In the electromagnetic theory one hears of gauge invariance and the difficulties that result from this. Similar obstacles arise in the general theory of relativity because of the coordinate covariance requirement. The actual nature of the effect of the invariance stipulations is usually not clearly understood because the theories investigated are themselves rather complicated. However, it is possible to pick a simple enough example so that one can clearly see the effect of invariance requirements. It is the purpose of this paper to pick a central problem of geometrical optics and to show what happens as a result of the parameter covariance.