Is it possible to calculate the effective aperture size by the parameters below?
If yes, what is the equation?
If no, what are the extra parameters needed in order to calculate the aperture size?
Yes. But you don't need sensor size or circle of confusion. The diameter of the effective aperture is the focal length of the lens in millimeters divided by the f-number. The inverse of that is by definition the f-number, so that's all you need.
The aperture size of a lens is a measurement of the actual diameter of diaphragm. The effective aperture is likely grater because probability converging lens elements precedes the diaphragm. Such a design causes the diameter of the aperture to appear to be larger than life. the effective aperture is computed by dividing the actual focal length of the lens by the effective aperture diameter.
You can measure the effective aperture, for yourself by placing tracing paper before the lens. Next, set the lens aperture to any desired f-number value. Now aim a flashlight into the lens from the rear. You will see, projected on the tracing paper, an illuminated circle. Measure this circles diameter and you have computed a imprecise measure of the effective aperture. This value will be good enough for most applications.
We divide the actual focal length by the effective aperture to calculate the f-number. The f-number is only valid for the center of the projected image on film or digital sensor. Should you examine a spot on the projected image that is off center, it will be dimmer. This is because; a circular aperture appears as a circle only on axis. Points off axis are seen, by the film / sensor as if the aperture has a elliptical shape. An ellipse shape has less surface area than a circle thus the resulting projected image from this viewpoint is dimmer.
Also, the actual focal length is only valid when the camera is imaging an object at infinity ∞. Objects closer than ∞ come to a focus further from the lens. When doing close-up work, the working focal length is elongated. The f-number computed using the published focal length will be invalid. This fact known as “bellows factor”, it becomes important when doing close-up and macro work, if underexposure is to be avoided.
A true macro lens has built-in countermeasures to avoid under exposure when working in close.
