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Focal length
Each side is a sphere section. They don't have to have the same radius, they are still simple to understand with different radiuses.
The two things you have to have in mind that this does are:
  • converges parallel light to a point at center at distance known as the focal length.
    This is for example why you can use lenses to burn things with Sun rays, which are basically parallel.
    Conversely, if the input is a point light source at the focal length, it gets converted into parallel light.
  • image formation: it converges all rays coming from a given source point to a single point image. This amplifies the signal, and forms an image at a plane.
    The source image can be far away, and the virtual image can be close to the lens. This is exactly what we need for a camera.
    For each distance on one side, it only works for another distance on the other side. So when we set the distance between the lens and the detector, this sets the distance of the source object, i.e. the focus. The equation is:
    where and are the two distances.