工程光学英文题加中文题含答案.docx
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工程光学英文题加中文题含答案.docx
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工程光学英文题加中文题含答案
EnglishHomeworkforChapter1
1.Inancienttimestherectilinearpropagationoflightwasusedtomeasuretheheightofobjectsbycomparingthelengthoftheirshadowswiththelengthoftheshadowofanobjectofknownlength.Astaff2mlongwhenhelderectcastsashadow3.4mlong,whileabuilding’sshadowis170mlong.Howtallisthebuilding?
Solution.Accordingtothelawofrectilinearpropagation,weget,
x=100(m)
Sothebuildingis100mtall.
2.Lightfromawatermediumwithn=1.33isincidentuponawater-glassinterfaceatanangleof45o.Theglassindexis1.50.Whatangledoesthelightmakewiththenormalintheglass?
Solution.Accordingtothelawofrefraction,Weget,
n′=1.50
n=1.33
water
45o
I′
Sothelightmake38.8owiththenormalintheglass.
3.Agoldfishswims10cmfromthesideofasphericalbowlofwaterofradius20cm.Wheredoesthefishappeartobe?
Doesitappearlargerorsmaller?
Solution.Accordingtotheequation.
andn’=1,n=1.33,r=-20
A
wecanget
Sothefishappearslarger.
R2=-20cm
R1=20cm
A
-10cm
4.Anobjectislocated2cmtotheleftofconvexendofaglassrodwhichhasaradiusofcurvatureof1cm.Theindexofrefractionoftheglassisn=1.5.Findtheimagedistance.
Solution.Refertothefigure.Accordingtotheequation
andn=1,n’=1.5,l1=-2cm,r1=1cm,weget
r1=1cm
A
A′
-l1=2cm
l2′
EnglishHomeworkforChapter2
1.Anobject1cmhighis30cminfrontofathinlenswithafocallengthof10cm.Whereistheimage?
Verifyyouranswerbygraphicalconstructionoftheimage.
-l=30cm
f′=10cm
y=1cm
Solution.AccordingtotheGauss’sequation,
andl=-30cmf’=10cm.
weget
Othersareomitted.
2.Alensisknowntohaveafocallengthof30cminair.Anobjectisplaced50cmtotheleftofthelens.Locatetheimageandcharacterizeit.
-l=50cm
f′=30cm
Solution.AccordingtoGauss’sequation,
andf′=30cml=-50cm
weget
Theimageisareal,largerone.
3.Theobjectistransparentcube,4mmacross,placed60cminfrontof20cmfocallength.Calculatethetransverseandaxialmagnificationanddescribewhattheimagelookslike?
Solution.FromGauss’sequation,wefindfortherearsurfaceofthecube(thefaceclosertothelens)
that,
Forthefrontsurface(thefacefartherawayfromthelens),
Thetransversemagnificationfortherearsurfaceis
Buttheaxialmagnificationis
Since
thecubedoesn’tlooklikeacube.
4.Abiconvexlensismadeoutofglassofn=1.52.Ifonesurfacehastwicetheradiusofcurvatureoftheother,andifthefocallengthis5cm,whatarethetworadii?
Solution.Supposingr1=-2r2(ρ2=-2ρ1),accordingtothelensequation
r1
-r2
weget,
∴r1=7.8(cm)r2=-3.9(cm)
返回
EnglishHomeworkforChapter4
1.Astop8mmindiameterisplacedhalfwaybetweenanextendedobjectandalarge-diameterlensof9cmfocallength.Thelensprojectsanimageoftheobjectontoascreen14cmaway.Whatisthediameteroftheexitpupil?
l’
-l
Image
Lens
Stop
Object
Solution.Refertothefigure.First,fromtheknownfocallengthandtheimagedistance,
wefindtheobjectdistance.
andl’=14f’=9l=-25.2(cm)
Thestopisone-halfthatdistanceisfrontofthelens,sols=12.6(cm)
∴ls’=31.5(cm)
∴
2.Twolenses,alensof12.5cmfocallengthandaminuslensofunknownpower,aremountedcoaxiallyand8cmapart.Thesystemisafocal,thatislightenteringthesystemparallelatonesideemergesparallelattheother.Ifastop15mmindiameterisplacedhalfwaybetweenthelenses:
1)Whereistheentrancepupil?
2)Whereistheexitpupil?
3)Whataretheirdiameters?
F1’(F2)
-l2’
L1’
Stop
f’=12.5cm
8cm
Solution.Refertothefigure.Forthesystemtobeafocal,thefocalpointsofthetwolensesmustcoincide.Sincef1’=12.5cm,andthetwolensesare8cmapart,sof2’=-4.5cm.Theentrancepupilistheimageofstopformedbythefirstlens.
AccordingtoGauss’sequation,
andl1’=4cm,f1’=12.5cm.Weget
Theexitpupil’slocationis
返回
EnglishHomeworkforChapter7
1.Apersonwantstolookattheimageofhisorherowneyes,withoutaccommodation,usingaconcavemirrorof60cmradiusofcurvature.Howfarmustthemirrorbefromtheeyeifthepersonhas
1)Normalvision?
2)4dioptermyopia,withoutcorrection?
3)4diopterhyperopia,withoutcorrection?
Solution.
1)Whenthepersonhasnormalvision,accordingtothefollowingscheme1,weget
l'=∞
l
Scheme1
so,
2)Accordingtothefollowingscheme2,
and
l
l'
Scheme2
25
or
Sothemirrormustbe75cmor10cmfromtheeye.
l'
l
Scheme3
25
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