Laser
Flashlight
Lightbulb
Incidentrayfromalightbulb
MANYreflectedrayscomefromallpartsofAlex,including
hisnose-adiffuseobject
BobseesAlex'snosebecauseareflectedlightrayentersBob'seye!
LightraysareinvisibleunlesstheyenterdirectlyintooureyeorarescaFeredbysmoke,fogorsomeobjectintoyoureye!
1
Raysbouncewhentheyreflectoffamirrororshinysurface
Mirror
• ThisiscalledspecularreflecMon.
• HowisitdifferentfromdiffusereflecMon?
2
Raysbendwhentheyaredirectedatananglefromairtowaterorglass
Air
Glassorwater
• Thisistheprinciplebehindlenses
3
WhenrayscomeoutinvariousdifferentdirecMonsfromanobjectorobjects,thewavefrontisdefinedasacurveor
surfaceperpendiculartoalltherays
• Inthiscasethewavefrontisexpandingoutsphericallyfromthelightbulb.
• Whereveritintersectsaraythewavefrontisperpendiculartothatray– Moretechnically,thetangentto
thewavefrontatthepointofintersecMonisperpendiculartotheray
• Thewavefrontmaybeeasiertovisualizethantherays– Youthrowapebbleintoapond.
Thecircularlyexpandingwaterwavesarethewavefronts
Lightbulb
Rays
Wavefront
4
Drawawavefrontforeachofthesesetsofrays;howcantheraysbeproducedineachcase?
• Producedbyalaser,forexample
• Producedbytwolightbulbs,forexample
5
Weseecolorwhenwavesofdifferentwave–lengthsenterenteroureyes!ColorisnotapropertyofEM
wavesbutasensaMoninthebrain.
Lightwithwavelengthof650nmappearsredwhenitentersaviewerseye
Lightwithwavelengthof520nmappearsgreenwhenitentersaviewerseye
Lightwithwavelengthof470nmappearsbluewhenitentersaviewerseye
Thespeedoflightinemptyspaceisthesameforallwavelengths6
Whathappenswhentwoormorewaveswithdifferentwavelengthsenteryoureyetogether?
Lightwithbothwavelengths650nmand520nmappearsyellowwhenitentersaviewerseye
Lightwithonlywavelength580nmALSOappearsyellowwhenitentersaviewerseye(ADEEPERYELLOWTHANFORTHECASEABOVE)
7
Whatiswhitelight?
Lightwhichisamixtureof650,520and470nmwavelengths(andohenmanymorewavelengths)appearsWHITEwhenitreachesyoureye
Nosinglewavelength(mono-chromaMc)waveappearswhitewhenitreachesyoureye!
8
AprismspreadsouttheoverlappingwavesofdifferentwavelengthsinwhitelightintodifferentspaMallocaMonswheretheycanbeseenascolors.
A point light source emits rays in all directions radially outwards
Rays from two�point light sources look like this (HW1)
The rays only tell us which directionthe light goes in. From wave theorywe know that the light gets dimmer as you move further away from the light source.
Rays that ARE blocked by the book
Shadows appear when rays are blocked
Point light source Book
Wall
Shad
ow
Rays that are NOT blocked by the book
2 point light sources Book
Wall
AB
What happens to the shadow if I move the screen back from the book?
umbra
bright
penumbra
penumbra
brightunblocked
unblocked
blocked
Thetwopartsofthepenumbraeachgetlightfromonlyoneofthetwobulbs.Thegetsnolightfromeitherofthetwobulbs.Thebrightregiongetslightfrombothofthebulbs.
An "extended object" consists of many points. Each point on the object emits or reflects rays in all directions (unless the
object is a mirror)
Incident rays from a �frosted light bulb
MANY reflected rays come�from each point on Alex.This is diffuse reflection
An extended light source such as the sun (or a large light bulb) also produces an umbra and penumbra in empty space behind
the Earth (or another object)
Sun
• All rays coming from point A on the sun between the two dashed rays are blocked by Earth• All rays coming from point B on the sun between the two dotted rays are blocked by Earth
• The umbra gets no light from any portion of the sun
• The umbra gets smaller not larger further behind Earth since the Sun is larger than Earth
• The penumbra gets light from part of the sun
– If you look back from the penumbra you can see part of the sun
• When the moon passes completely into the umbra there is a total eclipse of the moon.
– When the moon passes into the penumbra there is a partial eclipse of the moon
A
B
UmbraPenumbra
Penumbra
Rays from this part of the sun �DO reach the upper penumbra
Rays from this part of the sun �DON'T reach the upper penumbra�because they are blocked by Earth
The more rays that reach a�point the brighter the point
• This is why regions outside the penumbra and umbra are brighter– These regions get light rays
from both point light sources• The more lights you turn on
the brighter the reflected light from objects in the room– See rays at right
Light�source 2
Light�source 1
Reflected raysfrom light 1
Reflected raysfrom light 2
Your eye seesa brighter nosethan with eitherlight source alone
A pinhole camera works by blocking rays
Pinhole Camera
Light bulb
Image of�light bulb
blocked rays
• What is an image?• A real image is formed on a screen when one or
more rays from each point on the object reach the corresponding points on the screen and no other rays from other points on the object reach those points
• NoMcethatthisimageisupsidedownandleh-rightreversed.
If a lens is used instead of a pinhole the image is brighter because many of the previously blocked rays are bent so that they arrive
at the correct place on the screen image
Light bulb
Image� of light bulb
blocked rays
Not just ONE ray from the filament but MANY now arrive at the corresponding image point so the image is BRIGHTER
previously blocked rays
Camera with lens
The object photographed with a pinhole camera does not have to be self-luminous!
Pinhole Camera
Alex
Image of�Alex
blocked rays
• Onceagainthisimageisupsidedownandleh-rightreversed.Earlyphotographs(daguerreotypes)werealwaysleh-rightreversed.
One of many rays of light shining on Alex
Reflected rays �off the real Alex �go through the holeand make the image
Finding an image by using rays is called ray tracing.�Trace rays from the object through the pinhole in the camera to
find the image rather than trusting your intuition!
Is the image of Alex smaller or larger than the real Alex?a) Smallerb) Largerc) Same size
Is the image of Alex smaller or larger than the real Alex?a) Smallerb) Largerc) Same size
What is the difference in the image when a (translucent) screen, film or nothing is behind a pinhole?
• Translucent screen (groundglass) – scatters rays in all directions from each
ray from the pinhole– viewer sees each image point from many
vantage points– viewer sees entire (upside down) image
from many vantage points• Film (or digital CCD)
– records light info from ray at each point on (upside down) image
– after processing, the info on the film can be viewed by reflected or transmitted light as an image on paper or a screen which can be seen from any vantage pt.
• Nothing at back– entire image cannot be seen at once
because only one ray at a time enters eye– to see each pt. on the image you must
move your head to new vantage pt.– image is still upside down
Plasma frequency of silver
Materials like metals with many mobile electrons can cancel out the light wave field in the forward direction so there is no transmission
but only reflection at certain wavelengths.
• Metals reflect all waves below a certain frequency– the plasma frequency - which
varies from metal to metal• Silver is particularly interesting
because it reflects light waves at all visible frequencies– Its plasma frequency is at the top
of the violet so it reflects all of the wavelengths below and appears whitish
• Gold and copper have a yellowish-brownish color because they reflect greens, yellows and reds but not blues or violets– Red and green make yellow
Plasma frequency of gold
Plasmafrequencyofcopper
The plasma frequency is ωe =4πne2
me
.
Its magnitude goes as the square root of the density of electrons.
What is a mirror?• Since silver is such a good
reflector a coating of silver on glass makes a good (common) mirror.
• If the silver coating is thin enough the mirror can be made to transmit 50% of the light and to reflect the other 50%– This is called a half-silvered
mirror– A half-silvered mirror used with
proper lighting can show objects on one side or the other of the mirror
Reflection of waves occurs where the medium of propagation changes abruptly
• When light waves are incident on a glass slab they are mostly transmitted but partly reflected!
• The speed of the wave must change a lot as the wave travels from one medium to the other for reflection to occur
Glass slab
Law of specular reflection of a ray from a mirror
Mirror
This angle = this angle
The normal to the mirror is an imaginary�line drawn perpendicular to it from where the incident ray hits the mirror
Normal
• OneofmanyraysfromalightbulbhitsAlex'schin.
• Therayfromthelightbulbisdiffuselyreflectedoffhischin.Weshowoneofthemanyrayscomingoffhischinhijngamirror.– Thisiscalledanincidentray
• Theincidentrayundergoesspecularreflec>onoffthemirror– Notethereflectedray
• Drawthenormaltothemirror– Theangleofincidence=theangle
ofreflecMon
How is an image produced in a mirror?�Part 1: Ray-tracing
• To find out how Bob "sees" Alex by looking in the mirror we trace rays which obey the law of reflection– Consider an incident ray from Alex's chin
which reflects according to the law of reflection at a specific point on the mirror and goes into Bob's eye.
– Note - it is not easy to construct this ray! You cannot arbitrarly choose a point on the mirror and expect that the law of reflection will be satisfied
– Bob will see only this reflected ray from Alex's chin.
– Other refelected rays from Alex's chin will miss his eye (see right)
– A ray from Alex's hair will reflect at one point on the mirror into Alex's eye (and satisfies the law of reflection)
Mirror
Alex Bob looks at�Alex's image
• To find the image of Alex we must learn how Bob’s eye (and our eyes) interpret rays
• Bob cannot directly know whether the rays entering his eyes have been reflected or not!
• We interpret all rays coming into our eye as traveling from a fictitious image in a straight line to our eye even if they are reflected rays!
• To find the virtual (fictitious) image of Alex’s chin we extend each reflected ray backwards in a straight line to where there are no real rays– Extend the ray reflected into Bob's eye from
Alex's chin backward behind the mirror.– Extend the ray reflected towards Bob's chest
(why?) from Alex's chin backward (dashed line) behind the mirror.
– The image of Alex's chin will be behind the mirror at the intersection of the two backward-extended reflected rays.
– Note all reflected rays from his chin intersect at the same image pt. when extended backwards
How is an image produced in a mirror?�Part 2: The psychology of ray interpretation
Mirror
Alex Bob looks at�Alex's image
• To find the location of his hair in the virtual image we extend any reflected ray from his hair backwards
How is an image produced in a mirror?�Part 3: The meaning of a virtual image
• If we trace rays for every ray from every part of Alex which reflects in the mirror– we get a virtual image of the real Alex
behind the mirror. It is virtual because there is no light energy there, no real rays reach it, and it cannot be seen by putting a screen at its position!!
Virtual image of Alex�is behind mirror
Mirror
Alex
• WhenallofthereflectedraysfromAlex'schinaretracedbackwardstheyallappeartocomefromthevirtualimageofhischin– HenceAlex'simageisalwaysinthesame
placeregardlessofwhereBoblooks• Theimagechinisbehindthemirrorbya
distance=tothedistancetherealchinisinfrontofthemirror– ThisistrueforallpartsofAlex'simage– Alex'svirtualimageisthesamesizeas
therealAlex– Alex'simageisfurtherawayfromBob
thantherealAlex
Bob looks at�Alex's image
Bob sees Alex's image�in the same place whenhe moves his head
How is an image produced in a mirror?�Part 3: The meaning of a virtual image
• If we trace rays for every ray from every part of Alex which reflects in the mirror– we get a virtual image of the real Alex
behind the mirror. It is virtual because there is no light energy there, no real rays reach it, and it cannot be seen by putting a screen at its position!!
Virtual image of Alex�is behind mirror
Mirror
Alex
• WhenallofthereflectedraysfromAlex'schinaretracedbackwardstheyallappeartocomefromthevirtualimageofhischin– HenceAlex'simageisalwaysinthesame
placeregardlessofwhereBoblooks• Theimagechinisbehindthemirrorbya
distance=tothedistancetherealchinisinfrontofthemirror– ThisistrueforallpartsofAlex'simage– Alex'svirtualimageisthesamesizeas
therealAlex– Alex'simageisfurtherawayfromBob
thantherealAlex
Bob looks at�Alex's image
Bob sees Alex's image�in the same place whenhe moves his head
For simple (flat) mirrors the image location is therefore predictable without knowing where the observer's eye is
and without ray-tracing
Mirror
Mirror Mirror
Mirror
Mirror
Alex• Question: Where are
the images of Alex in the 2 mirrors?
a) At A onlyb) At B onlyc) At A and B onlyd) At C onlye) At A, B and C
Multiple mirrors - a virtual image can act as a real object and have its own virtual image
Mirror
A C
B
ThevirtualimageatAactsasanobjecttoproducethevirtualimageofC.Itactsasanintermediateimage.Morepreciselyitistheredrayswhichreflectasgreenrays.
A few words about virtual images• Here is the real Alex• Here are some (diffusely reflected)
diverging rays coming off his nose– They can be seen by eyes at various
locations• We only know his nose is there
because our eyes receive the rays • Therefore, we would see an image
(virtual) of Alex if those rays reached our eyes even when he wasn't there.
• Mirrors can provide those rays!• The (imaginary) extension of
(reflected) rays behind the mirror look just like the real rays from the real Alex
Mirror (incident�rays not shown)
Refraction is the bending of a ray after it enters a medium where its speed is different
• A ray going from a fast medium to a slow medium bends towards the normal to the surface of the medium
• A ray going from a slow medium to a fast medium bends away from the normal to the surface of the medium
• The speed of light in a medium is v = c/n, where n is a number larger than one called the index of refraction and�c = 3 x 108 m/s• n = 1.3 for glass• n = 1.5 for water
• Hence, a ray going into a medium with a higher index of refraction bends towards the normal and a ray going into a medium with a lower index of refraction bends away from the normal
Air (fast medium)
Glass orwater�(slow)
Normal
Glass orwater�(slow)
Normal Air (fast medium)
nair < nwater
1.001 < 1.5
Marching army analogy for ray bending towards the normal as light crosses a sharp boundary to a slower
medium
Incident ray
Rows of soldiers before they hit rough (muddy) slow terrain
Rows of soldiers after they hit slow terrain
• The rows of marching soldiers are analogous to the wave fronts of light
• When the soldiers hit muddy terrain they slow down
• This causes the rows or parts of rows in the mud to move less far in a given time.
• Another way of saying this is that the ray perpendicular to the rows of soldiers outside the mud bends towards the normal to the muddy region for rows in the mud
Ray-bending together with our psychological straight-ray interpretation determine the location of images underwater
• The precise amount of bending is determined by the law of refraction (sometimes called Snell's law): nisinθi = ntsinθt
• Here, θi = angle between incident ray and normal,
• and θt = angle between transmitted ray and normal
• ni and nt are the indices of refraction in the medium containing the incident ray and in the medium containing the transmitted ray
• YouTube Video of Archer fish
• YouTube Video of refraction
incident ray
transmitted ray
normal
image of fish for someone out of water
fish
• In order to observe the fish from outside the water a transmitted ray must enter your eye. • You will think it comes from a point obtained by tracing it backwards,• Extend any 2 of the many many transmitted rays from the nose of the fish backwards to find the image of the nose of the fish (where they intersect). • The location of that image will be the same for any observer outside of the water. �
Total internal reflection is an extreme case of a ray bending away from the normal as it goes from a higher to a lower index of
refraction medium (from a slower to a faster medium)
Glass orwater�(slow)
NormalAir (fast medium)
Just below the critical angle for total �internal reflection there is a reflected �ray and a transmitted (refracted) ray
Glass orwater�(slow)
Normal
Just above the critical angle for total internal reflection there is a reflected ray but no transmitted (refracted) ray
Critical�angle
