 Solution

Without the film, a sharp silicon-water boundary gives the usual Fresnel-like reflectivity governed by its scattering-length-density contrast. If the contrast-matched mixture from part (iii) is used, that ideal interface signal is strongly suppressed.

Polyethylene has a different scattering length density from both matched media. Its two interfaces generate interference oscillations, or Kiessig fringes, in reflectivity versus normal momentum transfer $q_z$. Their approximate spacing isfor $d=100\mathrm{nm}=1000\mathring{\mathrm{A}}$. Fit several fringes, with refraction, roughness and instrument resolution included if necessary, to determine the thickness accurately. Even with unmatched water the film changes the reflection envelope and adds thickness-dependent interference.