Make sure to read chapters 1, 8, and 9 in the Blain Brown cinematography text.
Light is “countable”–quanta. Because photons carry energy, doubling the photons doubles the energy, so light is “linear.”
Our vision system is not, though. It’s closely modeled by a “power law.” As light becomes very bright, it takes significantly more for us to register values as “brighter.” This should be intuitive–consider looking at clouds and they all seem relatively “bright” but actually have value ranges that are bright to extremely bright based on reflecting the sun. We care more about seeing things down near the ground, so have more sensitivity in lesser light intensities. (Because of rod and cone differences, though, our color perception is weaker in very low light).
Image “exposure” with a camera system is linked to the density in film relative to exposure (light over time) or to voltages that are converted to numbers in digital sensors and systems (through analog to digital converters). Aperture (f-stop, a ratio of focal-length to diameter, or the more precise t-stop calculated to account for lost light) dictates how much light reaches the film or sensor. Shutter speed in fractions of a second or in shutter angle (relative to the film frame rate, such as 180-degrees out of 360 at 24 fps resulting in 1/48 sec shutter speed), and sensitivity (ISO/ASA) affect the exposure and where tonal values from real-world irradiance get mapped to the stored image. Controlling where values are mapped in stored formats (physical films or digital files) is all part of the technique and artistry, and methods such as Ansel Adam’s Zone System help devise these mappings using light meters and knowledge of the changes in film or sensor and aperture, shutter speed/angle, and sensitivity. These ranges get mapped when we expose an image to film or a raw digital sensor based file, when they get mapped to a file such as a JPEG, when we display them on our monitors or other devices, when we edit them, when we output or save them, and when they are viewed finally on other display devices. Keeping track of tonal ranges and colors throughout this is a large part of cinematography.