Which 17th century French philosopher, mathematician, scientist, and writer showed, by using geometric construction and the law of refraction, that the angular radius of a rainbow is 42 degrees?
History of optics heavenly bodies. "Astronomiae Pars Optica" is generally recognized as the foundation of modern optics (though the law of refraction is conspicuously absent). Willebrord Snellius (1580–1626) found the mathematical law of refraction, now known as Snell's law, in 1621. Subsequently, René Descartes (1596–1650) showed, by using geometric construction and the law of refraction (also known as Descartes' law), that the angular radius of a rainbow is 42° (i.e. the angle subtended at the eye by the edge of the rainbow and the rainbow's centre is 42°). He also independently discovered the law of reflection, and his essay on optics was the
Rainbow the drop's surface normal is . Since the angle of refraction is , Snell's law gives us where is the refractive index of water. Solving for , we get The rainbow will occur where the angle is maximum with respect to the angle . Therefore, from calculus, we can set , and solve for , which yields Substituting back into the earlier equation for yields ≈ 42° as the radius angle of the rainbow. The term double rainbow is used when both the primary and secondary rainbows are visible. In theory, all rainbows are double rainbows, but since the secondary