# Calculating the reflectivity

For a set of slabs, that run from the front layer that the neutrons enter, (), to the bulk layer at the back, (), reflectivity can be calculated by the Parratt formalism. The measured wavevector transfer value is determined at scan time by the angle of the scan and the wavelength: . The incident wavevector normal to the surface in a layer () is related to that in vacuum () by

where is the index of refraction for a layer with total scattering length density .

The Fresnel reflectiviy between any two layers is given by

The total reflectivity is calculated from back to front assuming there is no refelctivity from the backmost () layer () since it is infinite in extent.

The reflectivity of the entire system is given by the reflectivity from the top surface, and is shown in the last line above. Here, and are real valued, and everything else, including , is complex.

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