Because light is a form of energy, it can be measured. Think of it like a stream of little balls hitting something that counts them. The number of balls in a specific time frame (wavelength) defines the colour of light.
Our eyes see by little cells that contain photosensitive proteins. When light hits the retina, the proteins only react to specific wavelengths and the brain interprets that to form an image.
With photographic film, the film is coated with photosensitive pigments that react to the wavelengths of light. With a bit of extra chemistry, those patterns are printed onto paper so you can see the image.
With digital sensors, millions of pixels detect light and convert it to information, which is then decoded to display on a screen, or print on paper.
So ultimately, the process is pretty similar. It all relies on the properties of light and light-detection.
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