This content explains the concept of electromagnetic wave polarization, how it's achieved using polarizers, and quantifies the intensity reduction with Malus's Law, demonstrating its crucial role in validating the transverse wave model of light.
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polarization and malice's law
electromagnetic waves consist of
electric and magnetic fields
which oscillate perpendicularly to one another
another
while these two fields must remain
perpendicular all times there can be
many pairs of these waves which are
orientated at different angles the
orientation of an electric field doesn't
need to be vertical as what's normally
illustrated in most diagrams but it can
be at an angle when the electric field
of an em wave is at an angle the
magnetic field must also be at a
different angle than what it's normally
illustrated such that the angle between
the magnetic field and electric field
will remain perpendicular
it is important to understand that only
transverse waves which electromagnetic
waves are also classified as can be
polarized longitudinal waves such as
sound cannot be polarized because the
direction of oscillation is parallel
not perpendicular to the direction of propagation
propagation
the axis along which the electric field
is oscillating
is referred to as its polarization or
polarizing axis
when a wave possesses many different
axes of polarization so that is when it
has electric fields to oscillate in
different directions
it is referred to as an unpolarized wave
in contrast when a wave consists of only
a single axis of polarization it is said
to be polarized
we'll discuss polarization using light
for the remainder of this video
unpolarized light can be transformed
into polarized light using a polarizer
a polarizer is able to transform
unpolarized light with many different
axis of polarization
into a single axis of polarization via
various mechanisms
you don't need to know how this is done
but one such mechanism is through the
absorption of light with unwanted axes
of polarization
the polarizing axis
of the light that passes through a
polarizer is always the same as a
transmission axis of the polarizer for
example the transmission axis of this
polarizer is vertically orientated which
causes a polarizing axis of the
polarized lights to be also vertically orientated
orientated
the effect of a polarizer on the
intensity of lights can be
quantitatively analyzed using malice's law
law
now suppose we have a vertically
polarized light about to pass through a
polarizer whose transmission axis is
inclined at an angle theta
relative to the vertical line
so in this case the angle between the
transmission axis and the original
polarizing axis of the light is marked
by angle theta
the electric field of the original and
the final polarized light can be
analyzed by drawing this right angle triangle
triangle
e naught is the electric field vector of
the original light
and e1 is the electric field vector of
the polarized light after it has passed
through the polarizer
e naught is a hypotenuse and e 1 is the
adjacent side next to the angle theta
so we can say that e 1 divided by e
naught is equal to cosine theta the
adjacent side divided by the hypotenuse
so by rearranging this equation we can
get e1 equals the e naught times by
cosine theta
we also know that the intensity of light
is directly proportional to the square
of its electric field vector
so by squaring both sides of my first equation
equation
i can obtain an expression in terms of
the intensity of the final light source
and the original light source
this equation is what we call malice's
law i equals the i naught times by
cosine squared theta
unpolarized light can be thought as
light consisting of polarizing axes
evenly distributed in all directions or
l or angles
since the average value of cosine
squared theta where theta can range from
0 degrees to 360 degrees is 0.5
the intensity of unpolarized lights is
always reduced by 50
that is it always halved after it passes
through a polarizer
this phenomenon applies to all
polarizers regardless of the
transmission axis
so it doesn't matter if the transmission
axis is vertical at an angle or horizontal
horizontal
whenever you have unpolarized light
passing through a polarizer the
intensity is always halved for example
if the intensity of the original
unpolarized light is 100 watts per meter
squared it will be reduced to 50 watts
per meter squared
after passing through a polarizer with a
vertical transmission axis
the final intensity here will always be
50 watts per meter squared even if the
angle of this transmission axis changes
when polarized light passes through a
polarizer its intensity is also affected
however unlike unpolarized lights the
extent to which its intensity is reduced
by depends on the angle between the
light's polarizing axis and the
transmission axis of the polarizer this
is given by the angle theta in malice's law
law
the final intensity as a proportion of
the initial intensity varies sunny sweatily
sweatily
specifically as a function of cosine
squared theta
the red curve on this graph shows the
shape of cosine squared function
now i want to compare this
to the blue curve which shows the normal
cosine function
when the angle between the polarizing
axis of light and the transmission axis
of the polarizer is equal to 90 degrees
that is when they're perpendicular the
value of cosine square theta becomes zero
zero
this means
no lights will be able to pass through
the polarizer as the final intensity
equals zero
let's take a look at a sample
calculation question a beam of light
passes through two polarizers the second
polarizer has a transmission axis at an
angle of 60 degrees so we draw a
vertical line down the middle this angle
here will be 60 degrees
the intensity of light before and after
the second polarizer is i naught and ib
what is the final intensity of light
compared to the original intensity
before it passes through the first polarizer
polarizer
the original intensity refers to the
intensity of light before the first
polarizer and the final intensity is ib
in this case we need to do this question
two steps because there are two polarizers
polarizers
the second polarizer can be analyzed
using manus law where i b equals i
naught cosine squared theta
i b divided by i naught would then equal
to cosine squared of 60 degrees
which yields a value of a quarter so
this means ib is exactly a quarter the
intensity of i naught
but the question wants the original
intensity if we assume that the beam of
light at the beginning is unpolarized
then after passing to the first polarizer
polarizer
the intensity will be reduced by 50
percent so that means i naught is half
the value of the initial intensity
so then ib
will be a quarter times by a half
of the original intensity so i original
which yields a value of 1 8 or 12.5
so the value of ib the final intensity
after passing the second polarizer is
only 12.5 percent of the original
intensity of the unpolarized light
let's take a look at another question
unpolarized light is passed through
three polarizers the three polarizers
have a transmission axis of zero degrees
45 degrees and 90 degrees relative to
the vertical
respectively what is the intensity of
light after it passes through the third
polarizer as a percentage of the initial intensity
