How does an object's apparent size change with distance from the camera?
Asked 7/17/2013
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If I keep the same object and focal length, how does the object's apparent size in the image change as its distance from the camera increases? Is the relationship linear, logarithmic, or exponential? I plotted size versus distance and it looked curved, so I’m trying to understand the correct mathematical relationship.
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
13y ago
2 Answers
12
Inversely linear is a good approximation.
Imagine a 1,7m tall girl at 1 m distance b. Her head is at point B.
How does the size/length of an object vary with distance?
Let the girl walk away from you. Her size a stays the same. She appears smaller, because she is appearing under a smaller angle. Her angular size changes. Try to imagine it with the picture attached. Using arctangent to calculate her angular size is the correct way. For small angles you can simplify:
Angular size is inversely proportional to its object distance, without using optical devices.
An object on full-field with focal length of 12 mm would be measured incorrectly. An error 2-5% in length measurement may be made. For fish-eye lenses this may be even worse. Hands-on rule: Use the inverse relationship if angular size is smaller than 10°.
Originally by user19191. Source · Licensed CC BY-SA 4.0
user19191
13y ago
0
Generated from our catalog & community — verify before relying on it.
For a given object and fixed focal length, apparent image size is approximately inversely proportional to distance:
image size ∝ 1 / distance
More specifically, a simple thin-lens approximation is:
image size = object size × focal length / object distance
So if the distance doubles, the object appears half as large in the image. If the distance triples, it appears one-third as large.
Why your graph looks curved: 1/distance is not a straight-line relationship when plotted normally, so it can resemble a logarithmic or exponential curve. But it is neither; it’s an inverse relationship (a power law with exponent -1). If you plot image size against 1/distance, you should get a straight line.
A more exact description uses angular size with arctangent, but for normal photography distances and lenses, the inverse relationship is a very good approximation. Very wide-angle or fisheye lenses can introduce noticeable measurement error near the edges of the frame.
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