Electromagnetic waves

l Now we’re back tothinking of light asspecifically being anelectromagnetic wave

u oscillating electric andmagnetic fieldsperpendicular to eachother propagating throughspace

u equal amounts of energystored in the electric fieldand in the magnetic field

u in interactions with matter,it’s the electric componentthat does most of the work

Example

Light from slit S2 has to travel further then light from S1path length difference is d sin q

if d sin q is an even multiple of the wavelength l, then constructive interference occursd sin q = ml m=0,+/-1, +/-2, …

y = L tan q > L sin qybright = (lL/d)m

m=0m=1

m=2

m=-1

m=0

Example

Light from slit S2 has to travel further then light from S1path length difference is d sin q

if d sin q is an odd multiple of the l/2, then destructive interference occursd sin q = (m+1/2)l m=0,+/-1, +/-2, …

y = L tan q > L sin qybright = (lL/d)(m+1/2)

m=0m=1

m=2

m=-1

Reflections from a thin film

l Wave #2 has to travel furtherby a distance 2t (ignore anyangle)

l So you might think that if 2t =ml(where m is an integer)that you would getconstructive interference

l But…ahh…the phaseshift…so I get constructiveinterference when 2t =(m+1/2)l

l But…ahh…I remember thatthe wavelength changesinside the film to ln=l/n

l …so, finally, I getconstructive interferencewhen

u 2t = (m+1/2) ln

u or 2nt = (m+1/2)l

Reflections from a thin film

l So I get destructiveinterference when

u 2t = m ln

u or 2nt = ml

l Two things influence whether Ihave constructive ordestructive interference (orsomewhere in between)

u difference in path lengthtravelled

u any phase changes onreflection

s in this example, I haveone 180o phase shiftbecause I’m goingfrom air to a film withan index n back to air

If this wasa material with an index > n, then I’dhave a 2nd 180o

phase shift

As for example

non-reflectivecoating for a solar cell

Constructive interferencewhen 2nt = ml

Destructive interference when 2nt = (m+1/2)l

What happens when I have a wedge-shaped film

have constructive interference when2nt =(m+1/2)lNote that bands of color show upwhenever the thickness leads toconstructive interference for thatcolor

Diffraction

noyes

Diffractionl Diffraction occurs when a

wave passes through a smallopening not so different insize from the wavelength ofthe wave

l The wave spreads out as wesaw on the previous slide

l So instead of a bright spot justin the middle we see aspread-out distribution of light

u but with some structure toit

l Type of diffraction we’restudying is called Fraunhoferdiffraction

u screen is far away from slitu …or there’s a converging

lens just after the slitu Demo

Don’t worry about the lens;Just think of the screen as far away

Where are the dark spots?

l Here’s where Huygen’s principlecomes in handy

l As the wave travels through theslit, treat each point in the slit asa source of waves

l Light from one part of the slit caninterfere with light from anotherpart

l Let’s divide the slit into halvesand consider the waveletscoming from point 1 and frompoint 3

l Wavelet 1 has to travel furtherl IF the additional distance, a/2sinq

is equal to l/2, then the waveletsfrom points 1 and 3 are exactlyhalf of a wavelength out of phase

u destructive interference

l Also true for 3 and 5, 2 and 4,any two points in the top andbottom of the slit separated bya/2

Can go through the same exercisedividing the screen in 4 parts, 6 parts,…

Dark spots

l So dark spots whenu a/2 sinq = l/2u …or a/2 sinq = 2l/2u …or a/2 sinq = 3l/2

l Corresponding tou sinq1 = l/au sinq2 = 2l/au sinq3 = 3l/au …

l Everything is in phase atq=0, so there’s a brightspot there

u and other bright spotsroughly half-way betweenthe dark spots

Back to 2 slits

lWhen I shinecoherent lightthrough two narrowslits, I see BOTHdiffraction andinterference

l I see the overalldiffraction patternwith the interferencefringes inside

l Back to demo

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 sinqbright = mlm=0,1,2,…

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

Polarization of electromagnetic waves

Remember our picture of lightas an EM wave; oscillating electricand magnetic fields

Here I’ve drawn the E field as oscillatingalong the y-axis but could be any orientation (but transverse to direction of propagation)The orientation of the E-field in the wave iscalled the polarization of the wave; for light, polarization is transverse

Polarizing filters

Polaroid material consists of long hydrocarbon chains which conductonly along the direction of the chainsSo they absorb light whose electric field vector is parallel to their

chains and transmit light whose electric fieldis perpendicular

I=Iocos2q

Example

Transmission through filters changes as relative orientation changes.

Polarization by reflection

l When unpolarized light isreflected from a surface,it can become partially(or even completely)polarized

l Portion of the EM wavethat has polarizationparallel to the surfacereflects more stronglythan does portion whichhas polarizationperpendicular to surface

u so reflected light ends uppartially polarized

Brewster’s angle

l At one particularangle (when reflectedand transmittedwaves form an angleof 90o with respect toeach other), thereflected light is100% polarizedl Brewster’s angle

(after Sir DavidBrewster) qp

u tan qp = n

going from air to a medium of index n

Polarization by scattering (what you’ve all been waiting for)

l When light passes through theearth’s atmosphere, theelectrons in the gas atomscan absorb and re-emit thelight

u this is called scatteringand is why the sky is notblack in the daytime

l The air molecules act like anantenna when they re-radiatethe EM waves

u if the EM polarization ofthe incident wave isparallel to the Earth’ssurface, the “antenna”radiates an EM wavedownward with the samepolarization

so sunlight isnot polarizedbut the lightfrom the skyis

But why is the sky blue?

l Sunlight has all visiblewavelength components(but peaks in yellow)

l High frequencycomponents of sunlightscatter more readily fromthe air molecules thanlow frequencycomponents

l So we see those highfrequency components,i.e. blue light, whenlooking away from thesun

Other examples

lWhat color is themoon’s sky?

lWhat color is sky onMars?

lWhat color is thesunset on Earth?