The reflection of neutrons at planar surfaces dates back to the mid–1940s when Fermi and Zinn [1] and later Fermi and Marshall [2] determined the sign of the average coherent scattering length bcoA by reflecting a beam of thermal neutrons off a number of flat metal surfaces. Similar experiments were performed by Compton for the determination of the X–ray refractive index [3]. Later, total reflection of cold neutrons was used for guiding them through curved beam tubes to experimental stations at far distances from their source [4]. Finally, ultra–cold neutrons were bottled up via total reflection for measuring their life time [5].