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Plane andPlane and

SphericalSpherical

MirrorsMirrors


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The Laws of ReectionThe Laws of Reection

Water

Air1. The angle of1. The angle ofinci- denceinci- dence iiisis

equal to theequal to the

angle ofangle of

reectionreection rr

i! r

i! r

i

N reection

r

All ra" angles are #easured with respect toAll ra" angles are #easured with respect to

nor#alnor#al NN..

$. The incident ra"%$. The incident ra"%the reected ra"%the reected ra"%

and the nor#aland the nor#al NNall lie in the sa#eall lie in the sa#e

plane.plane.

&. The ra"s&. The ra"sareare

co#pletelco#pletel

""

re'ersi(le.re'ersi(le.


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The Plane MirrorThe Plane MirrorAA #irror#irroris a highl" polished surfaceis a highl" polished surface

that for#s i#ages (" unifor#l"that for#s i#ages (" unifor#l"

reected light.reected light.

)otei#agesappear to(e equi-

distant(ehind#irror andare right-left

re'ersed.


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*e+nitions*e+nitions

,(ect distance,(ect distanceThe straight-lineThe straight-linedistancedistance ddoofro# the surface of a #irrorfro# the surface of a #irror

to the o(ect.to the o(ect.#age distance#age distanceThe straight-lineThe straight-line

distancedistance ddiifro# the surface of a #irrorfro# the surface of a #irror

to the i#age.to the i#age.

,(ectdistanc

e

#agedistanc

e

!

ddoo= ddii

i! r

,(ec,(ec

tt#age#age

ddoo ddii


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Real and /irtualReal and /irtual

Real i#agesReal i#agesandand

o(ects are for#edo(ects are for#ed

(" actual ra"s of(" actual ra"s of

light. 0Real i#ageslight. 0Real i#ages

can (e proectedcan (e proectedon a screen.on a screen.

/irtual i#ages/irtual i#agesandando(ects do noto(ects do not

reall" e2ist% (utreall" e2ist% (ut

onl" see# to (e atonl" see# to (e at

a location.a location.

/irtual i#ages are on/irtual i#ages are on

thethe oppositeoppositeside of theside of the

#irror fro# the#irror fro# the

inco#ing ra"s.inco#ing ra"s.

Realo(ect

/irtuali#age

Lightra"s

)o light


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#age of a Point ,(ect#age of a Point ,(ect

Plane#irror

Realo(ect

do

#age appears to (e at sa#e#age appears to (e at sa#e

distance (ehind #irror regardless ofdistance (ehind #irror regardless of

'iewing angle.'iewing angle.

#age appears to (e at sa#e#age appears to (e at sa#e

distance (ehind #irror regardless ofdistance (ehind #irror regardless of

'iewing angle.'iewing angle.

di /irtuali#age

ddoo= ddii


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#age of an 32tended#age of an 32tended

,(ect,(ectPlane#irror

do di

#age of (otto# and top of guitar#age of (otto# and top of guitar

shows forward-(ac4% right-leftshows forward-(ac4% right-left

re'ersals.re'ersals.

#age of (otto# and top of guitar#age of (otto# and top of guitar

shows forward-(ac4% right-leftshows forward-(ac4% right-left

re'ersals.re'ersals.

ddoo= ddii

/irtual

i#age


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Ter#s for Spherical MirrorsTer#s for Spherical Mirrors

AA spherical #irrorspherical #irroris for#ed (" theis for#ed (" the

inside or outsideinside or outside

surfaces of asurfaces of asphere.sphere.


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AA sphericalspherical#irror#irroris ais a

#irror in the#irror in the

shape of ashape of as#all section ofs#all section of

the surface of athe surface of a

sphere.sphere.


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ApertureAperture

the portion ofthe portion of

the hollowthe hollowsphericalspherical

surface fro#surface fro#

which thewhich the#irror#irror

reections ta4ereections ta4e

placeplaceAperture


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Center ofCenter of

CurvatureCurvature

the point inthe point inthe center ofthe center of

the sphere fro#the sphere fro#

which thewhich the

#irror was#irror was

slicedsliced5enter of

5ur'ature

5


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Principal AxisPrincipal Axis

the linethe line

passing throughpassing throughthe center ofthe center of

the sphere andthe sphere and

attaching to theattaching to the

#irror in the#irror in the

e2act center ofe2act center of

the #irrorthe #irrorPrincipal A2is

5


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VertexVertex

the point onthe point on

the #irror6sthe #irror6s

surface wheresurface where

the principalthe principal

a2is #eets thea2is #eets the

#irror. t is the#irror. t is thegeo#etricgeo#etric

center of thecenter of the

#irror#irror

5

/erte2


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Radius ofRadius of

CurvatureCurvature

the distancethe distancefro# the 'erte2fro# the 'erte2

to the center ofto the center of

cur'aturecur'ature

5

Radius of5ur'ature

R


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7or o(ects lo-7or o(ects lo-cated atcated at

in+nit"in+nit"% the% the

realreali#agei#age

appears at theappears at thefocusfocussincesince

ra"s of lightra"s of light

are al#ostare al#ost

parallel.parallel.

7or o(ects lo-7or o(ects lo-

cated atcated at


realreali#agei#age

appears at theappears at thefocusfocussincesince



parallel.parallel.

The 7ocus of a 5onca'eThe 7ocus of a 5onca'eMirrorMirror

The focusThe focus FFfor a conca'e #irror is the pointfor a conca'e #irror is the point

at which all parallel light ra"sat which all parallel light ra"s con'ergecon'erge..

a2is

ncident parallelRa"s

CF

7ocus7ocus

r

i


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The 7ocal LengthThe 7ocal Length ffof aof aMirrorMirror

a2is

r

i

ncident parallelra"

f

The focal length%

f

The focalThe focal

lengthlength ff isis

2

Rf =

The focal length f is equal to half the

radius R

The focal length f is equal to half the

radius R

SinceSince

ii!!

rr% we% we+nd that+nd that FFisis

#id- wa"#id- wa"

(etween(etween VVandand

CC8 we +nd8 we +nd

C VF

7ocus


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The 7ocal LengthThe 7ocal Length ffof aof aMirrorMirror

a2is

r

i

ncident parallelra"

f

C F

h

R


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ConcaveConcaveMirrorMirror

vsvs

Convex MirrorConvex Mirror


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99ca'ed in:ca'ed in:


99e2ede2edout:out:

99e2ede2edout:out:

ConcaveConcave ConvexConvex


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cated atcated at


realreali#agei#age

appears at theappears at the

focusfocussincesincera"s of lightra"s of light


parallel.parallel.


cated atcated at

in+nit"in+nit"% the% therealreali#agei#age

appears at theappears at the

focusfocussincesince



parallel.parallel.

The 7ocus of a 5onca'eThe 7ocus of a 5onca'eMirrorMirror

The focusThe focus FFfor a conca'e #irror is the pointfor a conca'e #irror is the point

at which all parallel light ra"sat which all parallel light ra"s con'ergecon'erge..

a2is

ncident parallelRa"s

CF

7ocus7ocus2

Rf =


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The 7ocus of a 5on'e2The 7ocus of a 5on'e2MirrorMirror

TheThe focusfocusfor a con'e2 #irror is the pointfor a con'e2 #irror is the point FF

fro# which all parallel light ra"sfro# which all parallel light ra"s di'ergedi'erge..

a2isCF

RR

ncidentRa"s

ReectedRa s

Virtual

focus;reectedrays

diverge.

2

Rf =


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Real focusReal focus

99ca'ed in:ca'ed in: Real focusReal focus

99e2ede2edout:out:

/irtual/irtual

focusfocus

99e2ede2edout:out:

/irtual/irtual

focusfocus

ConcaveConcave ConvexConvex


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5on'erging and *i'erging5on'erging and *i'ergingMirrorsMirrors

5onca'e5onca'e #irrors and#irrors and

con'erging parallel ra"scon'erging parallel ra"s

will (e calledwill (e called con'ergingcon'erging

#irrors#irrorsfro# this pointfro# this pointonward.onward.

5on'e25on'e2#irrors and#irrors and

di'erging parallel ra"sdi'erging parallel ra"s

will (e calledwill (e called di'ergingdi'erging

#irrors#irrorsfro# this pointfro# this pointonward.onward.

C F

ConvergingMirror

5onca'

e

C F

Diverging Mirror

5on'e

2


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Ray DiagrammingRay Diagramming

for Concave andfor Concave andConvex MirrorsConvex Mirrors


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Ra" 1Ra" 1*raw a ra"% starting fro# the*raw a ra"% starting fro# the

top of the o(ect% parallel to thetop of the o(ect% parallel to the

principal a2is and then through 9f:principal a2is and then through 9f:

after reection..after reection..





Ra" $Ra" $*raw a ra"% starting fro# the*raw a ra"% starting fro# the

top of the o(ect% through the focaltop of the o(ect% through the focal

point% then parallel to the principal a2ispoint% then parallel to the principal a2isafter reection..after reection..



point% then parallel to the principal a2ispoint% then parallel to the principal a2is


Ra" &Ra" &*raw a ra"% starting fro# the*raw a ra"% starting fro# the

top of the o(ect% through 5% then (ac4top of the o(ect% through 5% then (ac4

upon itself..upon itself..





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C F

5on'e2#irror

,(ect

Ra" 1










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C F

5on'e2#irror

Ra"$

Ra"1

#age


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C F

Ra" $

Ra" 1

#age

5on'e2#irror

Ra"&


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5onca'e 's 5on'e25onca'e 's 5on'e2

Ra" 1Ra" 1A ra" parallel to #irror a2isA ra" parallel to #irror a2ispasses through the focal point of apasses through the focal point of a

conca'e #irror or appears to co#econca'e #irror or appears to co#e

fro# the focal point of a con'e2 #irror.fro# the focal point of a con'e2 #irror.




C F

5on'e2

#irror,(ect

C F

5onca'e#irror

,(ect

Ra"1

Ra"1


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Ra" $Ra" $A ra" passing through the focusA ra" passing through the focusof a conca'e #irror or proceedingof a conca'e #irror or proceeding

toward the focus of a con'e2 #irror istoward the focus of a con'e2 #irror is

reected parallel to the #irror a2is.reected parallel to the #irror a2is.

Ra" $Ra" $A ra" passing through the focusA ra" passing through the focusof a conca'e #irror or proceedingof a conca'e #irror or proceeding

toward the focus of a con'e2 #irror istoward the focus of a con'e2 #irror is

reected parallel to the #irror a2is.reected parallel to the #irror a2is.

5onca'e#irror

C F

Ra"

$

Ra"1

#age C F

5on'e2#irror

Ra"$

Ra"1

#age



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Ra" &Ra" &A ra" that proceeds along aA ra" that proceeds along aradius is alwa"s reected (ac4 along itsradius is alwa"s reected (ac4 along its

original path.original path.

Ra" &Ra" &A ra" that proceeds along aA ra" that proceeds along aradius is alwa"s reected (ac4 along itsradius is alwa"s reected (ac4 along its

original path.original path.

C F

5on'e2

#irror

5onca'e#irror

C F

Ra"$

Ra"

1

Ra"&

Ra"

&

C F

Ra"$

Ra"1

#age



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C FC F

Ra"$

Ra"

1

Ra"&

Ra"

&

C F

Ra"$

Ra"1


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Formed at theFormed at the

intersection of theintersection of theactual reectedactual reected

raysrays

Formed at theFormed at theintersection of theintersection of the

extension ofextension of

reected raysreected rays


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No try to dra theNo try to dra theray diagram of !ray diagram of !

cases of Concavecases of ConcaveMirrorMirror

No try to dra theNo try to dra theray diagram of !ray diagram of !

cases of Concavecases of ConcaveMirrorMirror

#age 5onstruction#age 5onstruction


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#age 5onstruction#age 5onstructionSu##ar"Su##ar"







Ra" $Ra" $A ra" passing through the focusA ra" passing through the focus

of a conca'e #irror or proceedingof a conca'e #irror or proceeding

toward the focus of a con'e2;conca'etoward the focus of a con'e2;conca'e

#irror is reected parallel to #irror a2is.#irror is reected parallel to #irror a2is.

Ra" $Ra" $A ra" passing through the focusA ra" passing through the focus

of a conca'e #irror or proceedingof a conca'e #irror or proceeding

toward the focus of a con'e2;conca'etoward the focus of a con'e2;conca'e

#irror is reected parallel to #irror a2is.#irror is reected parallel to #irror a2is.

Ra" &Ra" &A ra" that proceeds along aA ra" that proceeds along a

radius is alwa"s reected (ac4 along itsradius is alwa"s reected (ac4 along its

Ra" &Ra" &A ra" that proceeds along aA ra" that proceeds along a

radius is alwa"s reected (ac4 along itsradius is alwa"s reected (ac4 along its

ori inal ath.ori inal ath.


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"hat did you"hat did youo#serve in theo#serve in the

formation offormation ofimages$images$

"hat did you"hat did youo#serve in theo#serve in the

formation offormation ofimages$images$


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5on'e2 Mirror #aging5on'e2 Mirror #aging

C F

5on'e2#irror

Ra"$

Ra"1

#age

All i#ages areAll i#ages are erecterect%% 'irtual'irtual% and% and

di#inisheddi#inished. #ages get larger as o(ect. #ages get larger as o(ect

approaches.approaches.

All i#ages areAll i#ages are erecterect%% 'irtual'irtual% and% and

di#inisheddi#inished. #ages get larger as o(ect. #ages get larger as o(ect

approaches.approaches.

C F

5on'e2#irror

Ra"1

$

#age getslarger as o(ect

gets closer


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Object Outside Center CObject Outside Center C

5onca'e

#irror

C FRa"&

Ra"$

Ra"11. The i#age is1. The i#age is

in'ertedin'erted8 i.e.%8 i.e.%

opposite of theopposite of theo(ect orientation.o(ect orientation.$. The i#age is$. The i#age is realreal88

i.e.% for#ed ("i.e.% for#ed ("

actual light ra"s inactual light ra"s infront of #irror.front of #irror.&. The i#age is&. The i#age is

di#inisheddi#inished in si


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C F

Ra"$

Ra"1

1. The i#age is1. The i#age is


opposite of theopposite of theo(ect orientation.o(ect orientation.

$. The i#age is$. The i#age is realreal88


actual light ra"s inactual light ra"s infront of #irror.front of #irror.

&. The i#age is&. The i#age is thethe

sa#e si


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1. The i#age is1. The i#age is


opposite of theopposite of theo(ect orientation.o(ect orientation.$. The i#age is$. The i#age is realreal88


actual light ra"s inactual light ra"s infront of #irror.front of #irror.&. The i#age is&. The i#age is

enlargedenlarged in si


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#age is locatedat in+nit" 0notfor#ed.

#age is locatedat in+nit" 0notfor#ed.

C

F

Ra"&

Reectedra"s areparallel

When the o(ectWhen the o(ect

is located at theis located at the

focal point of thefocal point of the#irror% the i#age#irror% the i#age

isis not for#ednot for#ed0or0or

it is located atit is located at

in+nit".in+nit".

When the o(ectWhen the o(ect

is located at theis located at the

focal point of thefocal point of the#irror% the i#age#irror% the i#age

isis not for#ednot for#ed0or0or

it is located atit is located at

in+nit".in+nit".

The parallel reectedThe parallel reected

ra"s ne'er cross.ra"s ne'er cross.

Ra"1

Object at Focal PointObject at Focal Point

5onca'e Mirror #aging5onca'e Mirror #aging


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1. The i#age is1. The i#age is erecterect88

i.e.% sa#ei.e.% sa#e

orientation as theorientation as theo(ect.o(ect.

$. The i#age is$. The i#age is

'irtual'irtual8 that is% it8 that is% it

see#s to (esee#s to (elocatedlocated (ehind(ehind#irror.#irror.&. The i#age is&. The i#age is

enlarged8enlarged8 (igger(igger

than the o(ect.than the o(ect.

#age islocated (ehind

the #irror

#age islocated (ehindthe #irror

C

F3rectandenlarged

/irtuali#age

Object Inside Focal PointObject Inside Focal Point

5onca'e Mirror #aging5onca'e Mirror #aging


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,(ser'e the #ages as,(ser'e the #ages as,(ect Mo'es 5loser to,(ect Mo'es 5loser to

MirrorMirror

5onca'

e#irror

C F

Ra"&

Ra"

$

Ra"1

C F

Ra"

$

Ra"1

Ra"

&

CF

Ra"

1Ra"&

Ra"$

C

F

Ra"&

Reected

ra"s areparallel

Ra"

1C

F3rectandenlarged

/irtual

i#age


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Su##ar"Su##ar"

Wate

r

Air1. The angle of1. The angle of

inci- denceinci- dence iiisis

equal to theequal to the

angle ofangle of

reectionreection rri! ri! r

i

N reection

r

All ra" angles are #easured with respect toAll ra" angles are #easured with respect to

nor#alnor#al NN..

$. The incident ra"%$. The incident ra"%the reected ra"%the reected ra"%

and the nor#aland the nor#al NNall lie in the sa#eall lie in the sa#e

plane.plane.

&. The ra"s&. The ra"sareare

co#pletelco#pletel

""

re'ersi(le.re'ersi(le.

0 + i i S 0* + i i


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Su##ar" 0*e+nitionsSu##ar" 0*e+nitions

,(ect distance,(ect distance

The straight-lineThe straight-line

distancedistance ddoofro# the surface of a #irrorfro# the surface of a #irror

to the o(ect.to the o(ect.#age distance#age distanceThe straight-lineThe straight-line

distancedistance ddiifro# the surface of a #irrorfro# the surface of a #irror

to the i#age.to the i#age.Real i#ageReal i#ageAn i#age for#ed (" realAn i#age for#ed (" real

light ra"s that can (e proected on alight ra"s that can (e proected on a

screen.screen./irtual i#age/irtual i#ageAn i#age that appears toAn i#age that appears to

(e at a location where no light ra"s(e at a location where no light ra"s

reach.reach.5on'erging and di'erging #irrors5on'erging and di'erging #irrorsRefer toRefer to

the reection of parallel ra"s fro# surfacethe reection of parallel ra"s fro# surface

of #irror.of #irror.


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Su##ar" 05ont.Su##ar" 05ont.

7or plane #irrors% the o(ect distance7or plane #irrors% the o(ect distance

equals the i#age distance and all i#agesequals the i#age distance and all i#ages

are erect and 'irtual.are erect and 'irtual.

7or con'erging #irrors and di'erging7or con'erging #irrors and di'erging

#irrors% the focal length is equal to one-#irrors% the focal length is equal to one-half the radius.half the radius.All i#ages for#ed fro# con'e2 #irrorsAll i#ages for#ed fro# con'e2 #irrors

are erect% 'irtual% and di#inished in si


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