The correlation function of director fluctuations in a slab of nematic liquid crystal is calculated taking into account a surface energy and external electrical or magnetic field, oriented a liquid crystal in the same direction as a surface. The calculations have been carry out by the method of path integral with the separation bulk and surface degrees of freedom. The planar and homeotropic geometries are considered for positive and negative anisotropy of permittivity or magnetic susceptibility. The detailed results are presented for homeotropic orientation. The obtained results are applied for analyses of possibilities of the light scattering experiments in considered systems. In particular, is shown that there is a possibility to measure an anchoring energy from dependence of light scattering intensity on the value of applied magnetic or electric field.