where the angle $\beta$ is the angle of inclination of the 'teeth' of the grating with respect to the plane of the grating and incident plane monochromatic waves normal to the plane of the grating. I am supposed to determine the angle $\theta$ for which the interference pattern for one 'saw-tooth' has a maximum. The diagram in the mark-scheme is as follows:
where the points $A,B$ both belong to the same 'saw-tooth' and the distance between $A$ and $B$ is $d$. The path difference between the two waves, according to the mark-scheme is given by $\Delta = BF - AE = d \sin \beta - d \sin \theta$. My question might seem trivial, but why are the two (BF and AE) not equal? In other words, shouldn't the two parallel incident waves (incident at an angle $\beta$) be simply reflected from the face of the 'saw-tooth' at exactly the same angle, in accordance with the law of reflection? Why even bother defining $\theta$? What am I missing here?