Paper
Theory of the rainbow
Published Oct 14, 1974 · V. Khare, H. Nussenzveig
Physical Review Letters
117
Citations
1
Influential Citations
Abstract
The rainbow is a bridge between the two cultures: poets and scientists alike have long been challenged to describe it. The scientific description is often supposed to be a simple problem in geometrical optics, a problem that was solved long ago and that holds inter est today only as a historical exercise. This is not so: a satisfactory quantitative theory of the rainbow has been devel oped only in the past few years. More over, that theory involves much more than geometrical optics; it draws on all we know of the nature of light. Allow ance must be made for wavelike proper ties, such as interference, diffraction and polarization, and for particlelike prop erties, such as the momentum carried by a beam of light. Some of the most powerful tools of mathematical physics were devised ex plicitly to deal with the problem of the rainbow and with closely related prob lems. Indeed, the rainbow has served as a touchstone for testing theories of op tics. With the more successful of those theories it is now possible to describe the rainbow mathematically, that is, to pre dict the distribution of light in the sky. The same methods can also be applied to related phenomena, such as the bright ring of color called the glory, and even to other kinds of rainbows, such as atomic and nuclear ones. Scientific insight has not always been welcomed without reservations. Goethe wrote that Newton's analysis of the rain bow's colors would "cripple Nature's heart. " A similar sentiment was ex pressed by Charles Lamb and John Keats; at a dinner party in 1817 they proposed a toast: "Newton's health. and confusion to mathematics. " Yet the sci entists who have contributed to the the ory of the rainbow are by no means in sensitive to the rainbow's beauty. In the words of Descartes: "The rainbow is such a remarkable marvel of Nature . . . that I could hardly choose a more suitable example for the application of my method. " The single bright arc seen after a rain shower or in the spray of a waterfall is
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