# Magnetic field H

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Electric field E. Magnetic field H. Direction of propagation. The light wave is comprised of an electric field and a magnetic field . The magnetic field, H is always perpendicular to the electric field. Phase. these two waves are in phase. 1/2 l difference = 180 deg. Phase. - PowerPoint PPT Presentation

### Text of Magnetic field H

• Phasethese two waves are in phase

• Phasethese two waves are out of phase

• SuperpositionA2A1Add amplitudes for waves that are in phase

• SuperpositionA2A1Subtract amplitudes for waves that are out of phase by 180 deg

• SuperpositionA2A1A1 = A2 but the waves are out of phase by 180 deg.Total destructive interference

• Mutual CoherenceTwo waves are said to be mutually coherent when the phase difference between the two waves does not change over time. (i.e. the crest of the first wave is always a fixed distance from the crest of the second wave)

When the phase difference between two waves varies over time, the waves are said to be mutually incoherent.

• Mutual CoherenceCoherent sources are generally derived from the same source. That way, both waves have the same wavelength and the same random fluctuations in phase*.

*The wavetrain from any source (including a laser) is not constant but undergoes random changes in phase

• Coherence LengthThe distance over which a wave can interfere with itself**or .The average length of a wavetraincoherence length for..laser: many meterslow-coherent laser: 10 nmsun: 2 mm

• Examples1.What is the intensity of two mutually coherent waves, one with amplitude 5 and another with amplitude 13 and a phase difference between the two of a) 90 degrees? b) 180 degrees?

2. What is the intensity of two mutually incoherent waves, one with amplitude 5 and another with amplitude 13?

• Consider this exampleIf two mutually coherent waves of amplitude 5 and 10 respectively have a combined intensity of 135, what is the phase difference between them?

• Interference

• Youngs Double Slitsingle light source

• Youngs Double Slitsingle light sourcescreenI

• Youngs Double Slit CalculationqqDdSlit separation = ays

• Youngs Double Slit CalculationSubstitute in the expression for phase difference

• Youngs double slitMaxima occur whenevery position on screenm counterl wavelengths distance from aperture to screena slit separation

• Youngs double slit interference pattern for monochromatic lightym=0m=-1m=-2m=-3m= 3m= 2m= 1

• Youngs double-slit interference pattern for white light

• ExampleGiven an aperture with a 0.1 mm slit spacing, a wavelength of 500 nm, and a screen held at a distance of 2 m. What is the separation between maxima?What is the separation for 400 nm light?

• Lloyds mirrorinterferenceSSmirror

• SS1S2interferenceFresnels double prismtwo thin prisms

• Michelson Interferometer

• Deformable Mirrors

• Michelson Interferometer to Characterize Actuator Deflection of a MEMS DM.

• Applications of Interference

• Retinal Interference PatternsPotential Acuity MetercataractThe laser beams bypass the cataract and generate scatter-free, high resolution interference fringes on the retina to test retinal function prior to cataract removal.

• Thin Film InterferenceWhat happens to a reflected wave when n2 > n1?n1n2Reflected wave is shifted in phase by 180 (1/2 cycle)reflected waveincident wave

• Thin Film Interferencen1n2n2 < n1Reflected wave continues with no change in phasereflected waveincident waveWhat happens to a reflected wave when n2 < n1?

• Reflectance of an AR Coating5504007001234lreflectance (%)

• Why do ARCs Appear Purplish?green reflection is eliminatedsome reddish and bluish reflectance remains (see graph)mixture of red and blue has purplish huereflected color will change with angle since effective thickness of coating changes

• Thin Film ProblemWhat is the reflectance of a glass (n=1.5) surface with a MgFl2 coating (n=1.38) optimized for 550 nm light for

550 nm light?400 nm light?

• Step 1What is the thickness of the coating?

• Step 2What is the amplitude of reflectance at the surfaces?

• Step 3For 550 nm light.

• Step 4For 400 nm light, what is the phase difference?

• Step 5For 400 nm light

• Newtons Rings

• SummaryIf the phase changes are common to both surfaces (eg ARC), then

• SummaryIf the phase changes are not common to both surfaces (eg soap bubble, or oil), then

• Fringes of Equal Thickness ProblemTwo flat microscope slides, 10 cm long, are touching at one end and are separated by three microns on the other. How many dark interference bands will appear on the slide if you look at the reflection for 450 nm light?

• Diffraction and Resolution

• DiffractionAny deviation of light rays from a rectilinear path which cannot be interpreted as reflection or refraction

Sommerfeld, ~ 1894

• Huygens PrincipleHuygens' principle applied to both plane and spherical waves. Each point on the wave front AA can be thought of as a radiator of a spherical wave that expands out with velocity c, traveling a distance ct after time t. A secondary wave front BB is formed from the addition of all the wave amplitudes from the wave front AA.

• Fresnel Diffraction

• Fraunhofer DiffractionAlso called far-field diffractionOccurs when the screen is held far from the aperture.Occurs at the focal point of a lens

• Diffraction and Interferencediffraction causes light to bend perpendicular to the direction of the diffracting edgeinterference due to the size of the aperture causes the diffracted light to have peaks and valleys

• rectangular aperturesquare aperture

• ???

• Airy Disccircular aperture

• Airy Diskq

• 00.511.522.512345678pupil diameter (mm)distance from peak to 1st minimum (minutes of arc 500 nm light)

• Point Spread Function vs. Pupil Size1 mm2 mm3 mm4 mm5 mm6 mm7 mmPerfect Eye

• Rayleigh resolution limitUnresolved point sourcesResolved

• Rayleigh Resolution LimitAt the Rayleigh resolution limit, the two points are separated by the angleThis is the same as the distance between the max and the first minimum for one Airy disk!!!

• 00.511.522.512345678pupil diameter (mm)minimum angle of resolution (minutes of arc 500 nm light)

• Minutes of arc20/2020/105 arcmin2.5 arcmin1 arcmin

• convolution6 mm3 mm1 mm20/20 E

• DH20/20 E

• First light AO image of binary star k-Peg on the 3.5-m telescope at the Starfire Optical Range September, 1997. uncorrectedcorrectedAbout 1000 times better than the eye!

• Keck telescope: 10 m reflector: about 4500 times better than the eye

• Point Spread Function vs. Pupil Size1 mm2 mm3 mm4 mm5 mm6 mm7 mmPerfect EyeTypical Eye

• 2.5.7: Image quality as a function of pupil sizeoptical quality(arb. units)Best overall quality ~ 2 - 3 mm02468pupil size (mm)

• Polarization

• Direction of Polarizationverticalhorizontaldiagonal

• Any Polarization can be Expressed as a Sum of a Vertical and a Horizontal ComponentqAAcosqAsinqdiagonal polarization(horizontal component)(vertical component)yx

• Unpolarized LightMost light is unpolarized. sun incandescent lampcandlelight

• Circular and Elliptical Polarization

• Generating Polarized Light

• Polarizing Filtersunpolarized light inpolarized light out

• ExampleUnpolarized light is incident on a polaroid filter whose orientation is vertical (90 degrees). It is followed by a filter whose orientation is 180 degrees. If 100 units of intensity are incident on the pair of filters, how many units of light will emerge?

• ExampleIf you add a 3rd filter oriented 45 degrees from the horizontal in between the two original filters, how much light emerges?

• Polarization by ReflectionEsEpEsEpEsqBEs is the component of the polarization that is parallel to the reflecting surface.Ep is the component of polarization that is perpendicular to Es.

• Polarization by Reflectionreflectance (%)angle (deg)51015203060900n=1.514.8 %RsRp56.3Rs is the reflectance of the Es component.Rp is the reflectance of the Ep component.At 90, both Rs and Rp are 100 %Brewsters angle

• Polarization by Scattering

• Applications of PolarizationHaidingers brushesPolarizing sunglassesreflections from flat surfaces (roads, water, snow, carhoods) are horizontally polarized.These are suppressed by having glasses that transmit only the vertically polarized component of lightReducing specular reflections

• LCD screen

• Calcite

• Haidingers Brush

• DepolarizedParallel PolarizedRandomly Polarized Glaucoma SuspectDisc HyperpigmentationCourtesy of Steve Burns and Ann Elsner, Schepens Eye Research Institute, Boston, MA

• GDX Laser Diagnostic TechnologiesThick NFLThin NFLlinear polarizationstrong elliptical polarizationlinear polarizationweak elliptical polarization

• GDX Image: AR left eye

When a parallel beam passes though an aperture, the light distribution does not simply take the shape of the aperture, like diffraction theory would predict.Because light interferes with itself, diffraction occurs and the light forms what is called a diffraction pattern. When the aperture is far from the screen, then one type of pattern, called a Fraunhofer pattern is formed.A Fraunhofer diffraction pattern also forms at the focal point of a lensRemember one important thing. Smaller apertures generate more diffraction.This shows the inverse relationship between pupil size and potential image quality. Larger pupils can resolve smaller objects. Recall

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