Focal Length as it relates to Field of View

Question

I understand that in physics, for a converging lens, the focal length is based on the refractive index of the lens material and its curvature. However, I started reading a bunch of photography articles and got to the topic of FOV. All of the articles I have come across provide a similar visual and formula to the one below...

However, this defines focal length as the distance from the lens to the image sensor which would mean it could change. This doesn't make sense to me as I thought the focal length was a property intrinsic to the lens itself. I am looking for clarification as to why there are two different distinctions here and why photography talks about focal length in this manner? The only explanation I could think of is that usually, we are focusing on objects so far past the 2F point that the resulting image location of our desired objects are always located so close to the 1F point that the difference in FOV angle would be negligible (because the distance between lens and sensor would be close to the actual focal length of the lense)?

Answer 1

The way the formula is given, implicitly tells us that an object at "infinite" distance has been focussed. And that's the situation assumed when writing the lens or camera data sheet.

Classical focussing mechanisms work by moving the whole lens farther away from the sensor plane. This way, the actual lens / sensor distance increases, and by replacing the value f in the formula with this distance, the FOV angle decreases.

But with modern lenses, it's no longer that easy. They often focus by moving only some of the internal elements, this way not only affecting the lens / sensor distance, but also the focal length. With these designs, the focal length no longer is a fixed, intrinsic property of the lens, but varies by a few percent.

Typically, as long as you're not doing macro photography, your objects are so far away that the difference in lens / sensor distance or focal length doesn't matter very much.

Answer 2

The focal length of a lens definitely is a property of the lens. The diagrams you show above are for two different setups with imaging devices and lenses at separate distances. Perhaps the camera has a mechanism where the lens can be moved relative to the imaging device? Like you were focusing the image.

Answer 3

The focal length is defined as the length where all rays come together for an object placed at infinity. That's why you have to adapt your eye lenses if you look at things nearby. Looking at a faraway object (for a normal eye lens) doesn't require any effort. The faraway object is practically at infinity and when it comes closer to your eye, your eye lens must make its curvature stronger.