You shouldknow how to find the orientation,height and position of the imagefrom a spherical
mirror (both concaveand convex)by using ray tracing. Ray tracing alwaysinvolves drawing
three light rays: thesetbree light rays are listed on page 594 for a concavemirror and on page
596 for a convexmirror.
V
To find the orientation,height, and position ofthe imageusing a more mathematicalapproacll
the mirror and magnification equationsareused.
.lrl
Themirrorequationis -+.=t
s is theimagedistance.
and/
wheresistheobjectdistance,
is the focal length. The focal length is given by f = /z R for a concavemirror and f - - % R for a
convexmirror, where R is the radius of cuwature.
The magnrficationequationis . : + = -!
wherch; andho arethe image andobjectheights.
nos
It is very important to know the sign conventionsfor sphericalmirrorsgiven on page764.T\ey
are listed below for your convenience.
;fis * for a concavemirror
/is - for a convexminor
s is + if the object is in ffont of the mirror (real object)
s is - if the object is behind ofthe mirror (virtual object)
s' is + if the imageis in front of the minor (r'ealimage)
s' is - if the imageis behindof the mhror (virtual image)
ln is * for an imagethat is upright with respectto the object
rz is - for an imagethat is inverted with respectto the object
Questionsand ExampleProblemsfrom Chapter 18
Question1
(a) Whenyou look at the backsideofa shinyteaspoon,
held at arm's length,you seeyourself
upright. Why? (b) When you look at the other side of the spoon,you seeyorrselfupside down.
whv?
( o)
fu Faa4.^v drh-Ue, 1%P.<n
59re ,2,a.A.rd6
1"""4e urq-A voh^'rtt dm uyt'^)lt, ^l*A<At NDfr,.2
a-ryrye
's,ff"$nz'^}e&ttu I)^ +d\1 4"t 1,,,&"
(U)
' 'ry
Jr*ro^td)^-rea.
,r%/A 0"."J.^^ -a-^-paQ
".'?'
Problem I '
and,17'0cm in length'
iwo piane mirrors are facing eachother. They areparallel,3'00 cm apart'
left edgeofthe
the
from
astnJOrawing indicates.A iaserbeamis directedat the top minor
top mirror, sucht}at
bottom mirror. What is the smallestangle of incidencewith respectto the
only once?
the laserbeam(a) hits only one ofthe mirrors and (b) hits eachmirror
...:. :..-
:.:-
ir-i,:.::in,ri::;:,ii!:*it]}3d;2:;:l,4];i';r
-l
3.00cm
__l
L4
3'ooc.r
I l.oo".
(")
,/"
L/l
e----)
,.
g , 5 oc o
l-.-, g = x.5oc"t
g ,5o crn
L---
|
---+
O = 1o'6"
5-o?<rr
to /crn
l-o g = S'b'l"r'
3sec tn
Problem2
a
by 120o,asthedrawingillustrates'If aray strikesmirrorM1at
i*" pf*" *it*s areseparaled
65oangleof incidence,at whatangle0 doesit leaveminor Mz?
t,att
)
*d't^rq
xx
ItrA| cl'
$^Q'^*
'"
.u,asO.= e.-
fu'le atwq'\eoi""
bt;*gh
Problem 3
A 2.O-cm-highobject is situated15.0cm in front ofa ooncavemirror that has a radiusof
curvatureof 10.0cm. Using a ray diagramdrawnto scale,measure(a) the location and (b) the
heightof the image.Themirror mustbe dravonto scale.
<d-
e
, a'e
\)
EL6
o
R
0nX
orr-Y
i _ag.."
rr t,,,..
"
aCt+-<z
l,
o 4' - t
6
ur -<
{
6
t
,erC:g 4 3
&,_
a6
sl
{ro
E
o
=1
t|
o
-\
c{
-(
r(
t?
14
q
1
\-/
Problem 4
A 10.0-cm-highobject is situated25.0 cm in ftont ofa convexmirror that hasa radius of
curvatureof 1.00x 102cm. Using a ray diagramdrawn to scale,measure(a) the location and (b)
the heigbt of the image. The mirror must be drawn to scale.
The ray diagramis shown below. (Note: / = -50'0 cm and do = 25.0 cm)
)
M
j'arx
t5_\+
-==:
^ ^A4 tr^^"{I"{ \. frv frr^,t;g& a$n *+I\ia^A h
/ccf.,* &a"r Jl, W
/o, /wu+-lvdAkn
^-P"<fuA
'%}
?.;e
-+h A!WL^D^
b,.,,-*^Aa Mo &xB] F"x}d "^/
t" #'' g/'^x'^r$
p,o^d.l,JAd
a ^Dul A.JAA^;A fur'
/r$"tsrfoJ ,Pr-$ )4^q
a'/^A
AJ t \, ,c,a^fr.,*8 "curvrdk'^4oA.'t
/fi"l{
Reflectedray
Virtuallmage
-e'--
The ray diagramindicatesthat the imase is 16.7crn behindthe mirror
The ray diagramindicatesthat the imageheightis 6.67cm
Problem 5
The focal lengthofa concavemirror'is 17 cm. Al objectis located38 cm in front ofthis minor.
Where is the image located?
C
T:
* /s'= /{
/s
\ t
r.\
l'lcrn'
ll
/s'= /+ - /s
S = 37"*
rt.
Il
ll
)t
l/
7
O. o3r5 c,,.'tt
_t
l?cro
l/
'/-
/>
38c."
-)
t
- 6'o345 cm
o" o 3ls.--l
9/ = 3 lcr,
Problem 6
The imagebehind a convexmirror (radiusof curvature= 68 cm) is located22 cm from the
minor. (a) Where is the object locatedand (b) what is the magnification of the mirror?
Determinewhether the imageis (c) upright or inverted and (d) larger or smaller than the object.
Y'
f:-YxA--33c,,,,
9' = -A?.cr.)
,/s
5=?
oa=?
I,.//
,/\
._L
>?c rq
= O. oll lc rn-(
=
/o"orltcn
S = 5a.rr \
,^/
(b/
fn=-t = gi:d
5\m
Cc) r-ilc!
tq 7 o I
*""4
(o) aa*, )* l< t, )I"^/gt,
m:O.Y?.
I
I
--;;.cfr,
Problem 7
Convex mirrors arebeing usedto monitor the aislesin a store.The mi]fors have a radiusof
curvatureof 4.0 m. (a) Wlat is the imagedistanceif a customeris 15 m in front of the mirror?
(b) Is the imagereal or virtual? (c) If a customelis 1.6 m tall, how tall is the image?
$--/xA=-a'o
wl
I = /5")
gt= ?
'/,
'/g=
Ys,
/g
+ t,=
(")
- -u
-L.= .-.i---l.ortr
s'
)3 t- _
:
/S'.,
-L-
- o.5d7.q
- o. sa?mt
-r -----)
5'= - l-8m
(b)
(c)
fq:
r):
-s2'= -
{A:---- hr=-\
C l.t.):
,5f\
+
= (D.ta)(1"6n
)
h' = D.l9 ,.,
Problem 8
A clown is using a concaveniakeupmirror to get ready for a show and is 27 cm in fiont of the
mirror. The imageis 65 cm behindthe mirror. Find (a) the focal length of the mirror and (b) the
magrrification.
S = A?c.q
9'=
C
-T
S' ,la r.*q,a}*;P h4ie$b
fi*
'A'"^al
)a Jb"'t\^r',.)
J*t, ^t,$r,,r"
-Io5.m
=3
/9=
-t-
+ J-
$,?cfr
m --?
/+=
(b)
\rh
-\
O" o?&.*,
|q' :
=
/.- (-tc$
--+
eva)
A?. -
S
11'1= l. ai
f:;-q
-L5c6
Problem 9
A concavemirror (/: 45 cm) producesan imagewhosedistancefrom the rnirror is one-third the
object distance-Detemine (a) the object distanceand (b) the (positive) image distance.
(
= ?l t r Dc.n-,
T
/t- /t'
t/zS
E'=
= '/t
t?
t/$ -
-->
4/t=I
(u) 5t = ;r/u =
5
-L-
)
=
-?
Ll+ -- e(tts.n\
lEoc^,
| 9Oc rt
3
zc9.!cr'\: Aa,4 L
+J6Oc co
lBoc'rq
I
=
a/5cm
Y,:t !
===Problem 10
placed
An object is
in flont ofa convex mirror, and the size ofthe imageis one-fourth that of the
object. What is the ratio rf of the object distanceto the focal length of the mirror?
f1-.1=
-9-,.. I
I
I
= l'l
*= 1 /r
-
-lr
-rA'tvt--*
..l"Y\P .fi!,|'}|4{n
rc,r'.Nv!4 ) )$a h^\r/\^) P* l" ^a
,/t6
l.cr > D 1 P^+"'b
tl
l') = '/4
4=:
t,t
-
t/q' -5/s
le
----) g'= -sA
'/r- /u' = /g
Ys'/ent /+
-%= ,1+----'
Yu-Ts' /;
s/. = -3
/+
).4
U