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
intensity
so after the amplifiers that pass
through the first polarizer it gets
reduced by fifty percent so only fifty
percent of the intensity is remaining
the angle between the transmission axis
of the second polarizer
and the polarizing axis of light coming
out the first polarizer will be 45 degrees
degrees
so we can say that the intensity
after coming out of the second polarizer
let's call the i2 and this is i1
i2 then will be equal to i1
cosine squared 45 degrees
so then i2 over i1 will be
a half
so going from i1 to i2 we are further
reducing this by half
so this was already 50 before so if we
halve this percentage we'll get 25
after i3
although this angle here is 90 degrees
relative to the vertical
what we are really concerned about in
malice's law
is the angle between the transmission
axis of the third polarizer and the
polarizing axis of i2
because i2 is already at 45 degrees and
the third polarizer is at 90 degrees
the difference between these two angles
is 45 again
so in my second equation for malice's
law i am using 45 degrees again
this will then give us i3 over i2 is
equal to a half
after passing through the third
polarizer my 25 intensity is halved once
again and that means i have 12.5 percent
of intensity remaining a very
interesting scenario to think about is
what happens to the intensity if we
remove the middle polarizer
now the polarizing axis that's exiting
the first polarizer will be vertical
due to the transmission axis of the
first polarizer being vertical when it
passes through the third polarizer
there's actually no light passing
through because now the angle between
the transmission axis of the third polarizer
polarizer
and the polarizing axis of light that's
about to enter the polarizer is equal to
90 degrees
and we know that cosine of 90 degrees
yields a value of zero which means i
three over i1 is equal to zero
polarization of light plays an important
role in the development and acceptance
of various models of
huygens wave model of light could not
explain polarization because he
described light as longitudinal
if this was the case
light will pass through all polarizers
without any reduction in intensity
because in longitudinal waves the
direction of oscillation is in the same
direction as propagation
so by having a polarizer it would not be
able to filter any of the light waves if
they were longitudinal similarly
similarly
newton's corpuscular model which
describes light as a stream of particles
also could not explain polarization as
light corpuscles would just pass through
polarizers unfiltered as well
the phenomenon of polarization of light
validated maxwell's electromagnetic
transverse wave mode of light
it is also a wave model however it is a
transverse wave model in this model
maxwell described light as a product of
oscillating electric and magnetic fields
that propagate in the same direction
the transit wave mode of light explains
why light intensity
will be reduced when light of a specific
polarizing axis tries to pass through a
polarizer as a polarizer will only let
light of a certain polarizing axis pass through
through
as we previously discussed using
monsters law if the polarizing axis that
is the direction of oscillation of the
electric field
is perpendicular to the transmission
axis of the polarizer then no light will
be able to pass through
in summary polarization validates
maxwell's transverse wave mode of light
and it refutes huygens longitudinal wave
model and newton's corpuscular model of
light this concludes the video on polarization
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