physical or wave optics - michigan state university...physical or wave optics in the last chapter,...
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Physical or wave optics In the last chapter, we have
been studying geometricoptics◆ light moves in straight lines◆ can summarize everything by
indicating direction of lightusing a ray
◆ light behaves essentially theway a stream of particles(photons) would
This has worked well for anumber of phenomena◆ reflection◆ refraction
…and has helped us tounderstand the workings of◆ mirrors◆ thin lenses
But our particle theory of lightgives out when we try tounderstand phenomena likeinterference, diffraction andpolarization◆ just doesn’t work
Have to resort to wave orphysical optics (in thischapter)◆ …and treat light like a wave
The first thing we’ll look at isinterference of light waves◆ not easy to observe because
of the short wavelengths oflight involved (4X10-7 m to7X10-7 m)
Along the way we’ve going tofind out why the sky is blue
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Electromagnetic waves
Now we’re back tothinking of light asspecifically being anelectromagnetic wave◆ oscillating electric and
magnetic fieldsperpendicular to eachother propagating throughspace
◆ equal amounts of energystored in the electric fieldand in the magnetic field
◆ in interactions with matter,it’s the electric componentthat does most of the work
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Young’s Experiment In order to observe
interference of 2 light waves,need to have 2 things present◆ sources must be coherent
(same phase with respectto each other)
◆ waves must have identicalwavelength
Laser produces coherent lightwhich can be split into twolight beam which then caninterfere with each other
But the first interferenceexperiment was carried out in1801◆ …no lasers then
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Young’s Experiment In order to observe
interference of 2 light waves,need to have 2 things present◆ sources must be coherent
(same phase with respectto each other)
◆ waves must have identicalwavelength
Laser produces coherent lightwhich can be split into twolight beam which then caninterfere with each other
But the first interferenceexperiment was carried out in1801◆ …no lasers then
Sunlight shines through a narrowslit; the light then spreads (Huygen’sprinciple) and illuminates a second screen with 2small slits
The waves through S1and S2 spread out andinterfere with eachother producing a series ofbright and dark fringes
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Interference fringes
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Huygen’s principle
Wrong!
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Remember example
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Constructive interference
When light arrives from S1 and S2 so that constructive interferencetakes place, a bright fringe results
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Destructive interference
If the light arrivesfrom S1 and S2 at apoint on the screenand there isdestructiveinterference, thenthere is a dark spot
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Interference patterns
Light from slit S2 has to travel further then light from S1path length difference is d sin θ
if d sin θ is a multiple of the wavelength λ, then constructive interference occursd sin θ = mλ m=0,+/-1, +/-2, …
y = L tan θ > L sin θybright = (λL/d)m
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Interference patterns
Light from slit S2 has to travel further then light from S1path length difference is d sin θ
if d sin θ is an odd multiple of the wavelength λ/2, then destructive interference occursd sin θ = (m+1/2)λ m=0,+/-1, +/-2, …
y = L tan θ > L sin θydark = (λL/d)(m+1/2)
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Example
Light from slit S2 has to travel further then light from S1path length difference is d sin θ
if d sin θ is an even multiple of the wavelength λ, then constructive interference occursd sin θ = mλ m=0,+/-1, +/-2, …
y = L tan θ > L sin θybright = (λL/d)m
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Diffraction
noyes
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Diffraction Diffraction occurs when a wave
passes through a small openingnot so different in size from thewavelength of the wave
The wave spreads out as we sawon the previous slide
So instead of a bright spot just inthe middle we see a spread-outdistribution of light◆ but with some structure to it
Type of diffraction we’re studyingis called Fraunhofer diffraction◆ screen is far away from slit◆ …or there’s a converging lens
just after the slit◆ Demo
Don’t worry about the lens;Just think of the screen as far away
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Where are the dark spots? Here’s where Huygen’s principle
comes in handy As the wave travels through the slit,
treat each point in the slit as a sourceof waves
Light from one part of the slit caninterfere with light from another part
Let’s divide the slit into halves andconsider the wavelets coming frompoint 1 and from point 3
Wavelet 1 has to travel further IF the additional distance, a/2sinθ is
equal to λ/2, then the wavelets frompoints 1 and 3 are exactly half of awavelength out of phase
◆ destructive interference
Also true for 3 and 5, 2 and 4, any twopoints in the top and bottom of the slitseparated by a/2
Can go through the same exercisedividing the screen in 4 parts, 6 parts,…
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Dark spots So dark spots when
◆ a/2 sinθ = λ/2◆ …or a/2 sinθ = 2λ/2◆ …or a/2 sinθ = 3λ/2
Corresponding to◆ sinθ1 = λ/a◆ sinθ2 = 2λ/a◆ sinθ3 = 3λ/a◆ …
Everything is in phase at θ=0,so there’s a bright spot there◆ and other bright spots roughly
half-way between the darkspots
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Let’s go crazy and put in lots of slits
Light diffractsthrough each of the slits
and we get interference between each ofthe diffractedwaves
A device like this is called adiffraction gratingbut there’s both diffraction andinterference takingplace
Again, there’s a pathlength difference between light passingthrough different slitsbright lines or spots when d sinθbright = mλm=0,1,2,…
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Intensity pattern
The more slits in the grating the sharper are the interference peaks;Can also make a diffraction grating by having finely etched lines on a reflectivesurface
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Application of interference
Laser is set up to reflect off of CDsurface
Surface has a series of bumpsand pits encoding information (i.e.the music)◆ depth of depression is equal to
1/4 of the wavelength of the laserlight
So when the laser light comes toan edge (leading or trailing), partof the light reflects from the top ofthe bump and part from thedepression (with a path lengthdifference then of 1/2 of awavelength)
◆ this insures destructive interference
Bump edges interpreted as one’sand depressions as 0’s DVD player uses a shorter wavelength
laser and smaller track separation, pit depth and lengthDVD can store 30X as much info
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Intensity pattern
The more slits in the grating the sharper are the interference peaks;Can also make a diffraction grating by having finely etched lines on a reflectivesurface, i.e. a CD (or DVD)
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Diffraction gratings in CD players
Diffraction gratings are alsoinvolved in CD players
Laser must follow the spiraltrack correctly
Laser light fed through adiffraction grating◆ central maximum is used to
read info
◆ maxima on either sided areused for steering
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Babinet’s principle
Diffraction patternfrom a thin object isthe same asdiffraction patternfrom a thin slit of thesame size◆ minima at asinθ = mλ
Can use to measurediameter of an object,for example students’hair
a