Ysarex
Been spending a lot of time on here!
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Read Helen's post again. You're talking about the projected cone of light coming off the back of the lens. That is not a function of focal length but is a function of the lens design type. Focal length is pragmatically related because with the lens in focus that cone of light will project a circle at the film/sensor plane of a given diameter. If the diagonal of the film/sensor doesn't fit inside that circle you've got a problem or a permanent instagram filter.
The focal length determines at what distance the lens will be from the film/sensor when the lens is focused. One focus distance is unique and particularly important: infinity. At that focus distance the lens will be closest to the film/sensor and the projected circle will be the smallest. The film needs to fit inside the circle at that point.
As the lens is focused on closer and closer subjects it moves away from the film/sensor and so the diameter of the circle at the film plane increases. The angle of that cone of light is staying constant. Think of a flashlight pointed at a wall and start backing up -- the projection circle gets larger while the angle of the cone of light stays the same.
The spread or angle of the cone of light projected from the back of the lens is not the lens's focal length and is not a factor in calculating field of view or angle of view. Those values are used to determine how much of the 360 degree world in front of you the lens is going to record and they require the film/sensor size to make that determination.
We can use lenses on cameras such that the projected circle from the lens at the film/sensor plane is much larger than needed to cover the film/sensor. Once the film/sensor is selected, it's size along with the focal length will determine the angle of view.
Joe
