The features of light refraction in liquid crystal cells with a continuously changing director distribution are studied. The theoretical description is constructed within the framework of the geometrical optics approximation. The neighborhoods of the turning points are considered, where due to the variable refractive index the ray smoothly changes the direction of propagation to the opposite one. It is shown that the applied electric field changes the nature of the extraordinary ray refraction. Electrically controlled refraction of light in cells with a planar and hybrid director orientation for incident angles exceeding the angle of total internal reflection is experimentally studied. The dependencies of the turn on and turn off times of the optical response on the applied voltage and the incident angles on the glass -liquid crystal boundary are obtained.