

Interference and Energy Density
Name: Eric D.
Status: educator
Age: 50s
Location: N/A
Country: N/A
Date: 4/22/2003
Question:
I understand the effects of constructive & destructive interference relative to
light waves (e.g. Young's doubleslit). My question is, when two light waves of the same
wavelength destructively interfere, where does the wave's energy go? Is the energy density at
the point of interference zero?
Replies:
Energy is always conserved (when people say we should conserve energy to save the environment,
they really mean we should reduce entropy. But that is another question  feel free to ask).
Energy, however, can be redistributed. In Young's double slit experiment, the light intensity
(power) goes like cos^2 of the angle from the optic axis. At the maximum (cos^2 = 1), the
intensity is four times the intensity from one slit, which is twice the sum of the intensities
if the two slits were independent. Since the average of cos^2 is 1/2, the average intensity is
exactly what it would be if there were no interference.
So the energy density (intensity) is zero where the destructive interference is complete and
exactly large enough elsewhere so the average comes out to conserve energy.
This is, of course, true for all kinds of interference. Energy is always
conserved.
Dick Plano
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Update: June 2012

