The qualitative situation is pictured in Fig.14.13,
which shows a "snapshot" of two outgoing spherical^{14.25}waves and the "rays" ( directions) along which
their peaks and valleys (or crests and troughs, whatever) coincide,
giving *constructive interference*. This diagram accompanied
an experimental observation by Young of "interference fringes""
(a pattern of intensity maxima and minima on a screen some
distance from the two sources) that is generally regarded as
the final proof of the wave nature of light.^{14.26}

The mathematical criterion for constructive interference is
simply a statement that the difference in path length,
, for the two "rays"
is an integer number of wavelengths ,
where the subscript on is a reminder
that this will be a different angle for each value of :

Conversely, if the path length difference is a

- . . . ballet.
^{14.24} - This notion of being "in phase" or
"out of phase" is one of the most archetypal metaphors in
Physics. It is so compelling that most Physicists incorporate it
into their thinking about virtually everything. A Physicist at a
cocktail party may be heard to say, "Yeah, we were 90
out of phase on everything. Eventually we called it quits."
This is slightly more subtle than, " . . . we were 180
out of phase . . . " meaning diametrically opposed, opposite,
cancelling each other,
*destructively interfering*. To be "90 out of phase" means to be moving at top speed when the other is sitting still (in , this would mean to have all your energy in*kinetic*energy when the other has it all in*potential*energy) and*vice versa*. The and fields in a linearly polarized wave are 90 out of phase, as are the "push" and the "swing" when a*resonance*is being driven (like pushing a kid on a swing) at maximum effect, so in the right circumstances "90 out of phase" can be productive . . . . Just remember, "in phase" at the point of interest means*constructive interference*(maximum amplitude) and "180 out of phase" at the point of interest means*destructive interference*(minimum amplitude - zero, in fact, if the two waves have equal amplitude). - . . . spherical
^{14.25} - OK,
they are
*circular*waves, not spherical waves.*You*try drawing a picture of spherical waves! - . . . light.
^{14.26} - Young's classic experiment is in fact the archetype for all subsequent demonstrations of wave properties, as shall be seen in the Chapter(s) on QUANTUM MECHANICS.

Jess H. Brewer - Last modified: Sun Nov 15 21:40:36 PST 2015