How are object distance, image distance, and focal length related in a lens?
Asked 12/9/2024
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Using an optics simulator, I noticed that for a convex lens: when the object is at 3f the image forms at 1.5f, at 2f the image forms at 2f, and at 1.5f the image forms at 3f. Is this relationship true for camera lenses as well, and what formula describes it?
Originally by Bram. Source · Licensed CC BY-SA 4.0
Bram
1y ago
2 Answers
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Conjugate Distances: F is the focal length of the lens u is the lens to object distance v is lens to projected image distance
1/F = 1/u + 1/v (called the lens maker formula)
Suppose a 100mm is mounted and subject is 2 meters (2000mm distance) 1/100 = 1/2000 + 1/v 0.010 = 0.0005 + 1/v Solve for v 0.010 – 0.0005 = 0.0095 thus v= 1/0.0095 1/0.0095 = 105.263mm Explanation: The focal length F is a measurement made when the camera is working a subject located at a far distance such as a distant mountain (object at infinity ∞).
When working objects that are near to the camera, you must focus the camera by racking the lens further away from the camera sensor. In other words, it will end up being situated at a lengthier distance than the focal length F. In this case, the distance lens to sensor will be located 105.3mm from the camera sensor. If the subject were at infinity, this lens would be located 100mm from the camera sensor.
Originally by Alan Marcus. Source · Licensed CC BY-SA 4.0
Alan Marcus
1y ago
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The basic relationship is the thin-lens equation:
1/f = 1/o + 1/i
where f is focal length, o is object distance, and i is image distance (distance from the lens to the image plane/sensor).
Your examples fit this exactly:
- o = 3f gives i = 1.5f
- o = 2f gives i = 2f
- o = 1.5f gives i = 3f
For a subject at infinity, 1/o becomes 0, so i = f. As the subject gets closer, the lens must be moved farther from the sensor, so image distance becomes greater than the focal length.
This is a very good approximation for a simple thin convex lens. Modern camera lenses are more complex, with multiple elements and principal planes, so the distances are not always measured from the physical front of the lens. But the same conjugate-distance relationship still describes focusing behavior in principle.
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