What does focusing mean in the thin-lens formula 1/u + 1/v = 1/f?
Asked 3/30/2020
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I’m trying to understand what “focusing” means in relation to the thin-lens formula:
1/u + 1/v = 1/f
where u is the object distance, v is the image distance, and f is the focal length.
Does focusing simply mean making both sides of this equation equal, or does it refer to adjusting the lens or sensor position so the image forms sharply on the sensor/film?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
6y ago
2 Answers
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Both sides of the formula are always equal (for theoretical, thin lenses; for real lenses, the formula is only an approximation). What it says is where you should place the image plane (the film or the sensor) to have a sharp image.
In practice
- focal length f is fixed (because you have a prime lens, or because you have choosen the desired focal length of your zoom lens)
- the object distance u is also fixed (almost: it changes a bit when moving the lens for changing focus)
- then it follows there is one specific image distance v
Focusing means changing the distance between lens and film/sensor so that it matches v.
Again, only approximately because real lenses are not theoretical thin lenses; also focusing generally moves the lens so that object distance u changes a bit.
Originally by user32390. Source · Licensed CC BY-SA 4.0
user32390
6y ago
0
Generated from our catalog & community — verify before relying on it.
For a theoretical thin lens, the equation is always the relationship between object distance (u), image distance (v), and focal length (f). Focusing does not mean “making the equation true” — it means placing the sensor/film at the image distance v required for the subject distance u and focal length f.
In practice, if the focal length is fixed and your subject is at a certain distance, there is one corresponding image distance where that subject will be sharp. Focusing is the act of moving the lens elements or lens-to-sensor spacing so the image forms exactly on the sensor/film plane.
If the sensor is not at that required image distance, the subject appears out of focus because a point in the scene is rendered as a blur instead of a point.
Real camera lenses are more complex than ideal thin lenses, so the formula is only an approximation, but the basic idea is the same: focus means adjusting the optical system so the subject’s image lands sharply on the sensor.
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