* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PHYS_3342_120611
Optical coherence tomography wikipedia , lookup
Ellipsometry wikipedia , lookup
Ultrafast laser spectroscopy wikipedia , lookup
Surface plasmon resonance microscopy wikipedia , lookup
Night vision device wikipedia , lookup
Speed of light wikipedia , lookup
Nonimaging optics wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Optical aberration wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
Birefringence wikipedia , lookup
Atmospheric optics wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Anti-reflective coating wikipedia , lookup
Thomas Young (scientist) wikipedia , lookup
Opto-isolator wikipedia , lookup
Nonlinear optics wikipedia , lookup
Transparency and translucency wikipedia , lookup
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 2f 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