1997 - the centennial year of the electron - provides a good occasion to publish the first English translation ever made of H.A. Lorentz's doctoral dissertation of 1875. Just 22 years old, Lorentz took up and handled magisterially one major unresolved problem of Maxwell's electromagnetic theory, the reflection and refraction of light. By then the superiority of Maxwell's electromagnetic ether theory over current elastic solid conceptions such as Fresnel's was not nearly a settled issue. In his dissertation, Lorentz strove with considerable success to make it that. Still, he found that neither theory allowed for a satisfactory account of dispersion. One intriguing aspect of Lorentz's earliest scientific achievement (which within two years was to earn him the chair of theoretical physics at Leyden University) is that a range of subjects soon to occupy him for the rest of his life are already clearly foreshadowed in it. So far, Lorentz's first step in science has existed only in the original Dutch, and in a French translation made long ago as part of the Collected Works. Here, the joint translators have striven to provide a fluently readable, full text while preserving the flavor of Lorentz' original language and style.