Chapter 33 Electromagnetic Waves Key contents Maxwell’s equations and EM waves Poynting vector Radiation pressure Reflection, refraction, polarization

EM waves in vacuum In vacuum, Ch 16:

# EM waves of different wavelengths are generated in different ways. Proof of Existence of Electromagnetic Waves Heinrich Rudolf Hertz (1857-1894) set up an apparatus like above and a receiving antenna to measure the produced electromagnetic waves in University of Karlsruhe (now Karlsruhe Institute of Technology) during 1887-88. (Karlsruhe Institute of Technology) # EM waves of different wavelengths are generated in different ways.

Its value is about 3.0 x108 m/s. (defined to be 299 792 458 m/s) The Traveling Wave   Its value is about 3.0 x108 m/s. (defined to be 299 792 458 m/s)

Maxwell’s Rainbow:

Maxwell’s Rainbow: Visible Spectrum:

Energy Transport and the Poynting Vector: Energy flux:

Example, Light Wave rms values of electric and magnetic fields:

(p: momentum; P: pressure) Radiation Pressure: (p: momentum; P: pressure) (Linear momentum of EM waves is equal to energy divided by c. This can be derived from Maxwell equations and the Lorentz force, or, one can understand this from Special Relativity, i.e., U2=p2c2+m2c4 with m=0 for photons.) (total absorption) (total reflection)

Polarization:

Polarization: If the intensity of original unpolarized light is Io, then the intensity of the emerging light through the polarizer, I, is half of that.

Polarization: Intensity of Polarized Light

Example, Polarization and Intensity:

The refraction law is also called Snell’s law. Reflection and Refraction: The index of refraction, n, of a medium is equal to c/v, where v is the speed of light in that medium and c is its speed in vacuum. The refraction law is also called Snell’s law.

Reflection and Refraction:

Reflection and Refraction:

The dependence of n on wavelength Chromatic Dispersion: The index of refraction n encountered by light in any medium except vacuum depends on the wavelength of the light. The dependence of n on wavelength implies that when a light beam consists of rays of different wavelengths, the rays will be refracted at different angles by a surface; that is, the light will be spread out by the refraction. This spreading of light is called chromatic dispersion.

Chromatic Dispersion:

Chromatic Dispersion and Rainbow:

Example, Reflection and Refraction of a Monochromatic Beam:

Example, Reflection and Refraction of a Monochromatic Beam:

Total Internal Reflection: For angles of incidence larger than qc, such as for rays f and g, there is no refracted ray and all the light is reflected; this effect is called total internal reflection. For the critical angle, Which means that

Polarization by Reflection: Brewster angle: The reflected light of an unpolarized incident light is partially or fully polarized in the direction shown in this figure (sunglasses application). When it is fully polarized (always in the direction perpendicular to the plane of incidence), the incidence angle is called the Brewster angle. In such a case, the reflected and refracted lights are perpendicular to each other.

Key contents Maxwell’s equations and EM waves Poynting vector Radiation pressure Reflection, refraction, polarization