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According to thin lens optics, an object focused at infinity should correspond to the sensor position exactly at F, which is the focal length of the lens. It also means that the image of every point in the scene will be diminished to a single point.

I understand that a double gauss lens does not ideally behave as a thin lens, and also that 'infinity focus' can mean different things (a range of distances where everything is in focus, focusing so far away that everything is in focus etc). However, when I focus my camera to its far end of the focus ring, is there a way to determine how far away the sensor is from F? Or is it safe to assume that it is at F? And if so, how does one understand the magnification (everything turning into a small point) at F?

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Does focusing at infinity mean the sensor is at F?

Yes. The definition of focal length is that it's the distance from the optical center of the lens to the image plane when the lens is focused at infinity.

an object focused at infinity should correspond to the sensor position exactly at F

True, although it's obviously the lens that moves and not the sensor.

It also means that the image of every point in the scene will be diminished to a single point.

No, it doesn't mean that at all. I can see how you'd get that idea, since simple lens diagrams tend to show two or three horizontal rays converging at the focal point, but in reality light rays are coming from all points inside the field of view, which means they're coming in at a range of angles. Rays coming in at different angles converge at different points, and together all those points form the image plane.

when I focus my camera to its far end of the focus ring, is there a way to determine how far away the sensor is from F?

As discussed above, with the lens focused at infinity, the distance from the optical center to the sensor is the focal length (usually written as ƒ). Just know that lenses typically have a focal length that's slightly different from the nominal focal length -- your 50mm lens might actually be a 49.3mm lens or a 51.4mm lens, but it's still known as a 50mm lens because that's a standard focal length that gets the idea across just fine.

And if so, how does one understand the magnification (everything turning into a small point) at F?

When a of light enters one kind of material from another, like from air into glass, that ray is bent by some amount. This is refraction. How much the ray is bent depends on several factors: the angle of incidence, the refractive indices of the materials, and to some degree the color of the light. But the rays coming from different angles don't all get bent so much that every ray ends up converging at the same point. An easy way to see that, if you're imagining a thin double-convex lens like you typically see in diagrams, is to consider all the rays that pass through the point that's located at distance F in front of the lens. Those rays end up exiting the lens so that they're parallel and don't converge at all, for exactly the same reason that parallel rays entering the lens converge at the focal point. If you can see that, then you know that rays coming from different parts of the scene, i.e. different directions, get mapped to different points in the image.

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    The definition of focal length is that it's the distance from the optical center of the lens to the image plane when the lens is focused at infinity.” Actually it's not the optical center, it's the image-side principal point. The principal points are coincident with the optical center only in a thin lens, which a photographic lens never is. – Edgar Bonet Mar 10 '16 at 16:52
  • @EdgarBonet Thanks for that correction. I'll edit to point to your comment in a little while. – Caleb Mar 10 '16 at 17:19
  • although it's obviously the lens that moves and not the sensor. The Mamiya Six -- not to be confused with the Mamiya 6 -- focused by moving the film plane. It is said that this simplified the mechanical connection between the focusing mechanism and the rangefinder. – user50888 Sep 12 '17 at 22:12
  • Also note that many lenses will actually focus a little bit past infinity, so you can't always rely on just turning the focus ring all the way round. The extra travel allows for thermal expansion/contraction, and may (I think) help with some autofocus schemes. – JerryTheC Sep 12 '17 at 22:14

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