PX275 - I2 - huygen's principle and point sources

this is the interference due to differing path lengths from multiple coherent sources
coherent light sources have the same time dependence: $e^{- i ω t} = e^{- i k c t}$
incoherent light sources offer random phases, so there cannot be interference, and the intensities simply add up

huygen's principle

each point on a coherent wavefront can be regarded as a secondary source of waves
the new wave front is the superposition of all (secondary) point sources

a wavefront is a constant phase surface, only well defined for coherent sources
a point source is a secondary source in huygen's principle
a point source is not the same as a plane wave
the intensity is given by: $I (r) = | u |^{2}$

\oint I (r) d r = constant

by the conservation of energy:

4 π r^{2} I (r) = constant

this is the luminosity

⟹ | u | \propto \frac{1}{r}

splitting $u (\vec{r}, t)$ into two parts:

u (\vec{r}, t) = \frac{v (\vec{r}, t)}{r}

where, $r = | \vec{r} |$