The final is Dec 13 at 2 PM. Remember that it will be 40% comprehensive and 60% on material covered...

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

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Wave number k = ω

cAngular frequency ω = 2πf

Wavelength λ =2π

k

Period T =2π

ω=

1

f

Frequency f

max

max

( , ) cos( )

( , ) cos( )

y

z

E x t E kx t

B x t B kx t

max

max

( , ) cos( )

( , ) cos( )

y

z

E x t E kx t

B x t B kx t

Ene

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ns (

EM

wav

e qu

anta

)

produced by electronic devices

produced by vibrations of molecules at room temperature

produced by electronic transitions in atoms and molecules

produced by decelerating high-energy electrons

produced during nuclear reactions

Spectrum of EM waves

Energy and Momentum in EM Waves

2 2 2 20 0

0

20

The magnitudes are related as

2 2 2

Densities of the magnetic energy equals density of the electric energy

2

All these energy densities oscillat

E B

E B E

E cB

E c B Bu u

u u u u E

e in space and time

EM Energy Flow and Pointing Vector

Travelling EM Waves carry energyin the direction of propagation

20

2 200

0 0

0

( )( )

1

1Pointing vector in vacuum

dU udV E Acdt

dU EBS cE E

A dt

S E B

For a sinusoidal wave, the average energy flux per period

(intensity of the wave)

0

2max max

0

22max max max

0 max0 0 0

max max

0

20 max

1( , ) ( , ) ( , )

( , ) cos ( )

1 1

2 2 2

2

The average energy density (quite general)2

x

av

S x t E x t B x t

E BS x t kx t

E B EI S EB c E

c

E BS

Eu I cu

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 propagationwhile 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

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At the boundary between different media, the wave experiences

(a) reflection; θ1 = θ1′ - the angle of reflection = the angle of incidence

(b) refraction; sinθ 2

sinθ1

=v2

v1

=n1

n2

- Snell' s law of refraction

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n =c

v index of refraction

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.

PHYS 3380 - Astronomy

AIR

GLASS / WATER

Slower Propagating Speed

Car

( Sand /Gravel)


AIR

GLASS / WATER


Car

( Sand / Gravel )


AIR

GLASS / WATER


NORMAL


AIR

GLASS / WATER


NORMAL LIGHT BENDING TOWARDS THE NORMAL

LIGHT RAY


n2

AIR

GLASS / WATER


NORMAL LIGHT BENDING TOWARDS THE NORMAL

n1

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Snell' s law of refraction

sinθ 2

sinθ1

=v2

v1

=n1

n2

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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

time-varying 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

avelengthshorter w the

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n

n

v

v

fvfv

Total Internal Reflection

sin bcrit

a

n

n

Fiber Optics

Dispersion of Light

Dispersion of light by the prism.

The band of colors is called a spectrum

Optical axis - axis normal to both sides of lens - light is not refracted along the optical axisFocus - the point where light rays parallel to optical axis converge; the focus is always found on the opposite side of the lens from the objectFocal length - the distance from the focus to the centerline of the lens

Geometry of a Converging (Convex) Lens

Optical axisFocus

Focal length

Focal Planel1 l2

o i

Geometry of a Simple Lens

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1

o+

1

i=

1

f

M =−i

o=

l2

l1

f

Lens formula

Linear Magnification

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 focal plane is where incoming light from one direction and distance (object distance o greater than focal length) is focused.

The image formed by a single lens is inverted.


Focal length

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1

o+

1

i=

1

f

For astronomical distances, o ≅ ∞ and

1

i=

1

f or f = i

Focal Plane

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.

The image is inverted as with a single lens - the brain interprets the image and rights it.

Eye accommodation

Nearsightedness – negative lens correctionFarsightedness – positive lens correctionOther eye diseases

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).

Magnification Using Two LensesRefracting Telescope and Microscope

f1 = 0.5 mf2 = 0.1 m

f1 = 0.5 mf2 = 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

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.

The Doppler Effect - Wavelength Shift Due to Motion.

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.

2. Light emitted from an object moving away from you will have its wavelength lengthened.

3. Light emitted from an object moving perpendicular to your line-of-sight will not change its wavelength.

BLUESHIFT

REDSHIFTREDSHIFT

v c

=

The amount of spectral shift tells us the velocity of the object:

PolarizationLight 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.

ISNS 3371 - Phenomena of Nature

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.

Polarization

Polaroid filters use optical dichroism – selective absorption

Long-chain molecules preferentially absorblight polarized along their length


Polarization by ReflectionUnpolarized 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?


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.


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.

The final is Dec 13 at 2 PM. Remember that it will be 40% comprehensive and 60% on material covered...

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Transcript of The final is Dec 13 at 2 PM. Remember that it will be 40% comprehensive and 60% on material covered...