directions, the intensity at a point is proportional to the inverse squale of the distance from theD

source to the.point. I = --j-:-4nr'

You should also know that when an object absorbs electromagnetic radiation, it receives

momentum: ttP : LUI c , where A U is the energy absorbed. When the radiation is reflected back

along tlre path of incidence, the momentum reseived is Lp=Zaulc, where AUis the reflectedenergy. For total absorption, the radiation pressure isp,: Ilc and the force on the object isF = IAlc, where A is the area struck by radiation. If the radiation is reflected back on its path ofincidence, the radiation pressure and force are both twice as great.

Some problems deal with polarization. You should know how to identifu the direction and plane

ofpolarization. You should also know how to compute the intensity of radiation transmitted by apoiarizing sheet. Remember that the exiting radiation is polarized in the polarizing direction of

the sheet.

Many problems deal with refraction at a single plane surface and with total intemal reflection.

For refraction problems, use Snell's 1aw: nfiinfit : nzsin)z. Remember to measure the angie from

the surface normal. For total intemal reflection, remember that t? $in?> nz, where ,,ll is the index

of retaction for the medium of incidence and n2 is the index of refraction for the medium

beyond the surface. other problems ask you to calculate the Brewster angle. Use tanqs = n2ln1,

*k "

n, is the index of reftaction for the medium ofincidence and riz is the index ofrefractionfor the medium ofthe refiacted light. ln some cases, you will also need to use geometry to trace

lays.

Questions and Example Problems from Chapter 33

Question IThe figure shows the electric and magnetic fields of an electromagnetic wave at acertain instant. Is the wave traveling into the page or out of it?

e 0..9"

Question 2Each part ofthe figure beiow shows light that reftacts through an interface between twomaterials. The incident ray (shown gray in the figure) consists ofred and blue light. Theapproximate index of reftaction for visible light is indicated for each material. Which of the three

parts show physically possible refraction?

n = 7 - 3

n f 1 .5

A--> ?.'"a^'P W^J ̂ X45;l$/e'cUl\v

b-'+ n'^+ t'l''""5 lx PPt."J orrrq 8l-" "{r-cw"-A

C-4 *b- al'-A W

(4

r e l

!,rt ,*rt, P' \ "*) ''-'/

Problem 1About how far apart must you hold yow hands for them to be separated by 1.0 nanoJight-second?

( -

=) 1-.o ,/na{\o- 9tQ'l--,tc*"*"J.,.+ -$.4-r &*-A4}* )rila;.& * -.e

d -- v f - (3-on lot*/ ,){ t .o" ro'1.)

d = o.3cr' ' . ,

Problem 2Frank D. Drake, an investigator in the SETI (Search for Extra-Terrestrial Intelligence) program,once said that the large radio telescope (see the figure below) in Arecibo, Puerto Rico, "candetect a signal which lays down on the enlire surface of the earth a power ofonly one picowatt."(a) What is the power that would be received by the Arecibo antema for such a signal? Theantenna diameter is 300 m. (b) What would be the power of a source at the center of our galaxytlrat could provide such a signal? The galactic center is 2.2 x 104 ly away. Take the source asradiating uniformly in all direclions.

/tn o./|.\a - -a-Lc,/a\-vul

l . o " 16 -9 =

c . = 3 .O, lO ? .q , / :

- f = lor i**= lDr,Ot;{

Ar= 6.3?' lobr, p= r .o*1o-,aWp= 3oo ro [ : /So r . r

(o) P."..-.d = P ( *r) = P(+k. )

t= O/o'7/A.*,^= **.,= I.tu.ro'! \ ?,= r('t-,r)?ri(ro.:?,ro6.) ' J ' = qr. lu.ror.r:1.)gr(r.or,rJ,.).

Prob lem 3 \ ' -m ' l ' , ' ' ' - ' ,

Al airplane flying at a distance of 10 km from a radio transmitter receives a signal of intensity = 1 l,l" lO'5v/ I10 prWm2. Calculate the total power of the transmitter assuming that the transmitter radiates L:'-1uniformly ir all directions. p

t -W <\ AJd\^^r.-e,[,t.',,]#h5/r^4-^-4 ,rq arl-/ Jj*,.11-.,,* "" f =i;t

t - r / L l

J- = iDFnr = l .O* lD n , P = Ut-r*)-f

4 ( b . : t , lo6*o) a

iP"a"' = t"Ll ̂ lo-""V I

v- . . '

Problem 4In the figure to the right, a laser beam of power 4.60 W and diamet er 2.60 mmis directed irpward at one circular face (of diameter d < 2.60 mm) of a perfectlyreflecting cylinder, which is made to "hover,, by the beam,s radiation piessure.The cylinder's density is 1.20 {cmJ. What is the cylinder,s height H?

F^i,*,;IIiIJm q

P= i.oowqr = t.rog/crr

-- | . !o x I o" fXl/,,, 3

l I - ?/ - t - ' -

,P4i4lfu -{&^iql , tr= \}9c

H= af r=9=_P.A rrr )

T= 4%nf

f ^/^L =

=

ce? -rr(JA )'

H = \(ur/nf)c ca

= g? =r ITr d ce?

8 ( 4.aovr)*n ( a.oo.tou,")\ (3.o"rae' lr)(t.lo,fig\,i*l

I s:_1:qr:-l*Problem 5A point source of light emits isotropically with a power of 200 w. what is the force due to thelight on a totally absorbing sphere of radius 2.0 cm at a distance of20 m from the source?

p = ?.oo\1y $f* o !Lr^,.rvr-r.e^ uli/tlA i,b"tt"o-F;."14: .| = %lnr^

I- = Ao.n T-t -

( eoow)-:----1-

4 rr (ao'n)\' - -- .) f : o.o4oV/^t

,a,c.dvrt.ileq g"ra.aa-,.r ?.

= f /. +t.at6it;.^/- al:eo'',Vn-t

4y", . -a-.p,hr.e, st/+-uL ,r.r4 ft = -rr i-\ = rr (o.o Xo n ). : I 2 r l n - - 4 .l o J ' t v t ' r

Zq=,.ror=6

ara =e

l*_- 2.60 mm---l

#wI]-

|. '?

(eu)s

RAHeQ AH+P

Problem 6In the figure below, initially unpolarized light is sent toward a system oftlree polarizing sheets.What fraction of the initial iight intensity emerges from the system?

| '?.. l - -r3

0= l lo"^ )o '

a{rla 6r.""""9 }}*u3& }r-!&" I ----: I, = Iofo ,Q,r,.c'.,"-r. )"4^} i"hr.aa

oi,}a p'4A/^a JA^ ̂ €4 -t!\ r- /^^_ Z1 rc-atr1o. r'un4arau"xc-J

M w*z )t'^r*g, E rra r -.-..-, ,. = ,*,r-.o.< 506

Problem 7An rmpolarized beam of light is sent into a stack of four polarizing sheets, oriented so that theangle between the polarizing sheets is 30o. What fraction of the incident intensity is tansmittedbv the svstem?

UE, -A^^it? ]iliVl A^i'bul4 -r,r'*p"e-''"ryJ

J-, = Z, rc;ct^3o- _ )<-t czst3o':;:----

Iu- f",c,oa:3o" -- t /r f , ,c,, t '3o'

J q = I , re,o-saJ6, = l/, f. lt o.L go"

r = o.oe.,Jo

Jr= o"etzof , = '/x r" rc-o4,3o' r-.

Problem 8In the figure below, two light rays pass fiom air through five transparent layers ofplastic whoseboundaries are parallel, whose indexes ofrefraction are as given, and whose thicknesses areunknown. The rays emerge back into air at the right. With respect to a normal to the lastinterface, what is the aagle of (a) emerging ray a and (t) emerging ray b? (c) What are youranswers if there is glass, with n = 1.5, instead of air on the left and right sides of the plasticlayers? (Hint: Save yourself much time by first solving the problems algebmically.)

l^\ , -a,n er =

n A.rl,vn O b. =Ia

n9-J'.,O \

n3 A/aA3

n, Alt ' t 01 = ng-\rw,O1 -- n3-4r.,Oa. ' . : A? 'U/Y'r S?

f \ , - t^^qS,= f t?-4- 'vn02 - - -+ -4 ,^m9 r= f in /^ , -a-^ /q e l

("),.u^^-* o,=o', lFFo{ c') :-"tr;3-=C)-r..a) ',urrnzrr or =o, lt2r

= u ,t .._/ :

'^? _N,g -_ (#)^,,

r_---.1 t)r= 4e

b) t l t**- f i ,=o?rlO"-O,=fo' I D

or=l.o = o.a3' -+ ?":,?- fe; = r3"FJ"-

Prob lem 9 " "1 ' ' ' J I

Or=O"i r------1

t , ' \ l n - A : 4 ^ o i( b / -a , "wt* I ) , : t t2 l l9 " i

-9 r - ao- I

In the figure below, a 2.00-m-long vertical pole extends fiom the bottom of a swimming pool to

a point 50.0 cm above the water. Sunlight is incident at angle 0 : 55.0". What is the length of theshadow of the pole on the level bottom of the pool?

Q,= 10-55'-_

350

A..-_ - h^ras,= to. ??/sr\o.*-

o,5oq ,r4

* X,= Co.5o,'\)F"{35" :::=:l ./ ' f-:::'_

|

nr^; D, -- CI*ejun 9. I, t l

_A.inD..= +"^D, = tT*r*='' /1,.,,, X":

-, tr^-rg*= O... l l l / ----J ga.= 15.5" 4

ls Pt "[ A^^A^'r. ." , X, iX".. =

l .o? f f )

' . /

/.5oq-F,'"r!5-5"

O.?) ,o '

Problem 10A beam of light is emitted 8.0 cm beneath tle surface ot'a liquid and striles the surface 7.0 cmfrom the poiirt directly above the source. Iftotal intemal reflection occurs, whal can you sayaboUt the indei ofrefraction ofthe liquitl?

er t 4t.\o

O,=9?-51.a=:!g

n'ar\O,' = f l laioOt € a't '" 9 =

i----------------

-lJfqo -- o.qst ----) I O = ).u.r" I

(b) )1tto\oaLt,v'g I z'ra.ulfu ,,t"" dfrlI

,\.,w\ttrAtd

O. =-A,,rnr-'(nyn,) --+ b^!t"b"-o^"Uj"Lt,o L 0 >e.

-;[lu^ O = t/t --+ I =.b,i' LVu) = z/ 1.1o

-,arv\-r ( ^%, ) a ai ,. a"

nr/n,, )vn 41.\" / '---

Problem 11

r \ - /D , ) " / t l * rL l l , \o

i , 2 / .5X, f )e

In tlre figure below, ligbt irlitia[y itr material 1 reftacts into mateial2, ffosses that material, andis then incident at the critical angle on the interface between materials 2 and3. The indexes ofrefract ionarenr=1.60,n2:1.40,andn::1.20.(a)Whatisangle0?(b)IfOisincreased,is there refraction of light into material 3?

f ) , -- l ,&o

f\ r- = l .9o

Oa = l 'XD

ntrt,;hp d,*q& "+ n^/no )/'&"Y^!c'4 )^ 2)"'%

e.= -D'' ("'/"^)

O. = E1.o'

fr*n-

= Ar;'(!Y \

-!.'{9.-a;'" 3l- D'l .b,o

O.-urrJ^A ̂ eAr^1,^t q'-&r^taatA a/ '4e Jn"/n. /"f^$.n

Problem 12The figure below depicts a simplistic opical fiber: a plastic core (n1 : 1.58) is surrounded by a

plastic sheatl (n2 : 1.53). A light ray is inoident on one end of tle fiber at angle 0' The rayis to undergo total intemal reflection at point d where it encormters the core-sheath boundary.(Thus there is no loss of light through that boundary.) Whaf is the maximum value of O thatallows total intemal reflection at A?

O, = 1O"-?5.8'= E

Do-arroO= nr-A,lvnell

^; D = -!} ,A,vq e,t.)*

-zf,r^., g -- L>-dr'r lzl"5'l .o

-2)q O--- n/n, - JE- = O.q68'' r l . b ,

O. ---ir,*q-'( o"l oa;

9"= ?5.5o--:-

0t-0,4=t 'ol l r = 1"59

: D' 31a --a O = -O,l"n-l (\.-/

o -316)

----) Op = 'x.,, '(t 'tN'')

Oe = 53' l "

Problem 13(a) At what angle of incidence will the light reflected from water be completely polarized? (b)

Does this angle depend upon the wavelength of the light?

g, = i,o^' ("%,)

D,= oo;4= l 'o

f ta= D*-5 = 1,33

(u) q+u,