Download PHYS_3342_120611

The final is Dec 13 at 2 PM. Remember that it will be 40% comprehensive
and 60% on material covered since the last exam, including today. You will be
allowed two 8 ½ X 11 sheets of paper for notes (both sides) and it is open
book.
Your grades will be available Dec 16. You may email me or come by my
office in WSTC if you want to know your grade on your final. I leave Dec 18,
so you must contact me by Dec 16 if you want to talk about your grade.
I will have a review session in FN 2.212 the day before the final starting at
noon and going until ????. You need to have studied for the exam prior to the
session for it to do any good as you need to know what you don’t understand
so I can review it.
While I am not here this week, you may email me with questions.
Sinusoidal (monochromatic) waves
The periodic solutions that are characteri zed
by a single " temporal" and " spatial"
frequency of variatio ns :
E  E0 cos( kx  t )
B  B0 cos( kx  t )
2E k 2 2E
 2  2 2  0    ck
x
 t
Wave number k 

c
Angular frequency   2f
2
Wavelength  
k
2 1
Period T 


f
Frequency f
E
B
  kE0 sin( kx  t )  
 B0 sin( kx  t )
x
t
 E0  ( / k ) B0  cB0
Superposit ion always works :
An arbitary solution is a sum of sinusoidal s
E y ( x, t )  Emax cos( kx  t )
E y ( x, t )  Emax cos( kx  t )
Bz ( x, t )  Bmax cos( kx  t )
Bz ( x, t )   Bmax cos( kx  t )
Energy of photons (EM wave quanta)
Spectrum of EM waves
produced during nuclear reactions
produced by decelerating highenergy electrons
produced by electronic
transitions in atoms and molecules
produced by vibrations of molecules
at room temperature
produced by electronic devices
Energy and Momentum in EM Waves
The magnitudes are related as E  cB
 uE 
0E 2
2

 0c 2 B 2
2
B2

 uB
2 0
Densities of the magnetic energy equals density of the electric energy
u  u E  u B  2u E   0 E 2
All these energy densities oscillate in space and time
EM Energy Flow and Pointing Vector
Travelling EM Waves carry energy
in the direction of propagation
dU  udV  ( 0 E 2 )( Acdt )
1 dU
S
  0 cE 2 
A dt

S
1
0
 
 0 2 EB
E 
0
0
E  B Pointing vector in vacuum
For a sinusoidal wave, the average energy flux per period
(intensity of the wave)

1
S ( x, t ) 
0
S x ( x, t ) 


E ( x, t )  B ( x, t )
Emax Bmax
0
cos2 ( kx  t )
2
Emax Bmax Emax
1
2
I S
EB 

 c 0 Emax
0
2 0
2 c 0 2
1
Sav
Emax Bmax

2 0
The average energy density u 
2
 0 Emax
2
 I  cu (quite general)
The Nature of Light
The importance of optics:
Eye – main human instrument of communication with the outside world
Design of various optical instruments (cameras, microscopes, telescopes, etc.)
Modern developments: laser, fiberoptics (telecommunications), imaging, etc.
Optics – gateway and instrument to explore intricacies of the materials
(remember, light is generated due to electron’s motions)
Light has two personalities – wavelike and corpuscular (photons)
Wave properties – interference, diffraction
Particle properties – photons, photoeffect
They are reconciled in quantum electrodynamics
More classically, light propagation is usually considered as a wave propagation
while light’s interaction with matter is regarded as photon-electron interaction
Optics
Waves, Wave Fronts and Rays
Wavefronts – surfaces of equal phase
Rays – trajectories perpendicular to
wavefronts
Geometrical optics deals with ray propagation
Physical optics deals with wave behavior
Reflection and Refraction

c
n  index of refraction
v
At the boundary between different media, the wave experiences
(a) reflection;     - the angle of reflection  the angle of incidence
1
1
sin  2 v 2 n1
(b) refraction;
 
- Snell' s law of refraction
sin 1 v1 n 2
Index of Refraction
As light passes from one medium (e.g., air) to another (e.g., glass, water, plexiglass,
etc…), the speed of light changes. This causes to light to be “bent” or refracted.
AIR
Car
GLASS / WATER
Slower Propagating Speed
( Sand /Gravel)
PHYS 3380 - Astronomy
AIR
GLASS / WATER
Slower Propagating Speed
PHYS 3380 - Astronomy
( Sand / Gravel )
AIR
NORMAL
GLASS / WATER
Slower Propagating Speed
PHYS 3380 - Astronomy
NORMAL
LIGHT BENDING
TOWARDS THE NORMAL
AIR
LIGHT RAY
GLASS / WATER
Slower Propagating Speed
PHYS 3380 - Astronomy
NORMAL
LIGHT BENDING
TOWARDS THE NORMAL
AIR
n1
Snell' s law of refraction
sin  2 v 2 n1
 
sin 1 v1 n 2
n2
GLASS / WATER
Slower Propagating Speed
PHYS 3380 - Astronomy
The speed of electromag netic waves (i.e., of light! )
in a medium differs from the speed of light in vacuum
This slowing down is described by the index of refraction
c
speed in vacuum
n 
1
v speed in a medium
Electromagnetic waves can propagate not only in vacuum but also in
various materials
When in a medium, electromagnetic fields can be substantially
affected by the dielectric polarization and magnetization of the
medium – electrons respond to the wave and produce their own timevarying fields
Such responses are medium-specific and generally depend on the
frequency of the wave (because electrons have their own natural
frequencies of motion in this particular medium)
Some frequency ranges can be prohibited – the wave would not
propagate in the bulk (but will be reflected from such a medium)
Waves can also be (partially) absorbed by a medium
Index of Refraction and Wave Aspects of Light
When EM wave (light) travels between
two media, the frequency does not change
but the speed and waveleng th do :
1  fv1 , 2  fv2
1 v1 n2
 
2 v2 n1
The larger refraction index,
the shorter w avelength
Total Internal Reflection
sin crit
nb

na
Dispersion of Light
Dispersion of light by the prism.
The band of colors is called a spectrum
Geometry of a Converging (Convex) Lens
Focus
Optical axis
Focal length
Optical axis - axis normal to both sides of lens - light is not refracted along the optical
axis
Focus - the point where light rays parallel to optical axis converge; the focus is always
found on the opposite side of the lens from the object
Focal length - the distance from the focus to the centerline of the lens
Geometry of a Simple Lens
l2
Focal Plane
l1
f
o
i
The focal plane is where incoming light from one direction and distance (object distance o
greater than focal length) is focused.
Lens formula
Linear Magnification
1 1 1
 
o i f
i l
M  2
o l1
Using the Gaussian form of the lens
equation, a negative sign is used on the
linear magnification equation as a
reminder that all real images are
inverted
The image formed by a single lens is inverted.
Focal Plane
Focal length
1 1 1
 
o i f
For astronomical distances, o   and
1 13380 - Astronomy
PHYS
 or f  i
i f
The Eye
The eye consists of pupil that allows light into the eye - it controls the amount of light allowed
in through the lens - acts like a simple glass lens which focuses the light on the retina - which
consists of light sensitive cells that send signals to the brain via the optic nerve. An eye with
perfect vision has its focus on the retina when the muscles controlling the shape of the lens are
completely relaxed - when viewing an object far away - essentially at infinity.
Eye accommodation
When viewing an object not at infinity, the eye muscles contract and change the shape of
the lens so that the focal plane is at the retina (in an eye with perfect vision).
Nearsightedness – negative lens correction
Farsightedness – positive lens correction
Other eye diseases
The image is inverted as with a single lens - the brain interprets the image and rights it.
Magnification Using Two Lenses
Refracting Telescope and Microscope
f1 = 0.5 m
f2 = 0.1 m
f1 = 0.5 m
f2 = 0.3 m
Microscope or refracting telescope - consist of two lenses - the objective and the eyepiece
(ocular). Incident light rays (from the left) are refracted by the objective and the eyepiece and
reach the eye of the person looking through the telescope (to the right of the eyepiece). If the
focal length of the objective (f1) is bigger than the focal length of the eyepiece (f1), the
microscope/telescope produces an enlarged, inverted image:
magnification = f1 /f2
The Doppler Effect
The Doppler Effect - Wavelength Shift Due to Motion.
Sound
Each circle represents the crests of sound waves going in all directions from the train whistle.
The circles represent wave crests coming from the train at different times, say, 1/10 second
apart. If the train is moving, each set of waves comes from a different location. Thus, the
waves appear bunched up in the direction of motion and stretched out in the opposite direction.
Doppler Shift for Light
We get the same effect for light as for sound.
The Doppler Effect
1. Light emitted from an object moving towards you will have its wavelength
shortened.
BLUESHIFT
2. Light emitted from an object moving away from you will have its wavelength
lengthened.
REDSHIFT
3. Light emitted from an object moving perpendicular to your line-of-sight will not
change its wavelength.
The amount of spectral shift tells us the velocity of the object:
 = v

c
Polarization
Light emitted by the sun, a lamp in the classroom, a candle flame, etc… is
unpolarized light - created by electric charges which vibrate in a variety of
directions – (transverse to propagation direction)
Helpful to picture unpolarized light as a wave which has an average of half its
vibrations in a horizontal plane and half of its vibrations in a vertical plane.
Polarized light waves - light waves in which the vibrations occur in a single plane.
Polarization - Process of transforming unpolarized light into polarized light.
Most common method of polarization uses a Polaroid
filter - made of a special material capable of blocking one
of the two planes of vibration of an electromagnetic
wave. When unpolarized light is transmitted through a
Polaroid filter, it emerges with one-half the intensity and
with vibrations in a single plane; it emerges as polarized
light.
Two filters with polarization axes perpendicular to each other will completely block the
light.
Light is polarized upon passage through the first filter - say, only vertical vibrations were
able to pass through. These vertical vibrations are then blocked by the second filter since if
its polarization filter is aligned in a horizontal direction.
Like picket-fence and standing wave on a rope - vibrates in a single plane. Spaces between
the pickets of the fence allow vibrations parallel to the spacings to pass through while
blocking vibrations perpendicular to the spacings.
Orient two picket fences such
that the pickets are both aligned
vertically - vertical vibrations
will pass through both fences align pickets of second fence
horizontally - the vertical
vibrations which pass through
the first fence will be blocked
by the second fence.
ISNS 3371 - Phenomena of
Nature
Polarization
Polaroid filters use optical dichroism –
selective absorption
Long-chain molecules preferentially absorb
light polarized along their length
Polarization by Reflection
Unpolarized light can also undergo polarization by reflection off of nonmetallic surfaces extent dependent upon the angle at which the light approaches the surface and upon the surface
material.
Metallic surfaces reflect light with variety of vibrational directions - unpolarized.
Nonmetallic surfaces (asphalt, snow, water, paint on a
car) reflect light such that there is a large concentration
of vibrations in a plane parallel to the reflecting surface.
A person viewing objects by means of light reflected off
of nonmetallic surfaces will often perceive a glare if the
extent of polarization is large.
Which pair of glasses is best suited for automobile
drivers, fishermen, snow skiers?
ISNS 3371 - Phenomena of
Nature
Adding a third filter with between two
filters polarization axis at 45º to the other
two will allow light though. How?
Remember, unpolarized light vibrates in all different directions. So not just the light with
horizontal vibrations passes through the first filter, but all light with a vibrational component
in the horizontal direction - in other words, all but the light with vertical vibrations has some
component in the horizontal direction that gets through.
ISNS 3371 - Phenomena of
Nature
Before the middle filter, the light is horizontally
polarized.
The component of horizontally polarized light
along 45º gets through the middle filter.
The component of that light in the vertical
direction then gets though the last filter.
ISNS 3371 - Phenomena of
Nature