Biomedical Engineering Reference
In-Depth Information
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FIGuRE 1.8 Huygen's. drawing. of. the. two-slit. interference. phenomenon.. (Picture. taken. from. Wiki. commons..
his.image.is.in.the.public.domain.because.its.copyright.has.expired.)
If.only.one.slit.is.open,.then.the.light.must.travel.from.the.illuminating.source.through.this.slit.and.
on.to.the.detector.plane.beyond.it..A.straight-line.theory.would.have.all.lines.that.pass.from.the.source.
to.the.detector.plane.build.an.illumination.pattern.on.the.plane..With.Fresnel's.theory,.this.area.is.larger.
since.the.slit.screen.is.an.intermediate.wavefront.surface.and.the.very.narrow.slits.act.themselves.like.
emitters..If.both.slits.are.open,.then.one.might.expect.the.sum.of.the.two.intensity.patterns.at.the.detec-
tor,.but.this.is.not.what.is.observed..Instead,.one.sees.(in.monochromatic.light).a.pattern.of.interference.
fringes,.the.fringe.spacing.being.on.the.order.of. L λ ,.where. d .is.the.separation.distance.between.the.
slits.and. L .is.the.distance.from.the.slit.plane.to.the.detector.plane..his.implies.that.waves.traversing.
through. slit. 1. are. combining. with. waves. traversing. through. slit. 2. and. that. the. illuminated. areas. are.
where. the. waves. add. constructively,. that. is,. the. OPDs. to. the. emitter. difer. by. integer. multiples. of. a.
wavelength.with.a.tolerance.of.within.one-half.wave.of.each.other..All.areas.are,.therefore,.illuminated.
because. of. the. plus. or. minus. half-wave. tolerance,. but. the. brightest. illumination. is. where. the. optical.
paths.match.exactly,.modulo.a.wavelength.and.the.darkest.part.is.where.they.exactly.cancel.at.a.half-
wave.diferent.from.each.other.
Huygens.drew.this.picture.depicting.the.waves.emanating.from.two.slits.with.waves.adding.and.can-
celling.coherently.depending.on.position.in.space,.as.shown.in.Figure.1.8.
1.3.4 Photons, Scattering, energy, and Momentum
he.early.evidence.for.light.being.a.wave-like.phenomenon.contrasts.with.later.evidence.that.showed.
that. light. is. composed. of. discrete. energy. particles.. Furthermore,. particles,. such. as. the. electron,. were.
demonstrated.to.exhibit.wave.like.behavior..For.example,.a.Young's.two-slit.experiment.performed.with.
electrons.shows.fringes.
he.hybrid.theory.that.tries.to.consistently.explain.these.disparate.observed.properties.is.based.on.
the.concept.that.the.electromagnetic.wave/photon.has.a.wave-particle.dual.nature..Light.acts.as.a.wave.
when.propagating.but.as.a.particle.when.detected..Formally,.the.light.is.composed.of.discrete.packets.
known. as. photons. which do not interfere with each other . (expect. in. extreme. cases. of. photon-photon.
collisions).but.only.with.themselves.individually.behaving.as.full-wave.ields.until.they.are.detected.as.
discrete.events..In.summary,
•.
light.originates.as.photons,.each.emitted.by.the.oscillation.of.a.single.atom,
•.
light. travels. as. a. wave. via. all. possible. paths. (with. most. of. the. energy. picking. paths. of. “least.
time”),.and
•.
light,. when. detected,. is. realized. as. random. single-photon. events,. probabilistically. distributed.
according.to.the.intensity.of.the.wave.at.the.detector.
Dirac.points.out.that.in.the.quantum.theory.of.light,.the.wave.amplitude.when.squared.is.an.indicator.
of.the.probability.of.detecting.the.photon.at.that.location.and.not.a.measure.of.the.density.of.photons.at.
 
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