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March 17, 2016 CH 34 IMAGES I.
TwoTypesofImages
A.
Foryoutoseeanobject,oureyeinterceptssomeofthelightraysspreading
fromtheobjectandthenredirectthemontotheretinaattherearoftheeye.Our
visualsystemidentifiesedges,orientations,textures,shapes,andcolorsandthen
rapidlybringstoyourconsciousnessanimage(areproductionderivedfromlight)ofthe
object.
B.
_________________________________________________________________________________________________
_________________________________________________________________________________________________________
(forexample,animagethatisformedbyamirrorappearstobepresentbehindthe
mirror),______________________________________________________________________________________________.
1.
AcommonMirage
2.
Thisisanexampleofavirtualimage
C.
Whenanimagecanbeformedonasurface,suchasacardoramoviescreen,
andwhentheexistenceoftheimagedoesnotdependonourseeingitanditis
presentevenifwearenot,thatimageistermed_________________________________________.
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March 17, 2016 II.
Mirrors
A.
PlaneMirrors
1.
________________________________________________________________________________________
_________________________________________________________________________________________________
_________________________________________________________________________________________________
_______________________________________________________________________________________________.
Ashinymetalsurfaceactsasamirror;aconcretewalldoesnot.Aplane
mirrorisaflatreflectingsurface.
2.
ThepointsourceisimageIofobjectO.Itiscalleda________________________
becauseitisapoint,anditisavirtualimagebecausetheraysdonotactually
passthroughit.(________________________________________________________________
_______________________________________________________________________________________________.)
3.
DepthofVirtualImage
Equation for a plane mirror: Page2
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March 17, 2016 4.
Onlyraysthatarefairlyclosetogethercanentertheeyeafter
reflectionatamirror.
5.
ExtendedObjects
6.
MirrorMaze
a)
Inamirrormazeeachwalliscovered,floortoceiling,witha
mirror.Ifonewalksthroughsuchamazethenwhatheseesinmost
directionsisaconfusingmontageofreflections.
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March 17, 2016 B.
SphericalMirrors
1.
Aconcavemirrorwherethemirror’ssurfaceisconcave(“cavedin”)
hasthefollowingcharacteristics:
a)
ThecenterofcurvatureC(thecenterofthesphereofwhichthe
mirror’ssurfaceispart)wasinfinitelyfarfromtheplanemirror;itis
nowcloserbutstillinfrontoftheconcavemirror.
b)
Thefieldofview—theextentofthescenethatisreflectedtothe
observer—waswide;itisnowsmaller.
c)
Theimageoftheobjectwasasfarbehindtheplanemirrorasthe
objectwasinfront;theimageisfartherbehindtheconcavemirror;that
is,|i|isgreater.
d)
Theheightoftheimagewasequaltotheheightoftheobject;the
heightoftheimageisnowgreater.Thisfeatureiswhymanymakeup
mirrorsandshavingmirrorsareconcave—theyproducealargerimage
ofaface.
2.
Wecanmakea________________mirrorbycurvingaplanemirrorsothat
itssurfaceis“____________________”convexasinfigure34‐8cabove.
Characteristics:
a) Center of curvature (C)  b) Field of view  c) Image d) Magnification Page4
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March 17, 2016 3.
Iffisthefocallength(________________________________________________________
________________,andrtheradiusofcurvature(theradiusofthesphere),then
(Eq 34‐3) 4.
ChangingtheLocationoftheObject
5.
________________________________________________________________________________________
_________________________________________________________________________________________________
________________________________________________________________________________________________.
6.
Whenlightraysfromanobjectmakeonlysmallangleswiththecentral
axisofasphericalmirror,asimpleequationrelatestheobjectdistancep,the
imagedistancei,andthefocallengthf:
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March 17, 2016 7.
Thesizeofanobjectorimage,asmeasuredperpendiculartothe
mirror’scentralaxis,iscalledtheobjectorimageheight.Lethrepresentthe
heightoftheobject,andh’theheightoftheimage.Thentheratioh’/hiscalled
thelateralmagnificationmproducedbythemirror.
m  C.
LocatingImagesbyDrawingRays
(Lateral magnification) Fig. 34-11 (a, b) Four rays that may
be drawn to find the image formed
by a concave mirror. For the object
position shown, the image is real,
inverted, and smaller than the object.
(c, d) Four similar rays for the case
of a convex mirror. For a convex
mirror, the image is always virtual,
oriented like the object, and smaller
than the object. [In (c), ray 2 is
initially directed toward focal point
F. In (d), ray 3 is initially directed
toward center of curvature C.]
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March 17, 2016 1.
Imagesmaybelocatedbydrawingthefollowingrays:
a)
Araythatis___________________________________________________________________
reflects______________________________________________________(ray1inFig.34‐11a).
b)
Araythatreflects________________________________________________________
thefocalpoint_____________________________________________________________________
(ray2inFig.34‐11a).
c)
Araythatreflectsfromthemirror_______________________________________
centerofcurvatureC_____________________________________(ray3inFig.34‐11b).
d)
Araythatreflects__________________________________________________________is
reflected_____________________________________________________________________________
(ray4inFig.34‐11b).
2.
Considerray4inFig.34‐11b.
a)
___________________________________________________________________________________
____________________________________________________________________________________________
___________________________________________________________________________________________.
b)
Thetworighttrianglesabcanddecinthefigurearesimilar
(havethesamesetofangles);sowecanwrite
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March 17, 2016 c)
Thequantityontheleft(apartfromthequestionofsign)isthe
lateralmagnificationmproducedbythemirror.Becauseweindicatean
invertedimageasanegativemagnification,wesymbolizethisas‐m.
However,cd=iandca=p;therefore
3.
SphericalMirrorExampleProblems
a)
A5xConcavemakeupmirrorhasacurvatureradiusof40cm.
Theinstructionmanualsaystoholdthemirrorapproximately6inches
fromthefacetoachievetheproper5timesmagnification.Isthisan
accuratestatement?Provewithequations.
b)
Considertheobject‐concavemirrorsystemshown.
(1) LabelthefocalpointwithanF,theradiusofcurvaturewithC, and the object with O. (2) Draw the ray diagram (at least 3 rays) for light originating at the tip of the object. (3) Draw the image. (4) If the distance from the object to the mirror is 5 m and the radius of curvature is 3 m, find the distance from the image to the mirror. Is the image real or virtual, upright or inverted? Show all work: Page8
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March 17, 2016 c)
As shown in the sketch drawn below, an object (arrow) is placed 20.0 cm in front of a spherical, convex mirror with a radius of curvature of 40.0 cm. (1)
Drawtheraydiagram(atleast3rays)forlightoriginatingat
thetipoftheobjectandshowthefinalimageincludingitslocation
numerically.
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March 17, 2016 D.
SphericalRefractingSurfaces
1.
________________________________________________________________________________________
_________________________________________________________________________________________________
______________________________________________________________________________________________.
2.
3.
________________________________________________________________________________________
________________________________________________________________________________________________.
4.
ExampleProblems
a)
Aconvexsphericalsurfacewithradiusrseparatesamedium
withindexofrefraction2fromair.Asanobjectismovedtowardthe
surfacefromfarawayalongthecentralaxis,itsimage:
A) changes from virtual to real when it is r/2 from the surface B) changes from virtual to real when it is r from the surface C) changes from real to virtual when it is r/2 from the surface D) changes from real to virtual when it is r from the surface E) remains real b)
Myswimmingcoachusedtosay,thatanobjectonthebottomof
thedeependofthepoolwhenviewedfromabove,willnotlookasdeepas
itreallyisbyafactorof¾.Washetellingthetruth,yesorno?Prove
usingthesphericalrefractingsurfaceequation.
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March 17, 2016 III.
Lenses
A.
Thinlenses
1.
Alensisatransparentobjectwithtworefractingsurfaceswhose
centralaxescoincide.Thecommoncentralaxisisthecentralaxisofthelens.
2.
Alensthatcauseslightraysinitiallyparalleltothecentralaxisto
convergeis(reasonably)calleda_________________________________.If,instead,it
causessuchraystodiverge,thelensisa_________________________________.
3.
Athinlensisalensinwhichthethickestpartisthinrelativetothe
objectdistancep,theimagedistancei,andtheradiiofcurvaturer andr of
1
2
thetwosurfacesofthelens.Ifoneconsidersonlylightraysthatmakesmall
angleswiththecentralaxis,andiffisthefocallength,then
4.
Also,
Thislastequationiscalledthelensmaker’sequation.
5.
________________________________________________________________________________________
_________________________________________________________________________________________________
_________________________________________________________________________________________________
________________________________________________________________________________________________.
6.
BendingLightraysthroughalens
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March 17, 2016 7.
Imagesfromthinlenses
a)
___________________________________________________________________________________
____________________________________________________________________________________________
___________________________________________________________________________________________.
Fig. 34-15 (a) A real, inverted image I is formed by a converging lens when the
object O is outside the focal point F1.
(b) The image I is virtual and has the same orientation as O when O is inside the
focal point.
(c) A diverging lens forms a virtual image I, with the same orientation as the object
O, whether O is inside or outside the focal point of the lens.
Most students struggle keeping lenses and mirrors separate so you might want to create some sort of table or chart or pneumonic to help you keep then straight. There are tables in the book that are blank, and it might help you to copy them here into your notes and complete the tables, but it is not an assignment. (Table 34‐1 on page 1018, and table 34‐2 on page 1026.) Page
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March 17, 2016 IV.
LocatingImagesofExtendedObjectsbyDrawingRays
1.
________________________________________________________________________________________
_________________________________________________________________________________________________
______________________________________________________________________(ray1inFig.34‐16a).
________________________________________________________________________________________
_________________________________________________________________________________________________
______________________________________________________________________(ray2inFig.34‐16a).
2.
3.
_________________________________________________________________________________________________
__________________________________________________________________________________________________________
____________________________________________________________________________.(ray3inFig.34‐16a).
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March 17, 2016 B.
TwoLensSystem
1.
Step1
a)
___________________________________________________________________________________
____________________________________________________________________________________________
___________________________________________________________________________________________.
b)
___________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
___________________________________________________________________________________________.
c)
2.
Findthelateralmagnificationm .
1
Step2
a)
___________________________________________________________________________________
____________________________________________________________________________________________
___________________________________________________________________________________________.
b)
___________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
___________________________________________________________________________________________.
c)
Findthelateralmagnificationm .
2
3.
Totalmagnificationis:
4.
IfMispositive,thefinalimagehassametheorientationastheobject.
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March 17, 2016 V.
ExampleProblems
A.
Considertheobject‐diverginglenssystemshown.Anobjectis
placed30cmtotheleftofthediverginglenswithafocallengthof‐20cm.
Theimageproducedis:
A.
B.
C.
D.
E.
Real, upright, smaller, and 12 cm to the left of the lens. Real, inverted, larger, and 10 cm to the right of the lens. Virtual, upright, smaller, and 12 cm to the left of the lens. Virtual, inverted, larger, and 10 cm to the right of the lens. Virtual, upright, larger, and 10 cm to the left of the lens. Page
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March 17, 2016 B.
Twoconverginglensesareplaced60cmapart.Thefocallengthof
thefirstlensis30cmandthefocallengthofthesecondlensis10cm.An
objectisplaced80cmtotheleftofthefirstlensasshown.Thefinal
imagecomparedtoobjectis:
1)
2)
3)
4)
Upright or inverted? Larger or Smaller? (Not draw to scale, verify with m calculation!) Real or Virtual? Located where in relationship to the center of Lens 2? Lens 1
F1
Lens 2
F1
F2
F2
Show all work (including ray traces to determine image 2): NOTE: Page
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March 17, 2016 C.
Atwo‐lenssystemisconstructedasshownwithanobjectplaced
ontheaxis35.0cmtotheleftofapositive30.0cmfocal‐lengthlens.If
lens2hasafocallengthof‐40.0cmandis120cmtotherightoflens1,
thefinalimageis…
a.
b.
c.
d.
e.
(1 point ) Upright or inverted? (2 points ) Larger or Smaller? (Including the magnification calculation to prove it) (2 points) Real or Virtual? (3 points) Located where in relationship to the center of Lens 2? (2 points) If the two lens system was replaced with a concave‐spherical mirror placed exactly where lens 1 is, what radius of curvature would be required to achieve a magnification of 2? Show all work (Note drawing is not to scale!): Page
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