In most materials, photoelasticity describes how the optical properties will change under mechanical deformation. In recent work, I have shown that two materials with zero photoelasticity can be combined to make a composite that is strongly photoelastic. Such behaviour is not observed when calculating the optical, acoustic, or thermal properties of composites, where effective values are given by some weighted average of the constituent values. I will examine the role of the unexpected photoelastic contribution in a selection of composite geometries, describing the effect in closed-form. I will also discuss implications for the homogenisation, opto-mechanics, and optics communities.