Sight and Wave Phenomena (A) Part 2

Sight and Wave Phenomena (A) Part 2

Mr. Klapholz

Shaker Heights
High School

Water waves incident on a barrier with
a gap. Diffraction.

Water waves incident on a barrier with
a gap. Diffraction.

Huygens’ Theory: Every wave is made
of ‘wavelets’ (sources of more waves).

http://
www.svi.nl/HuygensPrinciple

How would Huygens explain
diffraction?

http://
learn.uci.edu/oo/getOCWPage.php?course
=OC0811004&lesson=005&topic=006&page=10

Each wavelet is the source of the
next wave.

http://www.ux1.eiu.edu/~cfadd/1160/Ch25WO/Huygn.html

Sound waves bend (“diffraction”). How would
Huygens explain how sound goes around corners?

http://www.pa.op.dlr.de/acoustics/essay1/beugung_en.html

Shine light on a piece of cardboard. If you
make a narrow slice in the cardboard, then
the light will go through the slit, land on a
screen, and look like this….

Light waves incident on a barrier with
a slit make this pattern on a screen:

http://www.math.ubc.ca/~cass/courses/m309
-
03a/m309
-
projects/krzak/index.html

Light waves incident on a barrier with
a slit make this pattern:

http://electron9.phys.utk.edu/optics421/modules/m5/Diffraction.htm

The pattern of
intensity

due to single
-
slit diffraction
for any kind of wave always looks like this:

http://hyperphysics.phy
-
astr.gsu.edu/hbase/phyopt/sinint.html

Diffraction happens because of interference of
waves from the little wavelets in the gap:

http://hyperphysics.phy
-
astr.gsu.edu/hbase/phyopt/sinslitd.html

Here is how we label the “minima”.

‘Minima’ is the plural of ‘minimum’.

http://hyperphysics.phy
-
astr.gsu.edu/hbase/phyopt/sinint.html

q

for
n

= 1

q

for
n

= 1

q

for
n

= 2

q

for
n

= 2

q

for
n

= 3

q

for
n

= 3

Where are the minima?

b

sin

q

=
n
l


n

= 1,2,3, …

b

is the size of the opening (meters).

q

is the angular position of the minima (radians).

If

the angle is small, then …

sin

q

≈

q


So,
b

sin

q

=
n
l

becomes:

b

q

=
n
l

For the first minimum only,
n

= 1, and the
approximation is:

b

q

=
l

Or,

q
=
l

/
b

This is the approximate location of the first minimum.

Two objects, or one?

http://electron9.phys.utk.edu/optics421/modules/m5/Diffraction.htm

Basics of resolving two images

Consider your teacher holding up two fingers. The
two objects are in about the same direction. How
‘close’ can the objects be, while you still can tell that
there are two of them?

If you walk toward your teacher, then the fingers
seem to separate. The fingers are in different
directions. Even if you can’t see the difference
between objects that are 0.1 degrees apart, for
nearby objects it will not matter; the objects look
separate.

For this reason, nearby objects are easy to resolve.

Resolving Power (Rayleigh Criterion)

If you cannot move toward the objects, then what
determines if you can tell that there are two of them?
In other words, what is
q
min
?

q
min

= 1.22
l

⼠/.

A small value of
q
min

means that objects that are close
to each other can be see to be two separate objects.

You can resolve things better if the pupil of your eye is
greater. For greater D, the smaller
q
min
.

The smaller the wavelength, the smaller
q
min
.

Light is a wave

•
To understand what polarized light is, we need to
know some basics about light.

•
Light is made of Electric (
E
) & Magnetic fields (
B
) …

Light is an electromagnetic wave:

http://
www.google.com/imgres?imgurl
=http://learn.uci.edu/media/OC08/11004/OC0811004_ElectroWaves.jpg&imgrefurl=http://learn.uci.edu/oo/getOCWPage.php%3Fcourse%3
DOC
0811004%26lesson%3D005%26topic%3D002%26page%3D21&usg=___6vybCf
-
mHdTQyGUT0lrBOKoSiA=&
h
=350&w=350&sz=26&hl=
en&start
=0&zoom=1&tbnid=
dQcKUkHwLMwTaM:&tbnh
=117&tbnw=117&prev=/images%3Fq%3Dlight%2Bis%2Ban%2Belectromagnetic%2Bwave%26hl%3Den%26sa%3DX%26biw%3D1280%26bih%3D640%26gbv%3
D2%
26tbs%3Disch:1,isz:m0%2C12&itbs=1&iact=
rc&dur
=447&ei=FIaiTPa3AsSqlAeB7dnZAw&oei=mYWiTKyMAoSKlwfA4pSBAw&esq=7&page=1&ndsp=21&ved=1t:429,r:12,s:0&tx=42&ty=48&biw=1280&bih=6
40

Light is a wave

•
Light is made of Electric (
E
) &Magnetic fields (
B
) …

•
Light has wavelength (
l
).

•
And, most relevant to polarization, light is a
transverse

wave…

Light is a transverse wave:

http://www.sparknotes.com/physics/optics/light/section2.rhtml

Polarization

•
Without exception, when we are thinking about
polarization, we can just think about the
electric
field (and ignore the magnetic field).

•
Polarized light has an
organization
to its electric
field vectors.

•
Ordinary light is not polarized. Light in the room
has random orientations of electric field vectors.

•
Light that passes through polarized sunglasses has
very little electric field that oscillates left
-
right, and
it has a lot of electric field that vibrates up and
down.

These 2 photos show that
reflection
can
polarize light.

(
Photos were taken with a polarizing filter
)

http://en.wikipedia.org/wiki/Brewster%27s_angle

For this reason,
people

who are
fishing prefer polarized sunglasses.
They can see fish in the water.

Since ice produces ‘glare’, do downhill
skiers want polarized sunglasses?

http://photo.accuweather.com/photogallery/details/photo/73793/Sun+Glare+on+Ice+Covered+Snow

Polarization by reflection

•
If you bounce light off of a flat surface, it will be
somewhat polarized, and if you get the angle just
right, it will be completely polarized.

•
This is the source of ‘glare’ off of water, roads, and
ice.

•
If light hits a surface at Brewster’s angle, then the
reflected light will be completely polarized.

Brewster’s Angle

•
If light hits a surface at Brewster’s angle (
q
B
), then
the reflected light will be completely polarized.

•
q
B

=
InvTan

( n
1

/n
2

).

•
The incident light and the reflected light are in
medium 1, with index of refraction: n
1
.

•
Part of the light is transmitted into medium 2, with
index of refraction: n
2
.

See picture…


Notice where
q
B

is drawn.

http://en.wikipedia.org/wiki/Brewster%27s_angle

A quantitative look at
polarizers

(1 of 3)

•
If you shine
unpolarized

light through a polarizer,
what happens to the intensity?

•
In other words, if light of intensity
I
O

is incident on a
polarizing filter, what is the intensity of the light
that emerges from the filter?

•
The answer is ½
I
O
. All of this light is polarized, and
we could use it as a source for further exploration.

A quantitative look at
polarizers

(2 of 3)

•
Next, let the the light that comes out of the
polarizer go through another polarizer. If the two
filters are oriented the same way, then how much
light comes out of the second filter?

•
For a perfect polarizer oriented the same way as the
incoming light, all of the light that goes in, comes
out. So if goes ½
I
O

in, then ½
I
O

comes out.

•
Now, what if the second polarizer was rotated 90˚
so that its transmission axis was perpendicular to
the polarization of the incident light? How much
would come out?

Nada.

A quantitative look at
polarizers

(3 of 3)

•
Take polarized light and send it through a polarizer.
If the relative angle in their orientations is 0˚, then
all of the light that goes in, comes out.

•
If the relative angle is 90˚, then
none

of the light
comes out.

•
Hmm, what about in general, if the relative angle
was
q
, what is the equation that tells us how much
comes out? ...

If you send an intensity
I
O

onto a
polarizer, how much comes out?

Relative

Angle

Amount of light that comes
out

0˚

I
O

90˚

0

q

?

I

=
I
O

cos
2
q

This is the law of
Malus
.

Relative

Angle

Amount of light that comes
out

0˚

I
O

90˚

0

q

I
O

cos
2
q

Optically Active Materials

•
Amazingly, there are some natural materials
that will change the polarization of light.

•
If you transmit polarized light through quartz,
or even sugar water, the emitted light will
have a different polarization than the
incoming light.

Can
you feel the
stress?

http://
physics.info
/polarization/

Optically Active Materials

•
Amazingly, there are some natural materials
that will change the polarization of light.

•
If you transmit polarized light through quartz,
or even sugar water, the emitted light will
have a
different

polarization than the
incoming light.

Quantifying this effect…

•
How much does the light change polarization?

•
q

=
kh
, where:

–

q

is the
change

in polarization (degrees)

–
k

is the constant specific to the material (deg/
m
)

–
h

is the thickness of the material (meters)

•
Also, the change in polarization is proportional
to the
concentration

of a solution.