# symmetry-phase-remainder-spinners.mp4

Chapter section: Wave Propagation and Interference

Caption (verbatim):

No separate caption in the chapter.

Image description (verbatim):

Three trials accumulate a quarter turn at the longer wavelength while the shorter wavelength produces many rotations

## Before the animation

Chapter lines 1209–1212:

```math
\phi=\frac{2\pi L}{\lambda}=2\pi n+\theta,
\qquad 0\leq\theta<2\pi
```

Chapter lines 1214–1214:

Away from a stationary path, the phase winds through many cycles over a small range of paths, leaving an effectively random phase remainder so that contributions away from stationary paths largely cancel, while those near stationary paths dominate the sum.

## After the animation

Chapter lines 1220–1220:

In this limit, waves passing through slits behave as rays. A narrow beam through one opening reaches a small region of the screen, much as a thrown ball does.

Chapter lines 1222–1222:

Each path shares its color with its contribution to the tip-to-tail sum. As the wavelength shrinks, an increasingly narrow range of paths around the straight path carries the sum forward.