7.3 Polarization of Light
213
half-life of 10.3 min), producing energetic protons and electrons. 12 The biological
effectiveness of neutrons can be 10 times that of gamma rays of the same energy.
Some muons reach the ground before interacting or decaying, with a flux at the
surface of the Earth of about one muon per second per square centimeter. They cause
a radiation dose to humans of about 0.31 mSv/yr, compared to a total background
radiation dose of 2.4 mSv/yr.
As visible light does penetrate the atmosphere and can be used to form images
which resolve details on objects in sizes above about 10,000 Å, larger life forms
have evolved eyes to take advantages of long-range vision. Since the wavelengths
of radio waves are much larger than the sizes of animals that gravity allows, radio
eyes did not evolve, remaining unknown to life on Earth until Maxwell.
7.3 Polarization of Light
Maxwell’s theory predicted that electromagnetic waves are generated by accelerating charges, such as electrons forced to move up and down in a wire. That
wire becomes an antenna. 13 The electromagnetic wave itself is an oscillation in
the strength of the electric and magnetic fields measured some distance from the
originating charges. The wave moves out from the source at the speed of light. In
the radiation zone (far from the source), the electric and magnetic fields are always
perpendicular to each other and to the direction the wave is traveling.
These properties can be seen in the plane-wave solutions (i.e. single frequency
solutions) given in Eqs. (7.8) and (7.9), and depicted in Fig. 7.1. Electromagnetic
waves can be ‘linearly polarized’ by filtering the electric field oscillation to be along
one direction. The unit vector ε in Eqs. (7.8) and (7.9) is the polarization direction
of that wave. Light containing waves in a coherent mixture of polarizations are said
to be ‘elliptically’ polarized. Light reflecting from shiny surfaces with 90 ◦ between
refracted and reflected waves will be linearly polarized with an axis parallel to the
reflecting surface. Reflection at other angles will make elliptically polarized light. If
light passes through sugar solutions, it becomes, in part, ‘left-circularly polarized’,
which means that the direction of polarization in this light rotates across space,
instead of being fixed in direction across space. Light can be left or right-circularly
polarized. Maxwell’s equations and Einstein’s photon relation E = hf can be used
12 Secondary neutrons cause carbon-14 to build in the atmosphere. Carbon-14 gets incorporated
into plants. When the plants die, their carbon-14 slowly decreases by radioactive decay (with halflife of 5730 years), making carbon-14 an important component in determining the age when the
plant died.
13 The design of an optimal antenna is still an art, because the requirements for directional
sensitivity, efficiency, frequency range, size limitation, and effective segment dimensions as well
as nearby reflector and passive repeater design, are all variables. Curiously, the optimal design for
an antenna which most efficiently receives a wide band of frequencies is a wire in the form of a
fractal. Fractal antennas are used in cell phones.
213
half-life of 10.3 min), producing energetic protons and electrons. 12 The biological
effectiveness of neutrons can be 10 times that of gamma rays of the same energy.
Some muons reach the ground before interacting or decaying, with a flux at the
surface of the Earth of about one muon per second per square centimeter. They cause
a radiation dose to humans of about 0.31 mSv/yr, compared to a total background
radiation dose of 2.4 mSv/yr.
As visible light does penetrate the atmosphere and can be used to form images
which resolve details on objects in sizes above about 10,000 Å, larger life forms
have evolved eyes to take advantages of long-range vision. Since the wavelengths
of radio waves are much larger than the sizes of animals that gravity allows, radio
eyes did not evolve, remaining unknown to life on Earth until Maxwell.
7.3 Polarization of Light
Maxwell’s theory predicted that electromagnetic waves are generated by accelerating charges, such as electrons forced to move up and down in a wire. That
wire becomes an antenna. 13 The electromagnetic wave itself is an oscillation in
the strength of the electric and magnetic fields measured some distance from the
originating charges. The wave moves out from the source at the speed of light. In
the radiation zone (far from the source), the electric and magnetic fields are always
perpendicular to each other and to the direction the wave is traveling.
These properties can be seen in the plane-wave solutions (i.e. single frequency
solutions) given in Eqs. (7.8) and (7.9), and depicted in Fig. 7.1. Electromagnetic
waves can be ‘linearly polarized’ by filtering the electric field oscillation to be along
one direction. The unit vector ε in Eqs. (7.8) and (7.9) is the polarization direction
of that wave. Light containing waves in a coherent mixture of polarizations are said
to be ‘elliptically’ polarized. Light reflecting from shiny surfaces with 90 ◦ between
refracted and reflected waves will be linearly polarized with an axis parallel to the
reflecting surface. Reflection at other angles will make elliptically polarized light. If
light passes through sugar solutions, it becomes, in part, ‘left-circularly polarized’,
which means that the direction of polarization in this light rotates across space,
instead of being fixed in direction across space. Light can be left or right-circularly
polarized. Maxwell’s equations and Einstein’s photon relation E = hf can be used
12 Secondary neutrons cause carbon-14 to build in the atmosphere. Carbon-14 gets incorporated
into plants. When the plants die, their carbon-14 slowly decreases by radioactive decay (with halflife of 5730 years), making carbon-14 an important component in determining the age when the
plant died.
13 The design of an optimal antenna is still an art, because the requirements for directional
sensitivity, efficiency, frequency range, size limitation, and effective segment dimensions as well
as nearby reflector and passive repeater design, are all variables. Curiously, the optimal design for
an antenna which most efficiently receives a wide band of frequencies is a wire in the form of a
fractal. Fractal antennas are used in cell phones.