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The circle of confusion is not something very familiar for many photographers, and few are aware that it is behind visual effects like blurred city lights. It's time we explained to circle of confusion to everyone.
Whenever there is a point of light in front of your lens, the light coming from it travels through the lens. It is then bent to a matching point behind the lens and those beams of light cross each other, resulting in a focal point. When that focal point falls onto the focal plane, which is actually the film or image sensor, that's when the image is in focus. When you adjust the focus on your lens, the light coming from various distances comes in convergence at different points behind the lens, on the sensor or film.
As you shift focus, that point of convergence moves off the focal plane and turns that small dot of light into a circle. Shift focus in the opposite direction, and the light will diverge and ultimately you get a circle again.
The circle of confusion is therefore the measurement of where a point of light turns into a circle. It is measured in fractions of a millimeter and one of its best uses is in depth of field tables.
To get a clear idea of how the circle of confusion works, watch this video made by thekineticimage.