CH 34 IMAGES - United States Naval Academy 34...be drawn to find the image formed by a concave mirror. For the object position shown, the image is real, inverted, and smaller than

[SHIVOK SP212] March 17, 2016

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CH 34

IMAGES

I. TwoTypesofImages

A. Foryoutoseeanobject,oureyeinterceptssomeofthelightraysspreadingfromtheobjectandthenredirectthemontotheretinaattherearoftheeye.Ourvisualsystemidentifiesedges,orientations,textures,shapes,andcolorsandthenrapidlybringstoyourconsciousnessanimage(areproductionderivedfromlight)oftheobject.

B. __________________________________________________________________________________________________________________________________________________________________________________________________________(forexample,animagethatisformedbyamirrorappearstobepresentbehindthemirror),______________________________________________________________________________________________.

1. AcommonMirage

2. Thisisanexampleofavirtualimage

C. Whenanimagecanbeformedonasurface,suchasacardoramoviescreen,andwhentheexistenceoftheimagedoesnotdependonourseeingitanditispresentevenifwearenot,thatimageistermed_________________________________________.


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II. Mirrors

A. PlaneMirrors

1. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.Ashinymetalsurfaceactsasamirror;aconcretewalldoesnot.Aplanemirrorisaflatreflectingsurface.

2. ThepointsourceisimageIofobjectO.Itiscalleda________________________becauseitisapoint,anditisavirtualimagebecausetheraysdonotactuallypassthroughit.(_______________________________________________________________________________________________________________________________________________________________.)

3. DepthofVirtualImage

Equation for a plane mirror:


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4. Onlyraysthatarefairlyclosetogethercanentertheeyeafterreflectionatamirror.

5. ExtendedObjects

6. MirrorMaze

a) Inamirrormazeeachwalliscovered,floortoceiling,withamirror.Ifonewalksthroughsuchamazethenwhatheseesinmostdirectionsisaconfusingmontageofreflections.


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B. SphericalMirrors

1. Aconcavemirrorwherethemirror’ssurfaceisconcave(“cavedin”)hasthefollowingcharacteristics:

a) ThecenterofcurvatureC(thecenterofthesphereofwhichthemirror’ssurfaceispart)wasinfinitelyfarfromtheplanemirror;itisnowcloserbutstillinfrontoftheconcavemirror.

b) Thefieldofview—theextentofthescenethatisreflectedtotheobserver—waswide;itisnowsmaller.

c) Theimageoftheobjectwasasfarbehindtheplanemirrorastheobjectwasinfront;theimageisfartherbehindtheconcavemirror;thatis,|i|isgreater.d) Theheightoftheimagewasequaltotheheightoftheobject;theheightoftheimageisnowgreater.Thisfeatureiswhymanymakeupmirrorsandshavingmirrorsareconcave—theyproducealargerimageofaface.

2. Wecanmakea________________mirrorbycurvingaplanemirrorsothatitssurfaceis“____________________”convexasinfigure34‐8cabove.Characteristics:

a) Center of curvature (C)

b) Field of view

c) Image

d) Magnification


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3. Iffisthefocallength(________________________________________________________________________,andrtheradiusofcurvature(theradiusofthesphere),then

(Eq 34‐3)

4. ChangingtheLocationoftheObject

5. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

6. Whenlightraysfromanobjectmakeonlysmallangleswiththecentralaxisofasphericalmirror,asimpleequationrelatestheobjectdistancep,theimagedistancei,andthefocallengthf:


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7. Thesizeofanobjectorimage,asmeasuredperpendiculartothemirror’scentralaxis,iscalledtheobjectorimageheight.Lethrepresenttheheightoftheobject,andh’theheightoftheimage.Thentheratioh’/hiscalledthelateralmagnificationmproducedbythemirror.

C. LocatingImagesbyDrawingRays

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.]

m

(Lateral magnification)


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1. Imagesmaybelocatedbydrawingthefollowingrays:

a) Araythatis___________________________________________________________________reflects______________________________________________________(ray1inFig.34‐11a).

b) Araythatreflects________________________________________________________thefocalpoint_____________________________________________________________________(ray2inFig.34‐11a).

c) Araythatreflectsfromthemirror_______________________________________centerofcurvatureC_____________________________________(ray3inFig.34‐11b).

d) Araythatreflects__________________________________________________________isreflected_____________________________________________________________________________(ray4inFig.34‐11b).

2. Considerray4inFig.34‐11b.

a) __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

b) Thetworighttrianglesabcanddecinthefigurearesimilar(havethesamesetofangles);sowecanwrite


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c) Thequantityontheleft(apartfromthequestionofsign)isthelateralmagnificationmproducedbythemirror.Becauseweindicateaninvertedimageasanegativemagnification,wesymbolizethisas‐m.However,cd=iandca=p;therefore

3. SphericalMirrorExampleProblems

a) A5xConcavemakeupmirrorhasacurvatureradiusof40cm.Theinstructionmanualsaystoholdthemirrorapproximately6inchesfromthefacetoachievetheproper5timesmagnification.Isthisanaccuratestatement?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:


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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)forlightoriginatingatthetipoftheobjectandshowthefinalimageincludingitslocationnumerically.


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D. SphericalRefractingSurfaces

1. _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

2.

3. ________________________________________________________________________________________________________________________________________________________________________________________.

4. ExampleProblems

a) Aconvexsphericalsurfacewithradiusrseparatesamediumwithindexofrefraction2fromair.Asanobjectismovedtowardthesurfacefromfarawayalongthecentralaxis,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,thatanobjectonthebottomofthedeependofthepoolwhenviewedfromabove,willnotlookasdeepasitreallyisbyafactorof¾.Washetellingthetruth,yesorno?Proveusingthesphericalrefractingsurfaceequation.


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III. Lenses

A. Thinlenses

1. Alensisatransparentobjectwithtworefractingsurfaceswhosecentralaxescoincide.Thecommoncentralaxisisthecentralaxisofthelens.

2. Alensthatcauseslightraysinitiallyparalleltothecentralaxistoconvergeis(reasonably)calleda_________________________________.If,instead,itcausessuchraystodiverge,thelensisa_________________________________.

3. Athinlensisalensinwhichthethickestpartisthinrelativetotheobjectdistancep,theimagedistancei,andtheradiiofcurvaturer

1andr

2of

thetwosurfacesofthelens.Ifoneconsidersonlylightraysthatmakesmallangleswiththecentralaxis,andiffisthefocallength,then

4. Also,

Thislastequationiscalledthelensmaker’sequation.

5. __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

6. BendingLightraysthroughalens


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7. Imagesfromthinlenses

a) __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

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.)

Fig. 34-15 (a) A real, inverted image I is formed by a converging lens when the object O is outside the focal point F

1.

(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.


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IV. LocatingImagesofExtendedObjectsbyDrawingRays

1. _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________(ray1inFig.34‐16a).

2. _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________(ray2inFig.34‐16a).

3. _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.(ray3inFig.34‐16a).


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B. TwoLensSystem

1. Step1

a) __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

b) ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

c) Findthelateralmagnificationm1.

2. Step2

a) __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

b) __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

c) Findthelateralmagnificationm2.

3. Totalmagnificationis:

4. IfMispositive,thefinalimagehassametheorientationastheobject.


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V. ExampleProblems

A. Considertheobject‐diverginglenssystemshown.Anobjectisplaced30cmtotheleftofthediverginglenswithafocallengthof‐20cm.Theimageproducedis:

A. Real, upright, smaller, and 12 cm to the left of the lens. B. Real, inverted, larger, and 10 cm to the right of the lens. C. Virtual, upright, smaller, and 12 cm to the left of the lens. D. Virtual, inverted, larger, and 10 cm to the right of the lens. E. Virtual, upright, larger, and 10 cm to the left of the lens.


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B. Twoconverginglensesareplaced60cmapart.Thefocallengthofthefirstlensis30cmandthefocallengthofthesecondlensis10cm.Anobjectisplaced80cmtotheleftofthefirstlensasshown.Thefinalimagecomparedtoobjectis:

1) Upright or inverted?

2) Larger or Smaller? (Not draw to scale, verify with m calculation!)

3) Real or Virtual?

4) Located where in relationship to the center of Lens 2?

Lens 1 Lens 2 F1 F1 F2 F2

Show all work (including ray traces to determine image 2):

NOTE:


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C. Atwo‐lenssystemisconstructedasshownwithanobjectplacedontheaxis35.0cmtotheleftofapositive30.0cmfocal‐lengthlens.Iflens2hasafocallengthof‐40.0cmandis120cmtotherightoflens1,thefinalimageis…

a. (1 point ) Upright or inverted?

b. (2 points ) Larger or Smaller? (Including the magnification calculation to prove it)

c. (2 points) Real or Virtual?

d. (3 points) Located where in relationship to the center of Lens 2?

e. (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!):

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CH 34 IMAGES - United States Naval Academy 34...be drawn to find the image formed by a concave mirror. For the object position shown, the image is real, inverted, and smaller than