When I originally watched lecture, I was confused by why the half vector is representative of the normal vector, but just when I was about to ask on this slide, I realized it is because on the micro scale, we are treating each bounce as if it is a perfect specular reflection, which means the theta on both sides are the same.

When I originally watched lecture, I was confused by why the half vector is representative of the normal vector, but just when I was about to ask on this slide, I realized it is because on the micro scale, we are treating each bounce as if it is a perfect specular reflection, which means the theta on both sides are the same.