# symmetry-double-slit-candidate-paths-shortwave-arcs.mp4

Chapter section: Wave Propagation and Interference

Caption (verbatim):

Two Path Interference

Image description (verbatim):

The two contributions $ACB$ and $ADB$ from a point source through two narrow openings

## Before the animation

Chapter lines 1089–1089:

Because time is special, $\omega$ is called (angular) **frequency**, not wave number, but from a mathematical perspective, it is just another wave number.

Chapter lines 1091–1091:

Let us now ask the question: how do we find the amplitude at some point $B$ from some initial state of a wave? To do this, we can decompose the contributions into those from individual paths, starting with a very simple model. First, let's construct a point source of single-mode spherical waves emanating from $A$. Then let's add a barrier with two slits through which the wave can pass, $C$ and $D$. This setup allows us to calculate the amplitude at $B$ by combining only the amplitudes associated with the two paths $ACB$ and $ADB$.

## After the animation

Chapter lines 1099–1099:

First, let's figure out how any one straight segment of a plane wave contributes to the amplitude at its endpoint. From:

Chapter lines 1101–1103:

```math
e^{i\left[kx-\omega t\right]}.
```