PHYS1252. Sec. A, Th. 200116-0930

Image Formation:

Convergent (Concave) and Divergent (Convex) Mirrors:

Assignment to PHYS1252 Sec. A, Th. 200116-0930: Work through the Mirror Examples, see pgs. 5-12 below.

PHYS1252 Sec. B, Th. 200116-1230

Image Formation:

Convergent (Concave) and Divergent (Convex) Mirrors:

Assignment to PHYS1252 Sec. B, Th. 200116-1230: Work through the Mirror Examples, see pgs. 5-12 below.

ImageformationbyReflectionataSphericalMirror

AnimageisbeingformedbyamirrorwithasphericalradiusofR=+40cm.

Leftsideofroom: Drawmirrorsphericalsurfacecurvingtotheleft!Rightsideofroom: Drawmirrorsphericalsurfacecurvingtotheright!

Answerthesefourquestions/dothesefourtasksfirst:

1) Onwhichsideofmirroristhesphere’scenterC?DrawC!Hint:Whichwaydoesyourmirrorcurve?

A:Seedrawingsonlastthreepages,below.Thinkofthecurvedmirrorsurfaceaspartofacompletesphere:Whereisthecenter,C,ofthatsphere?Forleft-curvingmirror,Cistotheleftofmirror.Forright-curvingmirror,Cistotherightofmirror.

2)Whichsideofthemirrorisitsoutgoingside? Markitas“Out”.Hint:UseC,signofRandsignconventionforR.

A:RadiusRispositiveand,bysignconvention,CisontheoutgoingsideifR>0.Thus:Forleft-curvingmirror,outgoingsideistotheleftofmirror.Forright-curvingmirror,outgoingsideistotherightofmirror.Note:AmirrorwithR>0 isalsocalleda“concave”oralsoa“convergent”mirror.AmirrorwithR<0wouldbecalleda“convex”oralsoa“divergent”mirror.

SphericalMirrorCurvingtotheLeft SphericalMirrorCurvingtotheRight

3)Whichsideofthemirrorisitsincomingside?Markitas“In”.Hint:It’samirroràincomingraysarereflectedtoproduceoutgoingrays.

A:Themirrorreflectstheincomingraystoproducetheoutgoingrays.Theoutgoingraysarethustravelingawayfromthemirrortowardsthesameside fromwhichtheincomingraysarestrikingthemirror.So,foramirror,theincomingsideisalwaysthesameastheoutgoingside(regardlessofthesignofR!)andhence:Forleft-curvingmirror,incomingsideistotheleftofmirror.Forright-curvingmirror,incomingsideistotherightofmirror.4)Onwhichsideofmirroristheobjectbeingplaced? Drawobjectasuprightarrow.

Hint:Usesignofdandsignconventionford.Alld-valuesgivenintheinputtablearepositive.Bysignconventionford,theojectmustbeontheincomingsideifd>0,andhence:Forleft-curvingmirror,objectistotheleftofmirror.Forright-curvingmirror,objectistotherightofmirror.Thencalculated’,m,h’,foralld-valuesshowninthetablebelowanddothefollowingforeachofthesefourd-values,

d=15cm,d=25cm,d=40cm,d=60cm:

5)Drawtheimageonthecorrectsideofthemirror:totheleftortherightofmirror?Drawtheimagewiththecorrectorientation:erectorinverted?Drawtheimageatcorrectpositionrel.toobject:totheleftortherightofobject?

Hints:--Use the sign convention ford’ and the “Out”marking from2) to figure outwheretheimageislocatedrelativetothemirror:totheleftortotheright?--Usethesignconventionformtofigureouthowtheimageisorientedrelativetotheobject:erectorinverted?--Usetherelativemagnitudeof|d|and|d’|tofigureoutwhichisclosertothemirror:objectorimage?Fromthatandfromthepositioningofobjectandimagerelativetothemirror,figureoutwhethertheimageistotheleftortherightoftheobject.

A:Seethedrawingsandthetableford’,m,h’onpagesbelowandnotethefollowingtounderstandhowthedrawingsweremadeforeachofthefourd-valueslisted:

a)Ford=15cmàd’=-60cm,m=+4.0.d’<0àbyd’-sign-convention,imageisnotonoutgoingsideForleft-curvingmirror,outgoingside=leftofmirroràimagetorightofmirrorForright-curvingmirror,outgoingside=rightofmirroràimagetoleftofmirrorm>0àbym-sign-convention,imageiserect,foreitherleft-orright-curvingmirror.Imageandobjectareonoppositesidesofthemirror,forbothleft-andright-curvingmirror.Hence:Forleft-curvingmirror,outgoingside=leftofmirroràimagetorightofobjectForright-curvingmirror,outgoingside=rightofmirroràimagetoleftofobjectb)Ford=25cmàd’=+100cm,m=-4.0.d’>0àbyd’-sign-convention,imageisonoutgoingsideForleft-curvingmirror,outgoingside=leftofmirroràimagetoleftofmirrorForright-curvingmirror,outgoingside=rightofmirroràimagetorightofmirrorm<0àbym-sign-convention,imageisinverted,foreitherleft-orright-curvingmirror.Imageandobjectareonsamesideofthemirror,forbothleft-andright-curvingmirror.Also,|d’|>|d|meansthattheimageisfurtherawayfrommirrorthanobjectisfrommirror.Hence,Forleft-curvingmirror,imagetoleftofobjectForright-curvingmirror,imagetorightofobjectc)Ford=40cmàd’=+40cm,m=-1.0.d’>0,m<0àsameasinb):Forleft-curvingmirror,imagetoleftofmirrorForright-curvingmirror,imagetorightofmirrorForeitherleftorright-curvingmirror,imageisinvertedd’=dàimageandobjecthorizontalpositionscoincideonopticalaxis,foreitherleft-orright-curvingmirror.

d)Ford=60cmàd’=+30cm,m=-0.5.d’>0,m<0àsameasinb):Forleft-curvingmirror,imagetoleftofmirrorForright-curvingmirror,imagetorightofmirrorForeitherleftorright-curvingmirror,imageisinvertedImageandobjectareonsamesideofthemirror,foreitherleft-orright-curvingmirror.Also,|d’|<|d|meansthattheimageisclosertomirrorthanobjectistomirror.Hence,Forleft-curvingmirror,imagetorightofobjectForright-curvingmirror,imagetoleftofobject

Image formation by Reflection at a Spherical Mirror

d'= 1/ (1/f - 1/d)

m := h'/h = -d' / d

h' = m h

h= 3 cmR= 40 cm <-- R > 0

f=R/2= 20 cmimage imagevirtual inverted

d [cm] d' [cm] m h' [cm] or real? or erect?5.0 -6.7 1.333 4.0 virtual erect

10.0 -20.0 2.000 6.0 virtual erect15.0 -60.0 4.000 12.0 virtual erect

d~f, d<f 19.5 -780.0 40.000 120.0 virtual erectd~f, d>f 20.5 820.0 -40.000 -120.0 real inverted

25.0 100.0 -4.000 -12.0 real inverted30.0 60.0 -2.000 -6.0 real inverted

d=R --> 40.0 40.0 -1.000 -3.0 real inverted60.0 30.0 -0.500 -1.5 real inverted

10000.0 20.0 -0.002 0.0 real inverted

Sign conventions for d, d', R, m:d > 0 : object on incoming side of device (real object)

d < 0 : object not on incoming side of device (virtual object)

d' > 0 : image on outgoing side of device (real image)

d' < 0 : image not on outgoing side of device (virtual image)

R > 0 : center C on outgoing side of deviceR < 0 : center C not on outgoing side of device

m > 0 : image upright(erect) rel. to objectm < 0 : image upside-down(inverted) rel. to object

Now draw: Mirror with C and F, object and image for d=15cm, 25cm, 40cm, 60cm, and (A) Mirror curving to the Left (B) Mirror Curving to the RightSee next 3 pages ...

NotInNotOut

InOut

Cobj

NotInNotOut

InOut

Cobj

NotInNotOut

InOut

Cobj

NotInNotOut

InOut

Cobj

MirrorCurvingtotheLeftwithR>0,d>0 MirrorCurvingtotheRightwithR>0,d>0

NotInNotOut

InOut

C F

NotInNotOut

InOut

C F

NotInNotOut

InOut

F

NotInNotOut

InOut

C F

obj img objimg

objimgobj

img

d=15cm d’=－60cm d=25cm d’=100cm

d=40cm d’=40cm d=60cm d’=30cm

MirrorCurvingtotheLeft

NotInNotOut

InOut

CF

NotInNotOut

InOut

CF

NotInNotOut

InOut

F

NotInNotOut

InOut

CF

objimgobjimg

objimg obj

img

d’=－60cmd=15cmd’=100cmd=25cm

d’=40cmd=40cmd’=30cmd=60cm

MirrorCurvingtotheRight