Re: Difference between interfernce by division of amplitude and wavefront.

Optical set-ups, like Young's slits, the Fresnel bi-prism and Lloyd's
mirror, all create interference by redirecting two parts of a coherent
wavefront so that they later overlap.  These are therefore examples of
"division of wavefront".  In quantum mechanical terms, any given photon has
to be considered to take both paths from source to detector (providing
there is no physical information that one of the paths actually was taken),
and the interference pattern reflects the probability that each photon will
arrive at a particular spot.

A whole different class of interference configurations make use of partial
reflection (or refraction).  In optics this would typically use a
beam-splitter, like an air-glass surface (often partially silvered), where
some proportion of incident photons are transmitted across the boundary,
and the rest reflected.  Again, if the resultant beams are redirected to
overlap with each other, then interference is produced.  These are examples
of "division of amplitude", so named because the amplitude of transmitted
and reflected beams is reduced (and they don't take light from different
parts of the wavefront).  Other kinds of waves can also be partially
reflected in the same way: one only has to think of a sound wave hitting a
wall, where there is both an echo of the sound off the wall, but also
someone on the other side hears the sound because part of the energy
travels through.