Why a bigger diameter lens can gather more light.
Consider, on a dark night, you can see the glow of a burning match off in the distance. Your friends standing near you can also see this distant glow. Translated, the light from the match radiates outward in all directions. Your eyes only receive a fraction of its radiated light. For your friends to see its light, some of it must also play on their eyes. If this is true, do you suppose we could use a funnel-like devise and collect or accumulate more of the matches’ light rays? We can! Capturing and accumulating light, and then projecting an image is the job of the camera lens.
Opticians know that big diameter lenses capture more light then small lenses. this principle is used by astronomers. The largest lens ever made is 60 inches (1,524mm) in diameter. Larger is better but the glass lens is thick in the center and thin at the edges. It is believed that a large such lens will crack under its own weight. We can make bigger, but these are mirror lenses, supported from the rear.
Anyway, the bigger the diameter of a lens the more light it can capture. However, the lens must project an image of the outside world onto the light sensitive surface of film or digital sensor. The longer this projection distance, known as focal length, the more magnified the image will be.
Now everything has its pluses and minuses. When we make the focal length long, we get more magnification (telephoto effect). However, with this increased magnification comes a loss of image brightness. This loss can be severe. We need a way to know just how sever this light loss is.
f-numbers to the rescue: The f-number is short for “focal ratio”. When we compare one lens to another, as to image brightness, we use the f-number as a way to make this comparison. We measure the focal length (magnifying power) and the working diameter of the lens called aperture, both in millimeters and divide.
As an example, a 50mm focal length with an aperture of 25mm equal 50 ÷ 25 =2. We call this focal ratio f/2. This method gives us a simple way to compare lenses. Suppose someone has a camera with 500mm telephoto lens with an aperture diameter of 250mm (a big lens). The focal ratio is 500 ÷ 250 = 2 written f/2. Both the 50mm with aperture 25mm and the 500mm aperture 250mm, deliver the same image brightness. In fact, any lens operating at the same f-number as another, will deliver the same image brightness’.
The camera lens is adjustable as to its working diameter. We or the camera’s software make this adjustment. This system mimics the human eye which makes involuntary diameter adjustments based on vista brightness. The colored portion of our eyes, called the iris after the Greek goddess of the rainbow, make this adjustment by altering the pupil diameter.
The f-number system seems complex. It is based on an increment of change that doubles or half’s the amount of light that traverses the lens.
The f-number set from brightest to dimmest:
1 – 1.4 – 2 -2.8 – 4 – 5.6 – 8 – 11 – 22 – 32
Going right cuts the light in half. Going left doubles image brightness, each a 2X change. The f-number intertwines lens aperture (working diameter) with focal length (magnifying power). When we enlarge the aperture diameter we increase the lens’s working area of entry. This sequence sets an increment of adjustment. That increment is a 2X change. The f-number unit is what we use to control exposure via the lens setting and it also controls depth-of-field. The smaller the aperture setting (going right), delivers a greater span of depth-of-field.
To let in more light, the lens must have a larger diameter. It is more costly to make such a lens because the curve of the glass (figure) must be more accurate especially at the edges.
Nobody said this stuff was easy!