Jim Kelley wrote:
Perhaps you will understand it this way: the bright rings have an
intensity which is equal in energy to the sum of the energy in the two
superposed waves. Energy doesn't have to come from anywhere else to
balance the equation.

That just shows that you still don't understand the
interference process. The bright rings have an intensity
which is equal in energy to *double* the sum of the energy
in the two superposed waves. If P1 = P2, the total energy
in the bright rings is P1+P2+2*SQRT(P1*P2) = 2*(P1+P2).

That "extra" constructive interference energy has to come
from somewhere and it comes from the dark areas where
destructive interference occurs. In the dark areas,
P1+P2-2*SQRT(P1*P2) = 0. Taking the average of those two
equations yields (P1+P2) which is the sum of the energy
in the two superposed waves. That's only half as bright
as the bright rings.

The constructive interference energy has to exactly equal
the destructive interference energy or else the conservation
of energy principle is violated and, sure enough, they do
equal each other.
--
73, Cecil http://www.w5dxp.com