## Light takes the quickest route

Let us represent the path of the light by a 'ray' as a line with an arrow tip indicating the direction. A point source of light will in general give rise to rays spreading out from the point, uniformly in all directions. Some, or all, of these rays may then be reflected from certain surfaces, or bent (refracted) by a transparent medium. They can be guided by a lens or mirror and focused to pass through another point. In a complex optical instrument, many lenses and mirrors may repeat the procedure of refraction and reflection, to produce a final image.

Pierre de Fermat (1601-1665), proposed a fundamental law which applies to all light rays:

Fermat's law of least time

When light goes from point A to point B, it will always take the quickest possible path.

Fermat's law is beautiful in its simplicity, and generality. Imagine a light ray travelling by a complicated route through different media, or through an optical instrument. No matter how complicated the path between any two points, it will always choose the quickest possible route! The entire subject of geometrical optics is governed by this one law.

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