It is shown that any stationary three-dimensional velocity field or magnetic field is a potential field in the two dimensional subspace of the Bernoulli surfacesS(Q) or isobaric surfacesS(p), respectively. From this it is shown that the streamlines and the lines of force follow the optical ray paths inS(Q) andS(p) for indices of refractionvandB, respectively. This formal analogy shows how the lines are refracted by variations of the pressure applied by the fluid and field on either side. In particular, it is shown howcontinuousvariations of the pressure producediscontinuities(bifurcations) in the field, forming tangential discontinuities.