This hypothesis to explain why Becke Lines form requires that grain edges be vertical, which in a normal thin section most grain edges are believed to be more or less vertical.
With the converging light hitting the vertical grain boundary, the light is either refracted or internally reflected, depending on angles of incidence and indices of refraction.
Result of refraction and internal reflection concentrates light into a thin band in the material of higher refractive index.
If nmin > noil the band of light is concentrated within the grain.
If nmin < noil the band of light is concentrated within the oil.