14.1 Reflection, Refraction, Wavefronts, and Rays

A wavefront is a surface of constant phase. Rays are constructed lines normal to those wavefronts, pointing along energy transport. In homogeneous media this relationship is straightforward: equally spaced wavefronts imply constant wavelength and straight rays. At boundaries, wavefront orientation changes and the ray angle changes with it.

It is useful to switch between these views. Wavefront diagrams make spacing and wavelength changes visible. Ray diagrams make angle relations and Snell calculations efficient. Treat them as two projections of one phenomenon, not as separate topics.

Specular reflection requires surface irregularities much smaller than wavelength. If roughness is comparable to or larger than wavelength, different local normals produce many reflected directions and the reflected wavefront coherence is lost. This is why smooth mirrors preserve images while rough surfaces scatter.

At the interface, boundary points are driven at one common temporal rate, so frequency must remain continuous across media. Because v = f lambda and f is fixed, any speed change appears as a wavelength change. Slower medium means smaller wavelength and bending toward the normal for incidence from the faster medium.

This frequency-invariance idea prevents many errors. Students often assume light color changes when entering glass because wavelength changes, but observed color is tied to frequency. Wavelength adjusts to medium speed while frequency remains source-determined.

For incidence from denser to less dense optical medium, the refracted angle grows with incident angle and reaches 90 degrees at the critical angle. Beyond that angle no propagating refracted ray exists, so all power is reflected. Optical fibers exploit this effect to confine light over long distances with low loss.