Equation of Wavefront of Plane Wave
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Theorem
Direction Cosine Form
Let $\phi$ be a plane wave.
Let an arbitrary wavefront of $\phi$ be denoted $P$.
Let the direction of propagation of $\phi$ be expressed as:
- $x : y : z = l : m : n$
where $l$, $m$ and $n$ are the direction cosines of the normal to $P$.
This article, or a section of it, needs explaining. In particular: The notation needs to be explained. This will be done on the Definition:Direction Cosines page. $3$D analytic / coordinate geometry still woefully lacking on $\mathsf{Pr} \infty \mathsf{fWiki}$. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |
Then:
- $l x + m y + n z = K$
where $K$ is constant for a given plane wave $\phi$.
This article is complete as far as it goes, but it could do with expansion. In particular: To be expressed in a more convenient form. Propagating along the $x$ axis plus a coordinate transformation may be better for immediate comprehensibility. Coulson's too much like hard work. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |