Visualizing Plane Waves
Highlights of the activity
- This small group activity is designed to help upper-division undergraduate students visualize plane waves.
- Students work in small groups are given a two-dimensional vector $\vec{k}$ and are asked to calculate the value of $\vec k\cdot\rr$ for each point on a grid of points and then draw the set of points with constant value of $\Vec k\cdot\rr$ using rainbow colors to indicate increasing value.
- The whole class wrap-up discussion includes group presentations where students are asked to describe the set of points of constant $\Vec k\cdot\rr$ in three dimensions, the set of points of constant $\cos(\Vec k\cdot\rr)$, and the set of points of constant $\cos(\Vec k\cdot\rr-\omega t)$; allowing students to visualize what's planar about plane waves. For students that have studied complex numbers, a similar set of questions involving the complex exponential versions of these same expressions is also appropriate.
Reasons to spend class time on the activity
This activity was developed when a faculty member complained that senior-level students in an optics class were not aware of what was “planar” about a plane wave, i.e. that on a plane perpendicular to the direction of propagation, all the values of the field are constant.