The law of reflection can be derived from Huygens’s principle.
AB is a plane wave front of incident light.
The wave at A sends out a wavelet centered on A toward D.
The wave at B sends out a wavelet centered on B toward C.
AD = BC = c Δt
Triangle ABC is congruent to triangle ADC.
cos g = BC / AC
cos g’ = AD / AC
Therefore, cos g = cos g’ and g = g’
This gives θ1 = θ1’
This is the law of reflection.
Ray 1 strikes the surface and at a time interval Δt later, ray 2 strikes the surface.
During this time interval, the wave at A sends out a wavelet, centered at A, toward D.
The wave at B sends out a wavelet, centered at B, toward C.
The two wavelets travel in different media, therefore their radii are different.
From triangles ABC and ADC, we find
The preceding equation can be simplified to
This is Snell’s law of refraction.
For a given material, the index of refraction varies with the wavelength of the light passing through the material.
This dependence of n on λ is called dispersion.
Snell’s law indicates light of different wavelengths is bent at different angles when incident on a refracting material.
The index of refraction for a material generally decreases with increasing wavelength.
Violet light bends more than red light when passing into a refracting material.
Since all the colors have different angles of deviation, white light will spread out into a spectrum.
Violet deviates the most.
Red deviates the least.
The remaining colors are in between.