• Particle
• Newton
• Wave
• Huygens
• Maxwell
• equations in differential form



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• uncoupling the equations results in second order differential equations for E and B that are identical to the wave equation discussed earlier in the semester with a speed for the waves equal to
• The results can be summarized



1. The directions of oscillation of the electric and magnetic fields are perpendicular to the direction of propagation of the wave. (EM waves are transverse waves)
2. The electric and magnetic field oscillate in perpendicular directions.
3. The vector product of the electric field and the magnetic field gives the direction of propagation of the wave.
4. The electric and magnetic fields are sinusoidal.
1. 



• These electric and magnetic field carry energy and momentum.
• Poynting vector
• vector representing the rate of energy transfer per unit area



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• The intensity, I, is defined as the time average of the Poynting vector and is equal to
• Radiation pressure
• change in momentum for light



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• Young
• double slit experiment (Chapter 36)
• Speed of Light
• Galileo
• possibly infinite
• Roemer
• eclipsing moons of Jupiter
• 2.1 x 10⁸ m/s
• Fizeau
• rotating wheel
• 3.1 x 10⁸ m/s
• Begin by treating light as a wave.
• Huygen's Principle
• wave front composed of wavelets
• distance between wave fronts = d = c Dt

• Ray Approximation
• path of light is represented by arrows perpendicular to wave front.

• Waves exhibit
• Reflection
• Refraction
• Interference
• Diffraction
• Polarization
• but remember
• Speed of light is very fast.
• Wavelengths are very short.
• Reflection
• Specular
• smooth surface
• "bumps" < l
• Diffuse
• rough surface
• "bumps" > l

• wave fronts strike boundary             wavefronts reflect from boundary

• How does the incident angle compare to the reflected angle.
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• look at two rays



• compare the two triangles indicated






• If we can find a relationship between q₁ and q₁' then we also have a relationship between q_i and q_r. That is q₁ + q_r = 90^o and q₁' + q_i = 90^o



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Law of Reflection: The angle of incidence equals the angle of reflection.

• Refraction
• Light passes into material
• speed changes
• v < c (always)
• Index of Refraction (n)
• n = c/v
• n > 1 for any other material



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• Total Internal Reflection
• We can solve Snell's Law to predict the angle of refraction for a particular boundary





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• If n₂ > n₁, (light moving from a material with a low index of refraction to a material with a high index of refraction) we have no problems but
• if n₁ > n₂,
• it is possible that is greater than one and the arcsin is undefined for an argument greater than one.
• when light travels from a material with a high index of refraction to one with a low index of refraction, there is a critical angle, such that if the incident angle is greater than this critical angle, the light will not be refracted.
• to find this critical angle



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• When the angle of incidence is greater than the critical angle, no light will be refracted. All of the incident light will be reflected back into the material. This phenomena is called total internal reflection. Total internal reflection is possible only when n₂ < n₁.
• Dispersion
• the index of refraction for a material varies with wavelength,
• different colors of light are refracted by different amounts
• Prism
• small wavelengths are bent more than longer wavelengths