Why the direction of propagation of wave is perpendicular to wavefront at each point
Physics Asked by Shivansh J on February 16, 2021
Why is the direction of propagation of a wave perpendicular to the wavefront at each point? I know this sounds intuitively true, but a simple mathematical proof would be very helpful.
If I have an arbitrary point on a wavefront, then as time passes the wavefront expands in space, and it would appear that that point is moving in space. Now the velocity of that point at any instant of time, is said to be in the direction of normal vector of the wavefront at that point. But why?
One Answer
Take a point source
it is a tautology, since the wavefront is radial. One could call it a definition.
Look at the plane wave before the point source. Can there be another defintion of the direction of propagation of the wavefront, except perpendicular? (the image is from the description of the Huygens' principle)
I would consider it a matter of definition. Plane waves can mathematically build any shape.
Answered by anna v on February 16, 2021
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