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…


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

https://www.exploratorium.edu/bob-miller/light-walk/video

https://www.exploratorium.edu/bob-miller/light-walk/video

Reflection

Angleofincidence=Angleofreflec9on

θi=θr

θi

θr

That’sallofthephysics–everythingelseisjustgeometry!


TextNormal line

Mirr

or s

urfa

ce

Flat Mirror

AllyouseeiswhatreachesyoureyesYouthinkobject’sloca9oniswhereraysappeartocomefrom.

θrθi

Flat Mirror

Object

Allraysorigina9ngfrompeakwillappeartocomefromsamepointbehindmirror! Image


Flat Mirror

3)Linesappeartointersectadistancedbehindmirror.Thisistheimageloca9on.

VirtualImage:Nolightactuallygetshere

d d

1)Drawfirstrayperpendiculartomirror0 = θi = θr

2)Drawsecondrayatangle.θi = θr

θrθi


Clicker Question

Awomanislookingatherreflec9oninaflatver9calmirror.Thelowestpartofherbodyshecanseeisherknee.

Ifshestandsclosertothemirror,whatwillbethelowestpartofherreflec9onshecanseeinthemirror.

A)Aboveherknee

B)Herknee

C)Belowherknee


Clicker Question

Awomanislookingatherreflec9oninaflatver9calmirror.Thelowestpartofherbodyshecanseeisherknee.Ifshestandsclosertothemirror,whatwillbethelowestpartofherreflec9onshecanseeinthemirror.

A)Aboveherknee

B)Herknee

C)Belowherknee

Ifthelightdoesn’tgettoyoureyethenyoucan’tseeit


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:


object

1)Drawrayparalleltoaxis reflec9ongoesthroughfocus

2)Drawraythroughfocus reflec9onisparalleltoaxis

image

Younowknowtheposi9onofthesamepointontheimage

2f f

normal

normal

Note:anyotherrayfrom9pofarrowwillbereflectedaccordingtoθi = θr andwillintersectthetworaysshownattheimagepoint.

Recipe for Finding Image:


object

image

SSʹ

f

S > 2fimageis:

realinvertedsmaller

2f f


f > 0s > 0s’ > 0

SS’ f

object

image

S = 2f

2f

f

imageis:real

invertedsamesize


SS’f

object

image

2f > S > f

2f f

imageis:real

invertedbigger


f

objectimage(virtual)

f > S > 0 raysnolongermeetinfrontofthemirror

buttheydomeetbehindthemirror

S

f


S’< 0f


f > S > 0

S

f

imageis:virtualuprightbigger

f > 0s > 0s’ > 0


f

Convex:Considerthecasewheretheshapeofthemirrorissuchthatlightraysparalleltotheaxisofthemirrorareall“focused”toacommonspotadistancef behindthemirror:

Note:analogousto“diverginglens”Realobjectwillproducevirtualimage


You will also get Images from Curved Mirrors:


object image(virtual)

S > 0 Sʹ< 0

f < 0

S > 0 imageis:virtualuprightsmaller

f > 0s > 0s’ > 0


Two Different Types of Lenses


ConvergingLens:Considerthecasewheretheshapeofthelensissuchthatlightraysparalleltotheaxisofthemirrorareall“focused”toacommonspotadistance f behindthelens:

f

f


object

1)Drawrayparalleltoaxis refractedraygoesthroughfocalpoint

2)Drawraythroughcenter refractedrayissymmetric

image

Younowknowtheposi9onofthesamepointontheimage

f

Recipe for Finding Image:


f

3)Drawraythroughfocalpoint refractedraygoesparalleltoaxis

alternateorcheck

S > 0 S’ > 0

f > 0

S > 2fimageis:

realinvertedsmaller

object

image

f

Example


S > 0

f > 0

S = fimageis:atinfinity

object f

Example


S > 0S’ < 0

f > 0

object

imagef

0 < S < fimageis:virtualuprightbigger

Example


DivergingLens:Considerthecasewheretheshapeofthelensissuchthatlightraysparalleltotheaxisofthelensalldivergebutappeartocomefromacommonspotadistancefinfrontofthelens:

f


S > 0 S’< 0

f < 0

imageis:virtualuprightsmaller

object

imagef

Example


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)


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:


Cisnotcorrectasitdoesnotgothroughthefocalpoint.

0

15

30

45

60

1

CheckPoint 2


CheckPoints 4 & 5

0

20

40

60

80

1

0

20

40

60

80

1


0

13

25

38

50

1

Iftheobjectisbehindthefocallengthitwillreflectaninvertedimage.

Iftheobjectisinfrontofthefocallengthitwillproduceavirtualuprightimage.

CheckPoint 7

SS’

f

object

image

2f > S > f

2f f

imageis:real

invertedbigger

f


f > S > 0 raysnolongermeetinfrontofthemirror

buttheydomeetbehindthemirror

S

f


0

18

35

53

70

1

CheckPoint 9

object image(virtual)

S > 0 Sʹ < 0

f < 0

S > 0 imageis:virtualuprightsmaller


AnarrowislocatedinfrontofaconvexsphericalmirrorofradiusR = 50cm.The9pofthearrowislocatedat(−20cm,−15cm).

Whereisthe9pofthearrow’simage?

ConceptualAnalysisMirrorEqua9on:1/s + 1/sʹ = 1/fMagnifica9on:M = −s’/s

StrategicAnalysisUsemirrorequa9ontofigureoutthexcoordinateoftheimageUsethemagnifica9onequa9ontofigureouttheycoordinateofthe9poftheimage

Calculation

R = 50y

x(–20,–15)


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


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)


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)


Magnifica9onequa9on

Activity 30-3

DonotdoAc9vity30-3.

physics 141 lecture 27 - sfu

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