Or maybe only some types of lenses work like that?
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All lenses work like that. The basic idea is that light changes direction when it crosses an interface (place where substances change, like from air to glass, and back from glass to air), and if that interface is not flat, then the light that hits the surface at different locations will turn to different directions (how much depends on the light wavelength and the nature of the different materials). Lenses only work as magnifying (or shrinking) devices because they are made to concentrate the light down to a point.
The very reason that lenses are used is because of this very detail, that we can concentrate light from a wide area and focus it down to a small area. It is a form of magnification. Thus, your piece of film does not have to be the size of whatever you are trying to image. The lens shrunk it all down to fit on that small square.
The distance behind the lens (far side from whatever is being looked at) when the image is perfectly focused to the size of the viewer depends on a lot of things. The important thing to consider though, is that the light is no longer coming in parallel, but that the lens has forced it into a cone shape, and the “focus” point is the point of that cone. This is where ALL the light will come together.
When you take an image via a camera, you do not want to capture the point where ALL light comes together (like burning ants with a magnifying glass), but where the are of image being taken matches the down-size area of the film square (or whatever is used). You have to focus it to that plane (move the lens forward or backward a bit) or the different light waves do not match and the image is blurry (light comes in from different parts of the lens to the same place, so looking backward, you see the thing at different places, it is blurred).
Poorly-made lenses, including the human eye, can fail to focus to a point, and instead the zone of focus is a star (t-shape) or a linear blob. This aberration to the image is called astigmatism, and people like me who suffer from this problem do not see lights as points, but instead they look like lines or the letter t in detail, unless we are wearing glasses to help fix it. So we squint, to squeeze our eye lens and change its shape a little in an effort to get rid of the blurriness.
And that is about all I can do for basic optics without paper to draw on and show you how the light behaves and why there is a focal point in an ideal lens, and taking you to a wave tank and playing with water waves and how changing depths causes them to “Bend”.
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