Physics 141 Lecture 27 - SFU
Transcript of Physics 141 Lecture 27 - SFU
Physics 141Lecture 27
Today’sConcept:
A)Mirrors
Electricity&Magne9smLecture27,Slide1
Your Question
If white light refracts into a spectrum through a lens, then how can a camera take a colour picture properly, preserving the position of different coloured pixels as they are focused?
Achromatic doublet
Object Location
Lightraysfromsunbounceoffobjectandgoinalldirec9ons! Somehitsyoureyes
Weknowobject’sloca9onbywhererayscomefrom.
Wewilldiscusseyesinlecture28…
Electricity&Magne9smLecture26,Slide4
Your comments (and jokes)AOerthissemesterslackofjokeshere's2aboutlenses...
! 1)Whatmusicdooptometristlistento?• -itunes
! 2)Whatwasthelens’sexcusetothepoliceman?• I’vebeenframedofficer
Solhadlivedalonglife,whichwasdrawingtoitsend.Ashisfamilysurroundedhimonhisdeathbed,heaskedtoseehisoptometrist."Optometrist?"theyasked."Whyintheworlddoyouwanttoseeyouroptometrist?""Justgethimforme."SotheygogetDr.Kaplan,who,onseeingSolabouttodepartthislife,asked,"Sol,itpainsmetoseeyoulikethis.WhatcanIpossiblydoforyou?"Solopenedhiseyesslightlyandsaid,"Doc,beforeIgo,there'sonethingIhavetoknow.Whichonewasclearer-AorB?"
More
Hey,I'm18.WhendoIgetmyAdultSuperVision?
Eyehopewedon'thavemuchop9csmaterialonthefinal.
Hope again.
Last time: “Joke of the day:What is a pirate favorite letter. If you said r then you are wrong. It is the letter c.”
Today: “Thank you for the extra review questions. Explanation for my pirate joke is that the letter c sounds like sea and the letter r sounds like arr. What is a pirate favorite letter. If you said the letter r you are wrong. It is c.”
Sincewe'reintheop9csunit,canyoupleaseexplainthephenomenonofcrescentshapedshadowsduringthetotalsolareclipselastyear?Iheldupastrainerwhenithappened,andinsteadofgeangcircleshapedshadows,Igotweirdcrescents.Itwasprebycreepy.
! BobMiller'sLightWalk
Reflection
Angleofincidence=Angleofreflec9on
θi=θr
θi
θr
That’sallofthephysics–everythingelseisjustgeometry!
Electricity&Magne9smLecture27,Slide4
TextNormal line
Mirr
or s
urfa
ce
Flat Mirror
AllyouseeiswhatreachesyoureyesYouthinkobject’sloca9oniswhereraysappeartocomefrom.
θrθi
Flat Mirror
Object
Allraysorigina9ngfrompeakwillappeartocomefromsamepointbehindmirror! Image
Electricity&Magne9smLecture27,Slide5
Flat Mirror
3)Linesappeartointersectadistancedbehindmirror.Thisistheimageloca9on.
VirtualImage:Nolightactuallygetshere
d d
1)Drawfirstrayperpendiculartomirror0 = θi = θr
2)Drawsecondrayatangle.θi = θr
θrθi
Electricity&Magne9smLecture27,Slide6
Clicker Question
Awomanislookingatherreflec9oninaflatver9calmirror.Thelowestpartofherbodyshecanseeisherknee.
Ifshestandsclosertothemirror,whatwillbethelowestpartofherreflec9onshecanseeinthemirror.
A)Aboveherknee
B)Herknee
C)Belowherknee
Electricity&Magne9smLecture27,Slide7
Clicker Question
Awomanislookingatherreflec9oninaflatver9calmirror.Thelowestpartofherbodyshecanseeisherknee.Ifshestandsclosertothemirror,whatwillbethelowestpartofherreflec9onshecanseeinthemirror.
A)Aboveherknee
B)Herknee
C)Belowherknee
Ifthelightdoesn’tgettoyoureyethenyoucan’tseeit
Electricity&Magne9smLecture27,Slide8
Concave:Considerthecasewheretheshapeofthemirrorissuchthatlightraysparalleltotheaxisofthemirrorareall“focused”toacommonspotadistancefinfrontofthemirror:
ThesemirrorsareoOensec9onsofspheres
(assumedinthisclass).
Forsuch“spherical”mirrors,weassumeallanglesare
smalleventhoughwedrawthembigtomakeiteasyto
see…
Note:analogousto“converginglens”Realobjectcanproducerealimage
fElectricity&Magne9smLecture27,Slide10
2f f
Forasphericalmirror,R = 2f
R
centerofspheresome9meslabeled“C”
Aside:
Electricity&Magne9smLecture27,Slide11
object
1)Drawrayparalleltoaxis reflec9ongoesthroughfocus
2)Drawraythroughfocus reflec9onisparalleltoaxis
image
Younowknowtheposi9onofthesamepointontheimage
2f f
normal
normal
Note:anyotherrayfrom9pofarrowwillbereflectedaccordingtoθi = θr andwillintersectthetworaysshownattheimagepoint.
Recipe for Finding Image:
Electricity&Magne9smLecture27,Slide12
object
image
SSʹ
f
S > 2fimageis:
realinvertedsmaller
2f f
Electricity&Magne9smLecture27,Slide13
f > 0s > 0s’ > 0
SS’ f
object
image
S = 2f
2f
f
imageis:real
invertedsamesize
Electricity&Magne9smLecture27,Slide14
SS’f
object
image
2f > S > f
2f f
imageis:real
invertedbigger
Electricity&Magne9smLecture27,Slide15
f
objectimage(virtual)
f > S > 0 raysnolongermeetinfrontofthemirror
buttheydomeetbehindthemirror
S
f
Electricity&Magne9smLecture27,Slide16
S’< 0f
objectimage(virtual)
f > S > 0
S
f
imageis:virtualuprightbigger
f > 0s > 0s’ > 0
Electricity&Magne9smLecture27,Slide17
f
Convex:Considerthecasewheretheshapeofthemirrorissuchthatlightraysparalleltotheaxisofthemirrorareall“focused”toacommonspotadistancef behindthemirror:
Note:analogousto“diverginglens”Realobjectwillproducevirtualimage
Electricity&Magne9smLecture27,Slide18
You will also get Images from Curved Mirrors:
Electricity&Magne9smLecture27,Slide9
object image(virtual)
S > 0 Sʹ< 0
f < 0
S > 0 imageis:virtualuprightsmaller
f > 0s > 0s’ > 0
Electricity&Magne9smLecture27,Slide19
Two Different Types of Lenses
Electricity&Magne9smLecture26,Slide6
ConvergingLens:Considerthecasewheretheshapeofthelensissuchthatlightraysparalleltotheaxisofthemirrorareall“focused”toacommonspotadistance f behindthelens:
f
f
Electricity&Magne9smLecture26,Slide7
object
1)Drawrayparalleltoaxis refractedraygoesthroughfocalpoint
2)Drawraythroughcenter refractedrayissymmetric
image
Younowknowtheposi9onofthesamepointontheimage
f
Recipe for Finding Image:
Electricity&Magne9smLecture26,Slide8
f
3)Drawraythroughfocalpoint refractedraygoesparalleltoaxis
alternateorcheck
S > 0 S’ > 0
f > 0
S > 2fimageis:
realinvertedsmaller
object
image
f
Example
Electricity&Magne9smLecture26,Slide9
S > 0
f > 0
S = fimageis:atinfinity
object f
Example
Electricity&Magne9smLecture26,Slide10
S > 0S’ < 0
f > 0
object
imagef
0 < S < fimageis:virtualuprightbigger
Example
Electricity&Magne9smLecture26,Slide11
DivergingLens:Considerthecasewheretheshapeofthelensissuchthatlightraysparalleltotheaxisofthelensalldivergebutappeartocomefromacommonspotadistancefinfrontofthelens:
f
Electricity&Magne9smLecture26,Slide12
S > 0 S’< 0
f < 0
imageis:virtualuprightsmaller
object
imagef
Example
Electricity&Magne9smLecture26,Slide13
S > 2freal
invertedsmaller
2f > S > f real
invertedbigger
f > S > 0 virtualuprightbigger
S > 0 virtualuprightsmaller
f > 0
f < 0
Executive Summary – Mirrors & Lenses:
fConverging
Diverging ffConvex
(diverging)
fConcave(Converging)
Electricity&Magne9smLecture27,Slide20
Lenssignconven9ons
S:posi9veifobjectis“upstream”oflensS’ :posi9veifimageis“downstream”oflensf:posi9veifconverginglens
Mirrorssignconven9ons
S:posi9veifobjectis“upstream”ofmirrorS’:posi9veifimageis“upstream”ofmirrorf:posi9veifconvergingmirror(concave)
s’ isposi9veforarealimagefisposi9vewhenitcanproducearealimage
Youjusthavetokeepthesignsstraight:
It’s Always the Same:
Electricity&Magne9smLecture27,Slide21
Cisnotcorrectasitdoesnotgothroughthefocalpoint.
0
15
30
45
60
1
CheckPoint 2
Electricity&Magne9smLecture27,Slide22
CheckPoints 4 & 5
0
20
40
60
80
1
0
20
40
60
80
1
Electricity&Magne9smLecture27,Slide23
0
13
25
38
50
1
Iftheobjectisbehindthefocallengthitwillreflectaninvertedimage.
Iftheobjectisinfrontofthefocallengthitwillproduceavirtualuprightimage.
CheckPoint 7
SS’
f
object
image
2f > S > f
2f f
imageis:real
invertedbigger
f
objectimage(virtual)
f > S > 0 raysnolongermeetinfrontofthemirror
buttheydomeetbehindthemirror
S
f
Electricity&Magne9smLecture27,Slide24
0
18
35
53
70
1
CheckPoint 9
object image(virtual)
S > 0 Sʹ < 0
f < 0
S > 0 imageis:virtualuprightsmaller
Electricity&Magne9smLecture27,Slide25
AnarrowislocatedinfrontofaconvexsphericalmirrorofradiusR = 50cm.The9pofthearrowislocatedat(−20cm,−15cm).
Whereisthe9pofthearrow’simage?
ConceptualAnalysisMirrorEqua9on:1/s + 1/sʹ = 1/fMagnifica9on:M = −s’/s
StrategicAnalysisUsemirrorequa9ontofigureoutthexcoordinateoftheimageUsethemagnifica9onequa9ontofigureouttheycoordinateofthe9poftheimage
Calculation
R = 50y
x(–20,–15)
Electricity&Magne9smLecture27,Slide26
Whatisthefocallengthofthemirror?
A)f = 50cm B)f = 25cm C)f = −50cm D)f = −25cm
Rule for sign: Positive on side of mirror where light goes after hitting mirror
f = − 25 cm
< 0
Calculation
R = 50y
x(-20,-15)
AnarrowislocatedinfrontofaconvexsphericalmirrorofradiusR = 50cm.The9pofthearrowislocatedat(−20cm,−15cm).
Forasphericalmirror| f | = R/2 = 25cm.
f
Ry
Electricity&Magne9smLecture27,Slide27
Whatisthexcoordinateoftheimage?
A)11.1 cm B)22.5 cm C)−11.1 cm D)−22.5cm
s = 20 cmf = −25 cm
= −11.1 cm
Sincesʹ < 0 theimageisvirtual(onthe“other”sideofthemirror)
CalculationAnarrowislocatedinfrontofaconvexsphericalmirrorofradiusR = 50cm.The9pofthearrowislocatedat(−20cm,−15cm).
f = −25 cm
R = 50y
x
(-20,-15)
Electricity&Magne9smLecture27,Slide28
Mirrorequa9on
Whatistheycoordinateofthe9poftheimage?
A)−11.1 cm B) −10.7 cm C)−9.1 cm D)−8.3cm
x = 11.1cm
s = 20 cmsʹ= −11.1 cm
M = 0.556
yimage = 0.55 yobject = 0.556⨉(−15 cm) = −8.34 cm
CalculationAnarrowislocatedinfrontofaconvexsphericalmirrorofradiusR = 50cm.The9pofthearrowislocatedat(−20cm,−15cm).
f = −25 cm
R = 50y
x
(-20,-15)
Electricity&Magne9smLecture27,Slide29
Magnifica9onequa9on
Activity 30-3
DonotdoAc9vity30-3.