thin-lens approximation. A real bi-convex lens has thickness, so the effective principal planes are not exactly at the lens center. Don’t expect perfect accuracy to fractions of a millimeter.
  • Build in some adjustment travel, especially on the lens-to-sensor side.
  • You do not need a tube length equal to object distance + image distance unless the tube is physically spanning both sides of the lens. What matters is the object-to-lens distance and lens-to-sensor distance.
  • This only applies if your camera has no fixed lens already installed. If it’s a complete camera rather than a bare sensor, the existing lens must be accounted for, and this simple calculation won’t be enough.

UniqueBot

AI

2y ago

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