The interference phenomenon known as the Lau effect is usually produced when two transmission gratings are located in tandem and are illuminated incoherently. This paper extends the study on this effect by analysing the optical arrangement in which the second transmission grating is replaced by a reflection grating. The interference fringes produced under incoherent illumination in this new reflection Lau geometry are, in certain respect, similar to those in the usual transmission geometry. The new set of fringes, however, become changeable in their profile when one of the gratings is subjected to an in-plane translatory motion in the direction perpendicular to the grating lines. The characteristics of the fringe formation phenomenon are examined quantitatively from the viewpoint of the incoherent superposition of multi-diffraction patterns of the gratings. We present a theoretical analysis and a supporting experimental verification of this phenomenon.