POLARIZATION
OBJECTIVES:
**explain polarization
**understand how light can be polarized
**state & apply Malus’ law
**state & apply Brewster’s law
**understand optical activity & optically active substances
**outline some apps of polarized light including structure & operation of LCDs
--only applies to transverse waves; there are an infinite # of possible directions for the oscillations, all at
90 degrees to the energy transfer direction
--a wave that is plane polarized is one that only has 1 direction of oscillation; i.e., for EM waves, electric
field always lies in the same plane as the wave propagates
--e.g., radio waves used in broadcasting often polarized either horizontally or vertically; versus light from
a standard light bulb that is not polarized (means oscillations of the electric field associated w/ the light
take place in all directions – possible to be partially polarized, meaning that the electric field oscillations
are more common in 1 direction than in all other directions
--also, can add 2 plane-polarized waves together to create a wave whose plane of polarization varies,
said to be elliptically or circularly polarized depending upon phase of the 2 waves
--Polaroid: simplest method of polarizing light; man-made material consisting of long chain molecules
aligned together – chains absorb light that has its electric field in the same direction as chains & only
allows through light w/ an electrical field at 90 degrees to the chains – review advantages
--some materials (e.g., sugar solutions) are optically active, meaning that he plane of polarized light is
rotated as it passes thru the material – the rotation is a result of the interaction btwn the molecules in
the material & then incident light – the degree of rotation is measured using 2 polarizers, one of which is
called an analyzer – a polarimeter is used to find the maximum intensity of the transmitted light by
measuring the angle thru which the plane of polarization is rotated (depends upon length of sample &
its concentration
Polarization Math Calcs:
Malus’ Law (reduction of the intensity of transmitted light by a polarizer): I = I sub o * cos squared
theta – I is transmitted intensity and is proportional to the square of the amplitude – I sub o is the
intensity of the plane-polarized light; theta is the angle btwn the direction allowed by the analyzer & the
electrical field direction of the polarized light – analyzer only allows 1 component direction of the
electrical field thru; when theta = 0 (when the electric field is along the transmission axis), then I = I sub
o – when theta = 90 degrees (when electric field is at right angles to the transmission axis), then I = 0
Q1: Vertically polarized light of intensity I sub o is incident on a polarizer that has a transmission axis at
theta = 30 degrees to the vertical. The transmitted light is then incident on a 2nd polarizer whose axis is
theta = 60 degrees to the vertical. Calculate the factor by which the transmitted intensity is reduced.
A1: Passing thru 1st polarizer: I = I sub o *(cos squared) theta = I sub o * (cos squared) 30 degrees =
3/4 * I sub o
The 2nd polarizer has its transmission axis at theta = 30 degrees to the 1st: I = ¾ * (cos squared) 30
degrees = 9/16 I sub o
Thus intensity reduced by a factor of 9 /16
Brewster’s Law (polarization by reflection – application of Snell’s law): incident angle + refracted
angle = 90 degrees; n of refracted material = sin incident angle / sin refracted angle = sin incident angle /
cos incident angle = tan incident angle; if the transmitted ray & reflected ray are at right angles to one
another, then the reflected ray is totally plane polarized
Q2: Calculate the Brewster angle for light incident on the surface of the water. The refractive index for
water is 1.33.
A2: Applying Brewster’s law: tan (Brewster’s or polarizing angle) = refractive index of entering medium /
refractive index of incident medium = 1.33 / 1.00  inverse tan (1.33) = 53.1 degrees.
So angle of refraction, theta sub r, for an angle of incidence equal to the Brewster angle, theta sub B, is
expected to be 90 degrees – theta sub B = 36.9 degrees.
Check using Snell’s law n sub 1 * sin theta sub B = n sub 2 sin theta sub r.
Examples of Polarization:
1-Polaroid Dark Glasses: arranged to only transmit light that has a vertical electric field so hat intensity
of all reflections from horizontal surfaces will be greatly reduced & thus reflected light, or “glare”, will be
reduced
2-Concentration of Certain Solutions: optically active solutions (e.g., sucrose solutions) concentrations
can be measured by a polarizer & analyzer with determination of angle of rotation
3-Stress Analysis: when subjected to stress, glass & some plastics develop optical properties that are
dependent upon the plane of polarization of light passing thru it
4-LCDs: in calculator screens – one possible arrangement:
--a surface of tiny pixels, each w/ liquid crystals in btwn 2 glass plates; the liquid crystals are relatively
long, thin molecules that attract each other rather weakly; 1st glass plate has very thin (order of
magnitude of 1 nm) slits or scratches along its surface so that the long, rod-like molecules align
themselves w/ the slits; the other glass plate has similar slits but is rotated by 90 degrees w/ respect to
the 1st
--so that if the molecules next to the 1st glass plate are vertical then those in contact w/ the other glass
plate are horizontal or vice versa – the molecules in between will therefore, because of the forces
between them, slowly change orientation from vertical to horizontal
--now place a polarizer, with its axis vertical, in front of the top glass plate; the transmitted light will be
vertically polarized; as the light moves from molecule to molecule, its plane of polarization changes so as
to be aligned w/ the orientation of the molecules; by the time it reaches the back plate, the plane of
polarization has rotated 90 degrees
--if a 2nd polarizer with an axis of transmission at 90 degrees with respect to the 1st polarizer is placed
behind the back plate, then light will simply go thru & the pixel will be bright
--however if a potential difference is established between the 2 glass plates, the molecules will tend to
align their long axes w/ the electric field; the light reaching the back polarizer will therefore NOT be able
to go thru since it will still be vertically polarized and the pixel will be dark
--THEREFORE, the idea is to apply a voltage to certain pixels so they appear black against a bright
background of those pixels where no voltages is applied; the background can be made to look bright by
placing a mirror there to reflect the light that went thru the bottom polarizer
--PLUS color can be introduced by using green, red & blue filters on sub-pixels with various other colors
being perceived depending on relative brightness of the individual sub-pixels
5-Computer & TV LCD Screens: work on same basic principle for LCDs just substantially more
complicated