The twenty-first century version of Fermat's principle of least time states that an "Electromagnetic wave" such as a ray of light always takes the path of least time. When a ray of light starting at a point P, and traveling in a transparent medium, enters a different medium, it changes direction. This phenomenon is known as refraction. Use optimization techniques, and Fermat's principle of least time to derive both forms of Snell's law (of refraction): 1) n, sin 01 = n2 sin 02 2) sin e1 sin 02 V1 12 Where n1, n2 are the indices of refraction, and v1, v2 are the speeds of light in medium 1 and medium 2 respectively. 0, is the angle of incidence, and 02 is the angle of refraction in medium 2, as shown in the figure. Angle of incidence Incident ray Angle of Medium 1, refraction 02 refractive index ny Refracted ray