Fermat’s minimal time principle involves extremizing total time traveled by light by assuming straight line motion in a medium and writing time = distance / speed. It may be applied to examples such as a stationary or constantly moving mirror (in the y direction) or refraction. As shown in (1) to extremize one must take a derivative of time with respect to an invariant spatial variable. This leads to a conservation law which is equivalent to conservation of momentum in the direction of the invariant spatial variable as argued in (1). The wave dispersion relation velocity = frequency * wavelength may be written as E=pc for a photon using Maxwell’s equations and averaging. Next c may be written as x/t yielding: A= 0 = -Et+px where x/t =E/p = c (in a vacuum). In such a case dA/dx partial = p. For three dimensions, px is replaced with px x + py x + pz z. If x is the invariant variable as in reflection/refraction problems (which do not contain z) then dA/dx partial = px which is a conserved quantity (from Fermat’s principle or first principles). If one does not use a partial derivative then: 0=dA/dx = -E dt/dx + (px) where x is the invariant variable. For a refraction problem for which E is the same in both media: 0 = -E dt1/dx + (p1x) -E dt2/dx + (p2x). With conservation: p1x =p2x one obtains Fermat’s principle: dt1/dx + dt2/dx=0. For a constantly moving mirror in the y direction matters are a little more complicated. E1, p1 and E2, p2 differ with the speed of light being c because there is one medium. V is the speed of the mirror in the negative y-direction. There, however, exist two relative speeds in the problem along the incident and reflected ray directions namely: v(relative a) = c- vcos(A) and v(relative b) = c+ vcos(B) where A and B are the incident and reflected angles measured from the y-axis. If one uses (E1 special) = p1 v(relative a) and a similar expression for p2 then (E1 special) and (E2 special) are equal. There is still spatial invariance in the problem and (E1 special) = p1 (v(relative a) together with (E2 special) = p2 v(relative b) is equivalent to Fermat’s principle as will be shown.