The camera lens acts like a funnel in that it gathers light from the outside world and projects an image of this world on the flat surface of film or digital sensor. The focal length of a lens is that distance from the lens to the projected image when the subject is an object at an infinite distance. We call this distance infinity symbol ∞. The focal length describes the ability of the lens to magnify. If you double the focal length, say from 50mm to 100mm, the image enlargers 2X (twice). The hitch is, each doubling of the focal length results in a 4X loss in image brightness. This is because the light energy that comprises the previous image is now dispersed over four times more surface area, on film or chip.
Think about asking a kid to fill in, with paint, the outline of a box drawn on paper that measures 1 inch width by 1 inch length. The surface area of this drawn image is 1 square inch. If you enlarge this box to so that it measures 2 inches by 2 inches, the surface area is now 4 square inches. The kid will consume 4X more paint to do this task.
OK, we double the focal length to achieve a 2X increase in magnification. Now we must gain 4X more light gathering power to keep the same image brightness. That translates to a doubling of the working diameter of the lens. If we zoom from 18mm to 300mm, the magnification change is 16.6X.
Say at 18mm focal length the working diameter of a lens is 10mm
Zoom to 36mm focal length, now to keep a constant exposure the working lens diameter must be increased to 10 X 2 = 20mm. (3/4 inch)
Zoom to 70mm focal length, now to keep a constant exposure the working lens diameter must be increased to 20 X 2 = 40mm (1 ½ inch)
Zoom to 150mm focal length, now to keep a constant exposure the working lens diameter must be increased to 40 X 2 = 80mm (3 1/8 inch)
Zoom to 300mm focal length, now to keep a constant exposure the working lens diameter must be increased to 80 X 2 = 160mm (6 ¼ inch)
The point is, the diameter of the glass used to construct this lens makes it expensive to make. Additionally at 300mm, it sticks out 12 inches from the camera body.
Now the 12 inch length if used, technically makes this device a “long lens”. That’s a gadget that will be awkward to use. Our desire is to shorten this lens barrel. We can do this by what by making the front too strong, making the light rays converge too early. Then we add a lens at the rear of the barrel that reduces the strong convergence. The idea is to shorten the barrel making the array less clumsy. If we can shorten and keep the long focal length, we have made a telephoto lens!
After all this, it is our desire that the lens maintain a constant exposure (image brightness) throughout the zoom. We can accomplish if we install a mechanical iris that expands or contracts with the zoom. This has proven to be too costly. Next is to make the front lens array magnify the iris. This array moves with the zoom constantly changing the apparent size of the iris as the lens zooms. This is the design of a modern zoom lens, we have achieved a constant image brightness throughout the zoom.
Now we must concern ourselves with the seven aberrations that plague every lens. How to mitigate each as the lens is zoomed? This is a challenging task now the lens barrel must be fitted with moving lens arrays composed of different densities of glass, some convex, some concave and all moving, some together and some independent.
Yes sir, right away sir, here is your 18mm thru 300mm zoom with a constant aperture. Also sir, here is the bill for this magnificent apparatus.