A Compound Microscope This is an example for image formation in a compound microscope, similar to the one done in the lecture. The following gives a step-by-step description how to analyze the image formation process. Each of the 14 solution steps is illustrated by a drawing (figure), shown in a separate pdf- and ppt-file. You should download this figure file before starting on the problem and solution below. Look through the sequence of figures in this file to get an overview of the solution, when working through the 14 solution steps below. You must always begin the solution to problems like this by making a large, clean drawing. Start with the information given in the problem statement. Then fill in more details, as you work your way, step by step, through the solution. The (pdf/ppt) figure file accompanying this solution outline illustrates how such a drawing should be made, as you proceed with each step of your calculation. Problem Statement: A compound microscope is built with an objective lens (=Lens 1) of focal length f1=0.65cm, and an eyepiece lens (=Lens 2) of focal length f2=2.50cm with Lens 2 to the right of Lens 1. A small object (Obj1) of size 0.032cm is placed 0.70cm to the left of Lens 1. The distance between the two lenses is adjusted so that the final image (Img2), as seen by the eye, looking through the eyepiece, is located at the eye’s near point distance, 20cm to the left of Lens 2. State or calculate all image parameters: d1, d1’, d2, d2’, h1, h1’, h2, h2’. Calculate the lens-to-lens distance L. Calculate the angle Q e subtended at the Eye by the final image, Img2, when viewed through the eyepiece Lens 2. Calculate the angle Q ref subtended at the Eye by the original object, placed at the near point, 20cm in front of the eye and viewed without microscope. From Q e and Q ref, calculate the angular magnification MQ = Q e / Q ref. Solution Steps: 1. Draw lenses, original source object (Obj1) and receiver of final image (Eye) on optical axis, with Obj1 drawn as an arrow pointing upward. 2. Trace the general ray direction through lenses: from the source (Obj1) to the receiver (Eye).
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A Compound Microscope download this figure file · 2020-01-24 · A Compound Microscope This is an example for image formation in a compound microscope, similar to the one done in
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ACompoundMicroscopeThisisanexampleforimageformationinacompoundmicroscope,similartotheonedoneinthelecture.Thefollowinggivesastep-by-stepdescriptionhowtoanalyzetheimage formationprocess.Eachof the14solutionsteps is illustratedbyadrawing(figure),showninaseparatepdf-andppt-file.Youshoulddownloadthisfigurefilebefore startingon theproblemand solutionbelow.Look through the sequenceoffiguresinthisfiletogetanoverviewofthesolution,whenworkingthroughthe14solutionstepsbelow.Youmustalwaysbeginthesolutiontoproblemslikethisbymakingalarge,cleandrawing.Startwiththeinformationgivenintheproblemstatement.Thenfillinmoredetails,asyouworkyourway,stepbystep,throughthesolution.The(pdf/ppt)figurefile accompanying this solution outline illustrates how such a drawing should bemade,asyouproceedwitheachstepofyourcalculation.ProblemStatement:Acompoundmicroscope isbuiltwithanobjective lens (=Lens1) of focal lengthf1=0.65cm,andaneyepiecelens(=Lens2)offocallengthf2=2.50cmwithLens2totherightofLens1.Asmallobject(Obj1)ofsize0.032cmisplaced0.70cmtotheleftofLens1.Thedistancebetweenthetwolensesisadjustedsothatthefinalimage(Img2),asseen by the eye, looking through the eyepiece, is located at the eye’s near pointdistance,20cmtotheleftofLens2.Stateorcalculateallimageparameters:d1,d1’,d2,d2’,h1,h1’,h2,h2’.Calculatethelens-to-lensdistanceL.CalculatetheangleQesubtendedattheEyebythefinalimage,Img2,whenviewedthroughtheeyepieceLens2.CalculatetheangleQrefsubtendedattheEyebytheoriginalobject,placedatthenearpoint,20cminfrontoftheeyeandviewedwithoutmicroscope.FromQeandQref,calculatetheangularmagnificationMQ=Qe/Qref.SolutionSteps:
5. Drawandmarkobjectdistanced1asanarrowfromLens1toObj1.SinceObj1is, by definition, on the “in” side of Lens1, Obj1 is a real object andd1>0: d1=+0.70cm
6. Calculateimagedistanced1’ofImg1fromLens1: d1’=(1/f1-1/d1)-1=(1/0.65–1/0.70)-1cm=+9.10cm>0CalculatethelateralmagnificationofLens1: m1=-d1’/d1=-(9.10/0.70)=-13.0<0,sincebothd1>0,d1’>0.Sinced1’>0,Img1isreal,i.e.,onthe“out”sideofLens1.Sincem1’<0,Img1isinverted relative to Obj1. Draw Img1 on the optical axis accordingly: as adownwardarrowtotherightofLens1.Drawandmarkimagedistanced1’asandarrowfromLens1toImg1.Note:atthispoint,youmaynotknowyetwhetherImg1isplacedtotheleftortotherightofLens2!?Pickoneofthetwochoices!Ifitlaterturnsouttobewrongyoucancorrectthedrawingthen.Thepdf-FigureforStep6showsImg1to the left, i.e., on the “in” sideofLens2,which turnsout tobe thecorrectchoiceofplacement(seeStep8).
7. DrawImg2,theimageofLens2.SinceImg2isthefinalimage,tobeseenbytheEye,itmustbeplacedinfrontoftheEye,i.e.,atleastanear-pointdistanceaway,totheleftoftheEyeandLens2.SincethisplacesImg2onthe“notout”sideofLens2,Img2isavirtualimageanditsimagedistanced2’mustbenegative: d2’=-|d2’|=-dnear=-20.0cm<0Drawandmarkimagedistanced2’asanarrowfromLens2toImg2.Note: at this point, youmay not know yet whether Img2 has the same oropposite(invertedorerect?)orientationasObj2ºImg1!?Pickoneofthetwochoices!Ifitlaterturnsouttobewrongyoucancorrectthedrawingthen.Thepdf-Figure for Step 7 shows Img2 pointing down, i.e., having the sameorientation as Obj2ºImg1, which turns out to be the correct choice oforientation(seeStep8).
12. CalculatetheangleQe subtendedat theEyebythe final image, Img2,when
viewedthroughtheeyepieceLens2.Theheight,he,andapproximatedistancefromEye(piece),de,forthatfinalimagearegiven he=|h2’|=3.74cm and de=|d2’|=20.0cmThus: Qe»tan(Qe)=he/de=|h2’|/|d2’|=3.74/20=0.187radMark he, de,Qe in the microscope drawing. Draw he, de,Qe in a separatedrawing,ifneededforyourownclarification.
2. Repeat the foregoingcalculations,both forde=|d2‘|=20cm andde=|d2‘|=¥,usingthesameinputparameters,exceptthatLens2isreplacedbyadivergentlenswithnegativefocallength:f2=-2.50cm.Whathappenstod2andm2now?DoyouneedtomodifytheplacementofObj2relativetoLens2inyourdrawing?IsObj2ºImg1totherightortotheleftofLens2now?Note:Obj2maybeavirtualobjectnow,eventhoughImg1isstillarealimage.Do you need to modify the orientation of the final image, Img2, in yourdrawing?IsImg2anupwardoradownwardarrownow?HowdoesMQchangewhencomparedtothecasef2=+2.50cm?
3. Use the approximate angular magnification formula given in the textbookwhich,inournotationandignoringthesign,readsasfollows:
MQ=dneard1‘/|f1f2|[ThetranslationOurNotationßàTextbookNotationisasfollows:OurNotation: dnear d1‘ f1 f2TextbookNotation: N di fobjective feyepiece.]