Wave Optics

Lesson

Part 1 — light as a wave: how wavefronts move, why light bends at a boundary, and how two waves can add up to brightness or cancel to darkness.

In this lesson you will

Describe wavefronts and use Huygens’ principle to construct a new wavefront
Prove the laws of reflection and refraction with Huygens’ construction
Explain coherent sources and the conditions for sustained interference

Concept

Wavefronts

A wavefront is a surface on which every point oscillates in the same phase. Energy travels at right angles to it: rays are normals to wavefronts.

Point source: spherical wavefronts.
Line source (a long slit): cylindrical wavefronts.
Very distant source (the Sun, a star): small parts of the wavefront are plane.
Wavefronts one wavelength apart are in the same phase.

Diagram

Huygens’ principle

To find where a wavefront will be a time $t$ later:

Every point on the wavefront acts as a source of secondary wavelets, spreading at the wave speed $v$ .
After time $t$ each wavelet has radius $vt$ .
The new wavefront is the forward envelope (common tangent) of the wavelets. (The backward wave is ignored; a fuller theory shows it is absent.)

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