In the first part of the paper typical quotations are given to show how inadequately the theoretical side of the problem has been treated by earlier writers. The main body of the paper is devoted to the derivation of new, unexpectedly simple functions of the index of refraction which give directly the minimum value of the reflecting power and the associated values of the angles of incidence and refraction when the index is either less than 2−31/2 or greater than 2+31/2. This is followed by paragraphs which present, without detailed proofs, new formulae for the index of refraction and the angle of incidence in terms of the minimum value of the reflecting power, and for the index and reflecting power with the angle of incidence as independent variable. The closing paragraphs make the account complete by dealing with the behavior of the minimum of reflecting power corresponding to normal incidence, that is, to values of the index of refraction falling within the interval 2−31/2 to 2+31/2.
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