Huygens principle and wavefronts

Ray optics treats light as straight lines. Wave optics treats it as a wave, which explains effects that rays cannot: interference, diffraction and polarisation.

A wavefront is a surface joining points that vibrate in the same phase, like the crest of a ripple. Rays are lines perpendicular to the wavefronts, showing which way the energy travels.

• A point source gives spherical wavefronts.
• Far from the source (starlight reaching Earth), a small part of a huge sphere is flat: plane wavefronts, with parallel rays.
• A convex lens with a point source at its focus also turns spherical wavefronts into plane ones.

Huygens principle: every point on a wavefront acts as a tiny new source, sending out secondary wavelets. A moment later, the surface touching all the wavelets in front (their forward envelope) is the new wavefront.

Using this, Huygens explained reflection (angle of incidence = angle of reflection) and refraction. When a wavefront enters glass at an angle, the part that enters first slows down first, so the wavefront turns. This gives Snell's law, with n = c/v.

What changes on entering a denser medium (index n):

Example: 600 nm light enters glass with n = 1.5. Its wavelength inside becomes 600/1.5 = 400 nm, but its frequency, 5 × 10¹⁴ Hz, and its colour stay the same.

Light does not lose energy by slowing down: photon energy depends on frequency, which is unchanged.

In glass, n is a little larger for violet than for red, so violet travels more slowly and bends more. This is dispersion.