The Nature of Light and the Laws of Geometric Optics

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Section 35.6

Slide 42

Huygens’s Principle and the Law of Reflection

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

Section 35.6

Slide 43

Huygens’s Principle and the Law of Reflection, cont.

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.

Section 35.6

Slide 44

Huygens’s Principle and the Law of Refraction

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.

Section 35.6

Slide 45

Huygens’s Principle and the Law of Refraction, cont.

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

Section 35.6

Slide 46

Huygens’s Principle and the Law of Refraction, final

The preceding equation can be simplified to

This is Snell’s law of refraction.

Section 35.6

Slide 47

Dispersion

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.

Section 35.7

Slide 48

Variation of Index of Refraction with Wavelength

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.

Section 35.7

Slide 49

Refraction in a Prism

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.

Section 35.7

Slide 50