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ChapterChapter 34A34A -- ReflectionReflection andand MirrorsMirrors (Geometrical)(Geometrical) AAA PowerPointPowerPointPowerPoint PresentationPresentationPresentation bybyby PaulPaulPaul E.E.E. Tippens,Tippens,Tippens, ProfessorProfessorProfessor ofofof PhysicsPhysicsPhysics SouthernSouthernSouthern PolytechnicPolytechnicPolytechnic StateStateState UniversityUniversityUniversity

© 2007 Objectives:Objectives: AfterAfter completingcompleting thisthis module,module, youyou shouldshould bebe ableable to:to: •• ExplainExplain andand discussdiscuss withwith diagrams,diagrams, reflectionreflection,, absorptionabsorption,, andand refractionrefraction ofof lightlight rays.rays. •• IllustrateIllustrate graphicallygraphically thethe reflectionreflection ofof lightlight fromfrom planeplane,, convexconvex,, andand concaveconcave mirrors.mirrors. •• DefineDefine andand illustrateillustrate youryour understandingunderstanding ofof realreal,, virtualvirtual,, erecterect,, invertedinverted,, enlargedenlarged,, andand diminisheddiminished asas appliedapplied toto images.images. •• UseUse geometricalgeometrical opticsoptics toto drawdraw imagesimages ofof anan objectobject atat variousvarious distancesdistances fromfrom convergingconverging andand divergingdiverging mirrors.mirrors. GeometricalGeometrical OpticsOptics

InInIn thethethe studystudystudy ofofof howhowhow lightlightlight behaves,behaves,behaves, ititit isisis usefulusefuluseful tototo useuseuse “““lightlightlight raysraysrays””” andandand thethethe factfactfact thatthatthat lightlightlight travelstravelstravels ininin straightstraightstraight lines.lines.lines.

WhenWhen lightlight strikesstrikes thethe Air reflection boundaryboundary betweenbetween twotwo media,media, threethree thingsthings maymay happen:happen: absorption Water reflectionreflection,, refractionrefraction,, oror absorptionabsorption.. refraction Reflection,Reflection, Refraction,Refraction, andand AbsorptionAbsorption Air reflection Reflection:Reflection: AA rayray fromfrom airair strikesstrikes thethe waterwater andand absorption Water returnsreturns toto thethe air.air. refraction

Refraction:Refraction: AA rayray Absorption:Absorption: AA rayray isis bendsbends intointo thethe absorbedabsorbed atomicallyatomically waterwater towardtoward thethe byby thethe waterwater andand normalnormal line.line. doesdoes notnot reappear.reappear. TheThe LawsLaws ofof ReflectionReflection 1. The angle of inci- 1. The angle of inci- Air N reflection dencedence  isis equalequal i   toto thethe angleangle ofof i r reflectionreflection  :: r Water  =  i i = rr AllAll rayray anglesangles areare measuredmeasured withwith respectrespect toto normalnormal NN..

2.2. TheThe incidentincident ray,ray, thethe 3.3. TheThe raysrays areare reflectedreflected ray,ray, andand completelycompletely thethe normalnormal NN allall lielie reversible.reversible. inin thethe samesame plane.plane. TheThe PlanePlane MirrorMirror AA mirrormirror isis aa highlyhighly polishedpolished surfacesurface thatthat formsforms imagesimages byby uniformlyuniformly reflectedreflected light.light. Note: images appear to be equi-distant behind mirror and are right- left reversed. DefinitionsDefinitions

Object Image Object Image distance = distance

p = q pp qq i = r RealReal andand VirtualVirtual RealReal imagesimages andand Light rays No light objectsobjects areare formedformed byby actualactual raysrays ofof light.light. (Real(Real imagesimages cancan bebe projectedprojected onon aa screen.)screen.) Real Virtual object image VirtualVirtual imagesimages andand objectsobjects dodo notnot reallyreally VirtualVirtual imagesimages areare onon thethe exist,exist, butbut onlyonly seemseem oppositeopposite sideside ofof thethe mirrormirror toto bebe atat aa location.location. fromfrom thethe incomingincoming rays.rays. ImageImage ofof aa PointPoint ObjectObject

Plane mirror

q = p

p q Real Virtual object image

ImageImageImage appearsappearsappears tototo bebebe atatat samesamesame distancedistancedistance behindbehindbehind mirrormirrormirror regardlessregardlessregardless ofofof viewingviewingviewing angle.angle.angle. ImageImage ofof anan ExtendedExtended ObjectObject

Plane mirror q = p

p q Virtual image

ImageImageImage ofofof bottombottombottom andandand toptoptop ofofof guitarguitarguitar showsshowsshows forwardforwardforward-back,--back,back, rightrightright-left--leftleft reversals.reversals.reversals. TermsTerms forfor SphericalSpherical MirrorsMirrors AA sphericalspherical mirrormirror isis Concave Mirror formedformed byby thethe insideinside ((concaveconcave)) oror outsideoutside Axis ((convexconvex)) surfacessurfaces ofof R V aa sphere.sphere. C AA concaveconcave sphericalspherical Linear mirrormirror isis shownshown herehere aperture withwith partsparts identified.identified. Center of Curvature C TheThe axisaxis andand linearlinear Radius of curvature R apertureaperture areare shown.shown. Vertex V TheThe FocalFocal LengthLength ff ofof aa MirrorMirror

Incident parallel ray SinceSince i == r, , wewe find that F is mid-  find that F is mid- i wayway betweenbetween VV R r C F V andand CC;; wewe find:find: axis f TheThe focalfocal Focal point lengthlength ff is:is: R The focal length, f f  2

TheThe focalfocal lengthlength ff isis equalequal toto halfhalf thethe radiusradius RR TheThe FocusFocus ofof aa ConcaveConcave MirrorMirror TheThe focalfocal pointpoint FF forfor aa concaveconcave mirrormirror isis thethe pointpoint atat whichwhich allall parallelparallel lightlight raysrays convergeconverge..

Incident parallel Rays ForForFor objectsobjectsobjects lololo--- catedcatedcated atatat infinityinfinityinfinity,,, thethethe realrealreal imageimageimage F appearsappearsappears atatat thethethe C focalfocalfocal pointpointpoint sincesincesince axis raysraysrays ofofof lightlightlight areareare almostalmostalmost parallel.parallel.parallel. R f  FocalFocal pointpoint 2 TheThe FocusFocus ofof aa ConvexConvex MirrorMirror TheThe focalfocal pointpoint forfor aa convexconvex mirrormirror isis thethe pointpoint FF fromfrom whichwhich allall parallelparallel lightlight raysrays divergediverge..

Virtual focus; Incident Rays reflected rays diverge. RR

axis C F R f  2 Reflected Rays ImageImage Construction:Construction:

RayRayRay 1:1:1: AAA rayrayray parallelparallelparallel tototo mirrormirrormirror axisaxisaxis passespassespasses throughthroughthrough thethethe focalfocalfocal pointpointpoint ofofof aaa concaveconcaveconcave mirrormirrormirror ororor appearsappearsappears tototo comecomecome fromfromfrom thethethe focalfocalfocal pointpointpoint ofofof aaa convexconvexconvex mirror.mirror.mirror.

Ray 1 Convex Ray 1 mirror C F C F Object Object Concave mirror ImageImage ConstructionConstruction (Cont.):(Cont.):

RayRayRay 2:2:2: AAA rayrayray passingpassingpassing throughthroughthrough thethethe focusfocusfocus ofofof aaa concaveconcaveconcave mirrormirrormirror ororor proceedingproceedingproceeding towardtowardtoward thethethe focusfocusfocus ofofof aaa convexconvexconvex mirrormirrormirror isisis reflectedreflectedreflected parallelparallelparallel tototo thethethe mirrormirrormirror axis.axis.axis.

Ray 1 Convex Ray 1 mirror Ray 2 C F Ray 2 Image C F Image Concave mirror ImageImage ConstructionConstruction (Cont.):(Cont.):

Ray 1 Ray 3 Ray 1 Ray 2 Ray 2 C F C F Image Ray 3 Concave Convex mirror mirror TheThe NatureNature ofof ImagesImages

AnAnAn objectobjectobject isisis placedplacedplaced ininin frontfrontfront ofofof aaa concaveconcaveconcave mirror.mirror.mirror. ItItIt isisis usefulusefuluseful tototo tracetracetrace thethethe imagesimagesimages asasas thethethe objectobjectobject movesmovesmoves evereverever closerclosercloser tototo thethethe vertexvertexvertex ofofof thethethe mirror.mirror.mirror. We will want to locate the image and answer three questions for the possible positions: 1. Is the image erect or inverted? 2. Is the image real or virtual? 3. Is it enlarged, diminished, or the same size? ObjectObject OutsideOutside CenterCenter CC

1.1. TheThe imageimage isis invertedinverted;; Ray 1 i.e.,i.e., oppositeopposite ofof thethe Ray 2 objectobject orientation.orientation.

2.2. TheThe imageimage isis realreal;; i.e.,i.e., C F formedformed byby actualactual lightlight Concave Ray 3 raysrays inin frontfront ofof mirror.mirror. mirror 3.3. TheThe imageimage isis diminisheddiminished inin size;size; i.e.,i.e., smallersmaller ImageImage isis locatedlocated thanthan thethe object.object. betweenbetween CC andand FF ObjectObject atat thethe CenterCenter CC

1.1. TheThe imageimage isis invertedinverted;; Ray 1 i.e.,i.e., oppositeopposite ofof thethe Ray 2 objectobject orientation.orientation.

2.2. TheThe imageimage isis realreal;; i.e.,i.e., C F formedformed byby actualactual lightlight raysrays inin frontfront ofof mirror.mirror. Ray 3

3.3. TheThe imageimage isis thethe samesame sizesize asas thethe object.object. ImageImage isis locatedlocated atat C,C, inverted.inverted. ObjectObject BetweenBetween CC andand FF 1.1. TheThe imageimage isis invertedinverted;; i.e.,i.e., oppositeopposite ofof thethe Ray 1 objectobject orientation.orientation. Ray 3 C 2.2. TheThe imageimage isis realreal;; i.e.,i.e., F formedformed byby actualactual lightlight Ray 2 raysrays inin frontfront ofof mirror.mirror.

3.3. TheThe imageimage isis enlargedenlarged Image is outside inin size;size; i.e.,i.e., largerlarger thanthan Image is outside of the center C thethe object.object. of the center C ObjectObject atat FocalFocal PointPoint

WhenWhenWhen thethethe objectobjectobject isisis Ray 1 locatedlocatedlocated atatat thethethe focalfocalfocal Ray 3 C pointpointpoint ofofof thethethe mirror,mirror,mirror, thethethe imageimageimage isisis notnotnot F formedformedformed (or(or(or ititit isisis Reflected rays locatedlocatedlocated atatat infinity).infinity).infinity). are parallel

TheThe parallelparallel reflectedreflected ImageImage isis locatedlocated atat raysrays nevernever cross.cross. infinityinfinity (not(not formed).formed). ObjectObject InsideInside FocalFocal PointPoint 1.1. TheThe imageimage isis erecterect;; i.e.,i.e., samesame orientationorientation asas thethe object.object. C

2.2. TheThe imageimage isis virtualvirtual;; F Virtual thatthat is,is, itit seemsseems toto bebe Erect and image enlarged locatedlocated behindbehind mirror.mirror.

3.3. TheThe imageimage isis enlarged;enlarged; ImageImage isis locatedlocated biggerbigger thanthan thethe object.object. behindbehind thethe mirrormirror ObserveObserve thethe ImagesImages asas ObjectObject MovesMoves CloserCloser toto MirrorMirror

Ray Ray1 1 Ray 2Ray 1 Ray 3 Ray 2Ray 1 C C C C C FF F F Virtual ErectConcave andReflected Ray rays 3image enlarged RayRay 3 2 mirrorare parallel ConvexConvex MirrorMirror ImagingImaging

Convex Ray 1 Convex Ray 1 mirror mirror Ray 2 2 C F C F Image Image gets larger as object gets closer

AllAllAll imagesimagesimages areareare erecterecterect,,, virtualvirtualvirtual,,, andandand diminisheddiminisheddiminished... ImagesImagesImages getgetget largerlargerlarger asasas objectobjectobject approaches.approaches.approaches. ConvergingConverging andand DivergingDiverging MirrorsMirrors

ConcaveConcave mirrorsmirrors andand ConvexConvex mirrorsmirrors andand convergingconverging parallelparallel raysrays willwill diverdivergginingg parallelparallel raysrays willwill bebe calledcalled convergingconverging mirrorsmirrors bebe calledcalled diverdivergginingg mirrormirrorss fromfrom thisthis pointpoint onward.onward. fromfrom thisthis pointpoint onward.onward.

Converging Mirror Diverging Mirror F C C F

Concave Convex SummarySummary

Reflection:Reflection: AA rayray Air reflection fromfrom airair strikesstrikes thethe waterwater andand returnsreturns toto thethe air.air. absorption Water

refraction

Refraction:Refraction: AA rayray Absorption:Absorption: AA rayray isis bendsbends intointo thethe absorbedabsorbed atomicallyatomically waterwater towardtoward thethe byby thethe waterwater andand normalnormal line.line. doesdoes notnot reappear.reappear. SummarySummary (Cont.)(Cont.) 1. The angle of inci- 1. The angle of inci- Air N reflection dencedence  isis equalequal i   toto thethe angleangle ofof i r reflectionreflection  :: r Water  =  i i = rr AllAll rayray anglesangles areare measuredmeasured withwith respectrespect toto normalnormal NN..

ObjectObject distance:distance: TheThe straightstraight--lineline distancedistance pp fromfrom thethe surfacesurface ofof aa mirrormirror toto thethe object.object. ImageImage distance:distance: TheThe straightstraight--lineline distancedistance qq fromfrom thethe surfacesurface ofof aa mirrormirror toto thethe image.image. RealReal image:image: AnAn imageimage formedformed byby realreal lightlight raysrays thatthat cancan bebe projectedprojected onon aa screen.screen. VirtualVirtual image:image: AnAn imageimage thatthat appearsappears toto bebe atat aa locationlocation wherewhere nono lightlight raysrays reach.reach. ConvergingConverging andand divergingdiverging mirrors:mirrors: ReferRefer toto thethe reflectionreflection ofof parallelparallel raysrays fromfrom surfacesurface ofof mirror.mirror. ImageImage ConstructionConstruction Summary:Summary:

RayRayRay 3:3:3: AAA rayrayray thatthatthat proceedsproceedsproceeds alongalongalong aaa radiusradiusradius isisis alwaysalwaysalways reflectedreflectedreflected backbackback alongalongalong itsitsits originaloriginaloriginal path.path.path. SummarySummary (Cont.)(Cont.) ForFor planeplane mirrors,mirrors, thethe objectobject distancedistance equalsequals thethe imageimage distancedistance andand allall imagesimages areare erecterect andand virtual.virtual. ForFor convergingconverging mirrorsmirrors andand divergingdiverging mirrors,mirrors, thethe focalfocal lengthlength isis equalequal toto oneone--halfhalf thethe radius.radius. AllAll imagesimages formedformed fromfrom convexconvex mirrorsmirrors areare erect,erect, virtual,virtual, andand diminisheddiminished inin size.size. ExceptExcept forfor objectsobjects locatedlocated insideinside thethe focusfocus (which(which areare erecterect andand virtual),virtual), allall imagesimages formedformed byby convergingconverging mirrorsmirrors areare realreal andand inverted.inverted. CONCLUSION:CONCLUSION: ChapterChapter 34A34A ReflectionReflection andand MirrorsMirrors (Geometrical)(Geometrical)