| Topic: |
Science > Physics |
| User: |
"Wonky" |
| Date: |
20 Oct 2005 01:28:47 AM |
| Object: |
Birefringence |
If a beam of unpolarised light enters a birefringent crystal (like
Iceland spar calcite), it is split into two polarised beams whose
direction of polarisation are perpendicular. These two beams travel at
slightly different speeds, and so emerge at different points. This is
best illustrated by placing a piece of Iceland spar calcite on a page
of text; there are two images of the text visible through the crystal.
Rotating a polaroid over the crystal will block one image while
revealing the other, then reveal both, then block and reveal the other
way, clearly demonstrating the polarisation of the two images.
This also holds if the initial (incident) beam is polarised (in any
direction.)
Why?
Wonky
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| User: "CWatters" |
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| Title: Re: Birefringence |
20 Oct 2005 02:24:15 AM |
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"Wonky" <fishcustard@fastmail.com.au> wrote in message
news:1129789727.886574.13730@g49g2000cwa.googlegroups.com...
If a beam of unpolarised light enters a birefringent crystal (like
Iceland spar calcite), it is split into two polarised beams whose
direction of polarisation are perpendicular. These two beams travel at
slightly different speeds, and so emerge at different points. This is
best illustrated by placing a piece of Iceland spar calcite on a page
of text; there are two images of the text visible through the crystal.
Rotating a polaroid over the crystal will block one image while
revealing the other, then reveal both, then block and reveal the other
way, clearly demonstrating the polarisation of the two images.
Due to it having different refractive indicies in different directions.
This also holds if the initial (incident) beam is polarised (in any
direction.)
Nice interactive Java tutorials here..
http://molecularexpressions.com/primer/lightandcolor/birefringencehome.html
Birefringent Crystals in Polarized Light..
http://molecularexpressions.com/primer/java/polarizedlight/crystal/index.html
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| User: "RP" |
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| Title: Re: Birefringence |
20 Oct 2005 03:02:22 AM |
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CWatters wrote:
"Wonky" <fishcustard@fastmail.com.au> wrote in message
news:1129789727.886574.13730@g49g2000cwa.googlegroups.com...
If a beam of unpolarised light enters a birefringent crystal (like
Iceland spar calcite), it is split into two polarised beams whose
direction of polarisation are perpendicular. These two beams travel at
slightly different speeds, and so emerge at different points. This is
best illustrated by placing a piece of Iceland spar calcite on a page
of text; there are two images of the text visible through the crystal.
Rotating a polaroid over the crystal will block one image while
revealing the other, then reveal both, then block and reveal the other
way, clearly demonstrating the polarisation of the two images.
Due to it having different refractive indicies in different directions.
This also holds if the initial (incident) beam is polarised (in any
direction.)
Nice interactive Java tutorials here..
http://molecularexpressions.com/primer/lightandcolor/birefringencehome.html
Birefringent Crystals in Polarized Light..
http://molecularexpressions.com/primer/java/polarizedlight/crystal/index.html
Yep, that's pretty much how I was going to explain it. The question was
however, "Why?". To answer that a bit better I was going provide a
little math as applied to the E and B fields of the light beams. The
*simple vector analysis* that the article spoke of reduces to the fact
that the field intensity drops off as the cosine of the angle (in this
case the beam versus polaroid angle), and the perpendicular components
of the wave can propagate independently of one another, i.e. they can be
split. This is contradictory to the quantum interpretation that the
effect is due to discrete photons and their probabilities of passing
through the respective polarizers.
Richard Perry
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| User: "Wonky" |
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| Title: Re: Birefringence |
20 Oct 2005 02:54:45 AM |
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CWatters wrote:
"Wonky" <fishcustard@fastmail.com.au> wrote in message
news:1129789727.886574.13730@g49g2000cwa.googlegroups.com...
Nice interactive Java tutorials here..
http://molecularexpressions.com/primer/lightandcolor/birefringencehome.html
Birefringent Crystals in Polarized Light..
http://molecularexpressions.com/primer/java/polarizedlight/crystal/index.html
Thank you. Those tutorials are excellent; I can see myself spending a
lot of time playin with them.
Wonky
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| User: "Andy Resnick" |
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| Title: Re: Birefringence |
20 Oct 2005 07:45:02 AM |
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Wonky wrote:
If a beam of unpolarised light enters a birefringent crystal (like
Iceland spar calcite), it is split into two polarised beams whose
direction of polarisation are perpendicular. These two beams travel at
slightly different speeds, and so emerge at different points. This is
best illustrated by placing a piece of Iceland spar calcite on a page
of text; there are two images of the text visible through the crystal.
Rotating a polaroid over the crystal will block one image while
revealing the other, then reveal both, then block and reveal the other
way, clearly demonstrating the polarisation of the two images.
This also holds if the initial (incident) beam is polarised (in any
direction.)
Why?
As others have pointed out, it's because the index of refraction changes
depending on the direction of propogation in the crystal. There are
three major types of optical properties (most of the following comes
from Born and Wolf):
1) There are three mutually perpendicular optical axes in
crystallographically-equivalent directions (cubic system). These
crystals are optically isotropic and equivalent to an amorphous body.
That is, e_x = e_y = e_z = e, where e_a are the principal dielectric axes.
2) Crystals where two or more crystallographic directions lie in the
same plane (trigonal, tetragonal, and hexagonal). These types of
crystals are unixaial and e_x = e_y != e_z. Here, e_z corresponds with
a crystallographic axis, but e_x and e_y may not. Calcite is uniaxial,
and I believe is tetragonal. Sapphire is also uniaxial, and I think
quartz is as well.
3) Crystals in which the principal dielectric axes correspond with no
crystallographic axis: e_x != e_y != e_z. These are biaxial crystals,
and correspond to triclinic, monoclinic, or orthorhombic types.
Aragonite is the canonical material that gets trotted out.
To summarize, isotropic crystals have optical axes identical to crystal
axes, Uniaxial crystals have one optical axis coincident with a
crystallographic axis, and biaxial crystals have optical axes coincident
with no crystallographic axis.
From this follows what you observe: in uniaxial crystals, we can define
two preferred directions: the 'ordinary' axis and the 'extraordinary'
axis. The ordinary direction is in the e_z direction, and the
extraordinary direction lies in the plane containing e_x and e_y.
Incident light of an arbitrary polarization state will be decomposed
into these two directions, which propogate at different speeds, and if
the crystal is cut in a certain plane or direction, Snell's law dictates
that the two (crystal) polariation states will refract into different
directions. This is called birefringence or double refraction.
Light propogation in biaxial crystals is considerably more
complicated,and leads to something called conical refraction, where an
incident beam of light is refracted into a cone-shaped surface.
Both of these effects can be wavelength-dependent. Conical refraction
requires monochromatic light to see, but I think double refraction
applies over the entire visible range.
These properties of crystals allow for the constuction of all manner of
beamsplitters, prisms, etc. with all kinds of uses: microscopes use
matched sets of Wollaston prisms (devices made from calcite slabs glued
together) to perform "differential interference contrast" microscopy.
Glan-Thompson prisms can be used to adjust the output power of a laser.
Babinet-Soleil compensators allow for the generation of polarized
light in a (user-defined) arbitrary polarization state given a linaerly
polarized input. And there's tons more....
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "RP" |
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| Title: Re: Birefringence |
20 Oct 2005 02:01:10 AM |
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Wonky wrote:
If a beam of unpolarised light enters a birefringent crystal (like
Iceland spar calcite), it is split into two polarised beams whose
direction of polarisation are perpendicular. These two beams travel at
slightly different speeds, and so emerge at different points. This is
best illustrated by placing a piece of Iceland spar calcite on a page
of text; there are two images of the text visible through the crystal.
Rotating a polaroid over the crystal will block one image while
revealing the other, then reveal both, then block and reveal the other
way, clearly demonstrating the polarisation of the two images.
This also holds if the initial (incident) beam is polarised (in any
direction.)
Why?
That's very interesting, have you tried this yourself? One would expect
to see only one image if a polaroid was to be inserted between the
source and the crystal and was aligned with one of the polarization axes
of the crystal. OTOH, if the beam incident on the crystal is rotated wrt
both axes then two images would be expected. I can only assume that you
are pondering this latter situation, and cannot understand how the
polarized beam can be split into two beams with perpendicular
polarizations. In this case you're addressing just another version of
what's known as the three polarizer paradox.
Don't expect a coherent answer from the right, just a bunch of babble
about quantum rules of wave addition. When you've given up on
understanding that, I'll explain it to you in classical terms :)
Richard Perry
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| User: "Wonky" |
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| Title: Re: Birefringence |
20 Oct 2005 02:44:18 AM |
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RP wrote:
Wonky wrote:
If a beam of unpolarised light enters a birefringent crystal (like
Iceland spar calcite), it is split into two polarised beams whose
direction of polarisation are perpendicular. These two beams travel at
slightly different speeds, and so emerge at different points. This is
best illustrated by placing a piece of Iceland spar calcite on a page
of text; there are two images of the text visible through the crystal.
Rotating a polaroid over the crystal will block one image while
revealing the other, then reveal both, then block and reveal the other
way, clearly demonstrating the polarisation of the two images.
This also holds if the initial (incident) beam is polarised (in any
direction.)
Why?
That's very interesting, have you tried this yourself? One would expect
to see only one image if a polaroid was to be inserted between the
source and the crystal and was aligned with one of the polarization axes
of the crystal.
Yes, I have tried it; it's one of my favourite demonstrations for
children - it makes them think. I've tried polarising the light before
it enters the crystal in the direction of one of the axes of the
crystal; it always produces the two images. This is the bit I don't
understand.
OTOH, if the beam incident on the crystal is rotated wrt
both axes then two images would be expected. I can only assume that you
are pondering this latter situation, and cannot understand how the
polarized beam can be split into two beams with perpendicular
polarizations. In this case you're addressing just another version of
what's known as the three polarizer paradox.
I think Feynman, in one of his Lectures on Physics, addressed just this
topic; I looked at (though I probably don't really understand it) in
third year Physics at Uni.
Richard Perry
Thank you.
Wonky
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| User: "RP" |
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| Title: Re: Birefringence |
20 Oct 2005 03:22:01 AM |
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Wonky wrote:
RP wrote:
Wonky wrote:
If a beam of unpolarised light enters a birefringent crystal (like
Iceland spar calcite), it is split into two polarised beams whose
direction of polarisation are perpendicular. These two beams travel at
slightly different speeds, and so emerge at different points. This is
best illustrated by placing a piece of Iceland spar calcite on a page
of text; there are two images of the text visible through the crystal.
Rotating a polaroid over the crystal will block one image while
revealing the other, then reveal both, then block and reveal the other
way, clearly demonstrating the polarisation of the two images.
This also holds if the initial (incident) beam is polarised (in any
direction.)
Why?
That's very interesting, have you tried this yourself? One would expect
to see only one image if a polaroid was to be inserted between the
source and the crystal and was aligned with one of the polarization axes
of the crystal.
Yes, I have tried it; it's one of my favourite demonstrations for
children - it makes them think. I've tried polarising the light before
it enters the crystal in the direction of one of the axes of the
crystal; it always produces the two images. This is the bit I don't
understand.
OTOH, if the beam incident on the crystal is rotated wrt
both axes then two images would be expected. I can only assume that you
are pondering this latter situation, and cannot understand how the
polarized beam can be split into two beams with perpendicular
polarizations. In this case you're addressing just another version of
what's known as the three polarizer paradox.
I think Feynman, in one of his Lectures on Physics, addressed just this
topic; I looked at (though I probably don't really understand it) in
third year Physics at Uni.
Then I misunderstood your question, so disregard my most recent reply
while I ponder this, even though I'm fairly certain that it can be
easily solved from the basics provided in CWatters linked article :)
OTOH, the article didn't seem to support your statement, maybe I just
skimmed past it, but even if your statement is correct I agree with
their approach to the problem in general. I'm sure the answer is
contained in there somewhere.
I only skimmed over the article it because it's late. Like you, I'll be
looking forward to any more input on the subject that others might be
able to provide.
Richard Perry
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