# symmetry-many-slit-paths-phasors-interference.mp4

Chapter section: Wave Propagation and Interference

Caption (verbatim):

Seeing stationarity emerge in closely spaced paths

Image description (verbatim):

Many paths, their complex sum, and the resulting interference pattern

## Before the animation

Chapter lines 1191–1191:

We can repeat the same procedure with many more paths. As the path deviates more from a straight, minimum length path, it has a greater first-order change in phase. (This is the common result from calculus that near a function's minimum, there is no change to the value of the function in the first order of the argument.) When the candidate paths are far from the stationary value, their phases vary greatly, effectively cancelling out their contributions to the total sum. On the other hand, the phases of the paths near the stationary path align and dominate the sum. The green line in the tip-to-tail pane of the animation shows the sum of each of these contributions, giving the amplitude at $B$. The resulting intensity on the projection screen is the square of this magnitude.

## After the animation

Chapter lines 1199–1199:

We can extend this procedure to its limit and include infinitely many screens with infinitely many slits, and recover unobstructed propagation. In the following animation, we start with a plane wave and recover that same wave. This construction, which provides a bridge to Feynman’s path integral formulation of quantum mechanics, has its roots in Huygens’ wavelets from the late 1600s, extended by Fresnel to include interference in the early 1800s.