directions,the intensityat a point is proportionalto the inversesqualeof the distancefrom the
D
sourceto the.point.I = --j-:4nr'
You shouldalsoknow that when an object absorbselectromagneticradiation,it receives
momentum:ttP: LUI c , whereAU is the energyabsorbed.Whenthe radiationis reflectedback
alongtlrepathof incidence,themomentumreseivedis Lp=Zaulc, whereAUis thereflected
energy.For total absorption,the radiationpressureisp,: Ilc andthe force on the objectis
F = IAlc, whereA is the areastruckby radiation.If the radiationis reflectedback on its path of
incidence,the radiationpressureand force areboth twice as great.
Someproblemsdeal with polarization.You shouldknow how to identifu the directionandplane
ofpolarization. You shouldalsoknow how to computethe intensityof radiationtransmittedby a
poiarizingsheet.Rememberthat the exiting radiationis polarizedin the polarizing direction of
the sheet.
Many problemsdeal with refractionat a singleplanesurfaceand with total intemal reflection.
For refractionproblems,useSnell's1aw:nfiinfit : nzsin)z.Rememberto measurethe angiefrom
the surfacenormal.For total intemal reflection,rememberthat t?$in?> nz, where,,ll is the index
of retaction for the mediumof incidenceandn2is the index of refractionfor the medium
=
beyondthe surface.other problemsaskyou to calculatethe Brewsterangle.Usetanqs n2ln1,
n, is the index of reftactionfor the mediumofincidence andrizis the index ofrefraction
*k
" mediumofthe refiactedlight. ln somecases,you will alsoneedto use geometryto trace
for the
lays.
Questions and Example Problems from Chapter 33
QuestionI
The figure showsthe electricandmagneticfields of an electromagneticwaveat a
certaininstant.Is the wavetraveling into the pageor out of it?
e 0..9"
Question2
Eachpart ofthe figure beiow showslight that reftactsthroughan interfacebetweentwo
materials.The incident ray (showngray in the figure) consistsofred andblue light. The
approximateindex of reftactionfor visible light is indicatedfor eachmaterial.Which of the three
partsshowphysicallypossiblerefraction?
A--> ?.'"a^'PW^J ^ X45
rel
;l$/e'cUl\v
n= 7-3
."J
nf 1.5
b-'+ n'^+ t'l''""5 lx PPt
orrrq 8l-" "{r-cw"-A
C-4 *b(4
!,rt
al'-A
W
,*rt, P' \ "*) ''-'/
Problem 1
About how far apartmustyou hold yow handsfor themto be separatedby 1.0nanoJightsecond?
=) 1-.o ,/na{\o- 9tQ'l--,tc*"*"J.,.+ -$.4-r &*-A4}*
)rila;.&
* -.e
/tn o./|.\a - -a-Lc,/a\-vul
(-
l.o " 16-9=
d -- v f - (3-on lot*/,){t.o"
c . = 3 . O , l O? . q , / :
d = o.3cr''.,
ro'1.)
Problem2
FrankD. Drake, an investigatorin the SETI (Searchfor Extra-TerrestrialIntelligence)program,
oncesaidthat the largeradio telescope(seethe figure below) in Arecibo, PuertoRico, "can
detecta signalwhich lays down on the enlire surfaceof the eartha power ofonly onepicowatt."
(a) What is the powerthat would be receivedby the Arecibo antemafor sucha signal?The
antennadiameteris 300 m. (b) What would be the power of a sourceat the centerof our galaxy
tlrat could provide sucha signal?The galacticcenteris 2.2 x 104ly away.Take the sourceas
radiatinguniformlyin all direclions.
Ar= 6.3?'lobr,
p=
p= r.o*1o-,aW
3ooro[:/Sor.r
(o)P."..-.d
=P( *r)
iP"a"' =
4 ( b . : t , l o 6 * o )a
t"Ll^ lo-""V I
t= O/o'7/A.*,^=**.,=
I.tu.ro'! \
?ri(ro.:?,ro6.)'
J'
= P(+k.)
?,= r('t-,r)
=
qr.lu.ror.r:1.)gr(r.or,rJ
-m'l', '' ' - ',
\'
Problem
3
Al airplaneflying at a distanceof 10km from a radiotransmitterreceivesa signalof intensity= 1 l,l" lO'5v/ I
10 prWm2.Calculatethe total power of the transmitterassumingthat the transmitterradiates L:'-1
uniformly ir all directions.
p
<\ AJd\^^r.-e,[,t.',,]#h5/r^4-^-4
-W
t
t
-
r/
J- = iDFnr
-
f
=lori** =
v-..'
= l.O*lD Ll n,
lDr,Ot;{
,rqarl-/Jj*,.11-.,,*
P = Ut-r*)-f
"" f
=i;t
mm---l
l*_- 2.60
Problem 4
In the figure to the right, a laserbeamof power 4.60 W and diameter 2.60 mm
is directed irpward at one circular face (of diameter d < 2.60 mm) of a perfectly
reflecting cylinder, which is made to "hover,, by the beam,sradiation piessure.
The cylinder'sdensity is 1.20{cmJ. What is the cylinder,sheight H?
P= i.oow
F^i,*,;
qr = t.rog/crr
i
--
#w
I
I
f ^/^L =
mq
lI-?
/-t-'-
=
,P4i4lfu -{&^iql , tr= \}9
c
r=9=_P.
A rrr )
]-
Zq=,.ror=6
I
J
| . !o x I o" fXl/,,,3
af
H= ce?
I
|.'?
(eu)s
RAHe
=
AH+
ara
Q
e
P
-rr(JA
)'
T= 4%nf
= g?
H = \(ur/nf)
c ca
=
Trdr I ce?
8 ( 4.aovr)
*n ( a.oo.tou,")\
(3.o"rae'
lr)(t.lo,fig\,i*l
s:_1:qr:-l*
I
A point sourceof light emits isotropicallywith a power of 200 w. what is
Problem 5
the force due to the
light on a totally absorbingsphereof radius2.0 cm at a distanceof20 m from the source?
p = ?.oo\1y
I- = Ao.n
$f*
T-
t-
( eoow)
'---.) f
4 rr (ao'n)\
-:----1-
,a,c.dvrt.ileq g"ra.aa-,.r
4y", . -a-.p,hr.e,st/+-uL
.| = %lnr^
o !Lr^,.rvr-r.e^uli/tlA i,b"tt"o-F;."14:
?.
=f
/.
: o.o4oV/^t
+t.at6it;.^/- al:eo'',Vn-t
,r.r4 ft = -rr i-\ = rr (o.o Xo n ).
:
I
loJ'
2r
ln
tv
--4.
t'r
Problem6
In the figure below, initially unpolarizedlight is senttoward a systemoftlree polarizing sheets.
What fraction of the initial iight intensityemergesfrom the system?
|
'?..
l--r3
0= llo"^ )o'
a{rla
6r.""""9 }}*u3& }r-!&" I
oi,}a p'4A/^a JA^ ^€4 -t!\
M
r-
----:
r'un4arau"xc-J
/^^_ Z1 rc-atr1o.
)t'^r*g, E rra r -.-..-,
,.
w*z
)"4^} i"hr.aa
I, = Iofo ,Q,r,.c'.,"-r.
= ,*,r-.o.< 506
r = o.oe.,
Jo
Problem 7
An rmpolarizedbeamof light is sentinto a stackof four polarizing sheets,orientedsothat the
anglebetweenthe polarizing sheetsis 30o.What fraction of the incident intensityis tansmitted
bv the svstem?
-A^^it?]iliVl
UE,
J-, = Z, rc;ct^3o- _ )<-t
:;:---Iu-
A^i'bul4 -r,r'*p"e-''"ryJ
czst3o'
f",c,oa:3o" -- t/rf ,,c,,t'3o'
J q = I , re,o-saJ6,=
f
,
l/, f.
lt o.L go"
= '/x r" rc-o4,3o' r-.
Jr= o"etzo
Problem 8
In the figure below, two light rayspassfiom air throughfive transparentlayersofplastic whose
boundariesareparallel,whoseindexesofrefraction areas given, andwhosethicknessesare
unknown.The rays emergeback into air at the right. With respectto a normal to the last
interface,what is the aagleof (a) emergingray a and (t) emergingray b? (c) What areyour
answersif there is glass,with n = 1.5,insteadof air on the left andright sidesof the plastic
layers?(Hint: Saveyourselfmuch time by first solving the problemsalgebmically.)
l^\, -a,n er = n9-J'.,O \
n A.rl,vn O b.= n 3 A / a A 3
I
a
'. : A? 'U/Y'rS?
f i n / ^ , - a - ^ / qe l
ft?-4-'vn02 ---+ -4,^m9 r=
n, Alt't 01 = ng-\rw,O1 -- n3-4r.,Oa.
f\,-t^^qS,=
'^?
c')::-"tr;3-=C)-r.
_N,g -_(#)^,,
D
=
=u
=o, Or=O"
("),.u^^-*
o,=o',
or
.a) ',urrnzrr
,t
lFFo{
lt2r
i
r------1
r_---.1
ln
-- A9: 4 ^ o
t,'\
.._/
t)r= 4e
i
( b)
),: tt2 ll9"i
b / -tlt**a , " w t * Ifi,=o?rlO"-O,=fo'
r- ao- I
' -+
o.a3
or=l.o
= r3"FJ"?":,?fe;
'''J
I
""1
P r o b l e m9
In the figure below, a 2.00-m-longvertical pole extendsfiom the bottom of a swimmingpool to
a point 50.0 cm abovethe water. Sunlightis incidentat angle0 : 55.0". What is the lengthof the
shadowof the pole on the level bottom of the pool?
Q,= 10-55'
-_
A..-_
/sr\o.*-
*
nr^;
h^ras,=
to.
o,5oq
??
ls Pt "[ A^^A^'r
..", X, iX".. =
,r4
:::=:l
X,= Co.5o,'\)F"{35"
./'
-:::'_
D,
350
f
l.o?ff)
|
-- CI*ejun
9.
,tl
I
'./
=
_A.inD..=
+"^D, tT*r*='' /1,.,,, X":/.5oq-F,'"r!5-5"
O.?),o'
-,tr^-rg*=O...lll/ ----J ga.= 15.5"
4
Problem 10
A beamof light is emitted 8.0 cm beneathtle surfaceot'a liquid and striles the surface7.0 cm
from the poiirt directly abovethe source.Iftotal intemal reflection occurs,whal canyou say
aboUttheindei ofrefractionofthe liquitl?
O. =-A,,rnr-'(nyn,) --+ b^!t"b"-o^"Uj"Lt,o
L 0 >e.
--+ I =.b,i' LVu) = z/1.1o
-;[lu^ O = t/t
t 4t.\o
er
( ^%, ) a ai,.a"
-,arv\-r
nr/n,, )vn 41.\" /'---
r\- /
"/tl*rLll,\o
D,
)
i,
2 /.5X, f)e
Problem 11
In tlre figure below, ligbt irlitia[y itr material 1 reftactsinto mateial2, ffossesthat material,and
is then incidentat the critical angleon the interfacebetweenmaterials2 and3. The indexesof
refractionarenr=1.60,n2:1.40,andn::1.20.(a)Whatisangle0?(b)IfOisincreased,
is thererefractionof light into material3?
f) ,-- l,&o
f\ r-= l.9o
Oa= l'XD
)^ 2)"'%
ntrt,;hp d,*q&"+ n^/no )/'&"Y^!c'4
e.= -D''("'/"^) = Ar;'(!Y
\
O. = E1.o'
O,=9?-51.a=:!g
n'ar\O,' = fllaioOt €
a't'" 9 =
fr*n-
-!.'{9.-a;'"3l- D'
l.b,o
i----------------
-lJfqo-- o.qst ----) I O = ).u.r" I
(b)
)1tto\oaLt,v'g I
z'ra.ulfu ,,t""
dfrl
,\.,w\ttrAtd
-urrJ^A^eAr^1,^t q'-&r^taatA a/'4e Jn"/n.
I
O.
/"f^$.n
Problem 12
The figure below depictsa simplistic opical fiber: a plastic core (n1: 1.58)is surroundedby a
plasticsheatl (n2: 1.53).A light ray is inoidenton oneendof tle fiber at angle0' The ray
is to undergototal intemal reflection at point d whereit encormtersthe core-sheathboundary.
(Thusthereis no lossof light throughthat boundary.)Whaf is the maximumvalue of O that
allowstotal intemal reflectionat A?
n/n, - JE-2)q O--'r
l. b,
= O.q68'
o"l oa;
O. ---ir,*q-'(
9"=
?5.5o
--:-
O, = 1O"-?5.8'=E
Do-arroO= nr-A,lvnell
^;
0t-0,4=t'o
llr = 1"59
D = -!} ,A,vqe,
\.-/
t.)*
g --zf,r^.,
L>-dr'r
--a
lzl"5' : D' 31a
O = -O,l"n-l ( o -316)
l.o
Problem13
(a) At what angleof incidencewill the light reflectedfrom waterbe completelypolarized?(b)
Doesthis angledependuponthe wavelengthof the light?
g, =i,o^' ("%,)
D,= oo;4= l'o
fta= D*-5 = 1,33
----) Op = 'x.,,'(t'tN'')
Oe = 53' l"
(u) q+u,