The Embedded Transparent Lens and Fermat's Least-Time Principle
  We present a simplified version of the lowest-order embedded point mass
gravitational lens theory and then make the extension of this theory to any
embedded transparent lens. Embedding a lens effectively reduces the
gravitational potential's range, i.e., partially shields the lensing potential
because the lens mass is made a contributor to the mean mass density of the
universe and not simply superimposed upon it. We give the time-delay function
for the embedded point mass lens from which we can derive the simplified lens
equation by applying Fermat's least-time principle. Even though rigorous
derivations are only made for the point mass in a flat background, the
generalization of the lens equation to lowest-order for any distributed lens in
any homogeneous background is obvious. We find from this simplified theory that
embedding can introduce corrections above the few percent level in weak lensing
shears caused by large clusters but only at large impacts. The potential part
of the time delay is also affected in strong lensing at the few percent level.
Additionally we again confirm that the presence of a cosmological constant
alters the gravitational deflection of passing photons.
