Success at making a good picture has many ingredients. Getting the exposure “correct” is surely one key factor. As you know, the camera lens collects the light reflected off the subject. This light transverses the lens in such a way that an image of the outside world is projected on a screen inside the camera. It is this projected image that is recorded by the camera. The brightness of this projected image must be within certain limits. If it is too dim, an under-exposure results and the resulting image will be too dark. If the projected image is too bright, an over-exposure results and the picture will turn out too light.
How can the photographer or the automation built into the camera control the brightness of the image projected by the lens? The modern camera has a built-in light-measuring sensor. Armed with this information, the camera automatically or the photographer manually makes an adjustment. The result is a correct exposure, not too dark, not too bright.
There are several ingredients (adjustments) that can be manipulated to get the exposure correct. The main one is the working diameter of the lens. You see, the lens acts like a light funnel in that it gathers light. The greater the diameter of the lens, the more light it captures. The camera lens has a built in adjustable aperture that changes the working diameter of the lens. This action mimics the human eye. Our pupil in our eye does the same thing.
Now, matters pertaining to the lens are a little complicated. The brightness of the projected lens has another key ingredient. This is the focal length of the lens. When the lens is made, the distance the image-forming rays travel from lens to screen must be determined. This is called the focal length. Long focal lengths magnify like a telescope, short focal lengths deliver a wide-angle view. Now the brightness of the projected image is intertwined. We are talking working diameter (aperture) intertwined with focal length.
Because there are zillions of cameras, each with lenses that are different, it is nearly impossible to set the lens to always deliver the correct projected image brightness.
Math to the rescue: If we divide the focal length of the lens by the working diameter, we get a value we call the focal ratio. This number takes into account the two intertwined values. The result is a single number that tells us or the camera’s automation how to set the working diameter of the lens.
When we adjust the working diameter to suit the brightness of the scene, we are adjusting the focal ratio. We just say f-number or f/number or just “F” for short.
The f-numbers are a number set that allows the camera to be adjusted by doubling or halving the light energy projected on the screen inside the camera.
Here is the f-number set from brightest to dimmest:
1 – 1.4 – 2 – 2.8 – 4 – 5.6 – 8 – 11 – 16 – 22
Each going right is its neighbor on the left multiplied by 1.4. This number set pertains to the geometry of circles. Multiplying or dividing the diameter of any circle by 1.4 computes a revised circle with a capture area change of 2X.
We use the f-number to help set our lens for correct exposure. We cannot use the f-number to help us determine the distance camera to subject.