Feb 16, 2011. Finish Polarization The Radiation Spectrum HW & Questions. LCD Displays. Bees can see polarized light polarization of blue sky enables them to navigate. Humans: Haidinger’s Brush. Vikings: Iceland Spar?.
The Radiation Spectrum
HW & Questions
polarization of blue sky enables them to navigate
Not to navigate (they don’t go far)
Perhaps they can see transparent jellyfish better?
In a transparent object, each wavelength of light is polarized by
a different angle. Passing unpolarized light through a polarizer,
then the object, then another polarizer results in a colorful pattern
which changes as one of the polarizers is turned.
Polarization is also used in the entertainment industry to produce and show 3-D movies. Three-dimensional movies are actually two movies being shown at the same time through two projectors. The two movies are filmed from two slightly different camera locations. Each individual movie is then projected from different sides of the audience onto a metal screen. The movies are projected through a polarizing filter. The polarizing filter used for the projector on the left may have its polarization axis aligned horizontally while the polarizing filter used for the projector on the right would have its polarization axis aligned vertically. Consequently, there are two slightly different movies being projected onto a screen. Each movie is cast by light which is polarized with an orientation perpendicular to the other movie. The audience then wears glasses which have two Polaroid filters. Each filter has a different polarization axis - one is horizontal and the other is vertical. The result of this arrangement of projectors and filters is that the left eye sees the movie which is projected from the right projector while the right eye sees the movie which is projected from the left projector. This gives the viewer a perception of depth.
(- 45 degrees):
Rybicki & Lightman, Section 2.3
What is the spectrum?
Energy / time as a function of frequency
Radians / sec
Define the Fourier Transform of
The inverse is
Take complex conjugate of Eqn. (1):
From Eqn. (a), (b)
Parseval’s Theorem for Fourier Transforms:
Poynting Theorem: Energy /time/area
Integrate over pulse:
Rybicki & Lightman, Chapter 3
Instead of worrying about E and B, we can use the scalar and vector
1 scalar and 1 vector quantity instead of 2 vector quantities.
Relativistic treatment is simpler.
Therefore, there exists a φ such that
what about the others?
For reasons which will become clear in a minute, we re-write this
last equation as
The 4 Equations –th Maxwell equation
GUAGE TRANSFORMATIONS Equations –
(1)-(4) do not determine A and φ uniquely:
one can add the gradient of an arbitrary scalar ψ to A
and leave B unchanged
Likewise E will be unchanged if you add
These are called GUAGE TRANSFORMATIONS
For the Equations –LORENTZ GUAGE we take
so that (3) and (4) simplify to
RETARDED POTENTIALS Equations –
It turns out that the solutions to (5) and (6) can be expressed
as integrals over sources of charge, provided you properly
take into account the fact that changes in the E and B fields
can move no faster than the speed of light.
RETARDED POTENTIALS Equations –
At point r =(x,y,z), integrate over charges at positions r’
where [ρ] evaluate ρ at retarded time:
Similar for [j]