matriculation physics physical optics
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PHYSICS CHAPTER 2
CHAPTER 2:CHAPTER 2:Physical opticsPhysical optics
(9 Hours)(9 Hours)
The study of
interference, diffractioninterference, diffraction
and polarization ofand polarization of
lightlight !i"ht is treated as#a$es rather tha% as
rays
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PHYSICS CHAPTER 2
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At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
ExplainExplainHuygens principle governing the propagation ofHuygens principle governing the propagation of
wave fronts.wave fronts.
Include spherical and plane wavefronts.Include spherical and plane wavefronts.
ExplainExplaindiffraction patterns by using Huygens principle.diffraction patterns by using Huygens principle.
earning !utco"e:
2& Huy"e%'s pri%ciple (& hour)
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PHYSICS CHAPTER 2
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#.$.$ %avefronts is defi%ed as a line or surface, in the path of a wave "otion,a line or surface, in the path of a wave "otion,
on which the disturbances at every point have the sa"eon which the disturbances at every point have the sa"ephasephase
+i"ure 2& sho#s the #a$efro%t of the si%usoidal #a$es
!i%e ,oi%i%" all poi%t of ad,ace%t #a$e- e" A- . a%d C or /-Ea%d + are i% phase
0a$efro%t al#ays perpe%dicular to the directio% of #a$epropa"atio%
&igure #.$&igure #.$
#.$ Huygens principle
A
.
C
/
E
+
#a$efro%t
v
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PHYSICS CHAPTER 2
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'ype of wavefronts'ype of wavefronts (ircular wavefronts(ircular wavefrontsas sho#% i% +i"ure 22 are produced 1y a
poi%t source "e%erates t#odie%sio%al #a$es
&igure #.#&igure #.#
circular #a$efro%t
ray
poi%t source
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PHYSICS CHAPTER 2
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)pherical wavefronts)pherical wavefrontsas sho#% i% +i"ure 23 are produced 1ya poi%t source "e%erates threedie%sio%al #a$es
&igure #.*&igure #.*
spherical #a$efro%ts
rays
poi%t source
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PHYSICS CHAPTER 2
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+lane wavefronts+lane wavefrontsas sho#% i% +i"ures 24a a%d 241 areproduced 1y a poi%t source "e%erates threedie%sio%al #a$es
at lar"e dista%ce fro the source
rays
pla%e #a$efro%t
&igure #.a : -*/0&igure #.a : -*/0pla%e #a$efro%t
rays
&igure #.b : -#/0&igure #.b : -#/0
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PHYSICS CHAPTER 2
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1ay1ay
is defi%ed as a line represents the direction of travel of aa line represents the direction of travel of a
wavewave It is at ri"ht a%"le to the #a$efro%ts as sho#% i% +i"ure 25
2ea" of light2ea" of light
is a collection of rays or a colu"n of lighta collection of rays or a colu"n of light parallel 1ea- e" a laser 1ea (sho#% i% +i"ure 26a)
&igure #.3&igure #.3
ray
#a$efro%t
Source of li"ht
fro i%fi%ity
&igure #.4a&igure #.4a
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PHYSICS CHAPTER 2
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di$er"e%t 1ea- e" a lap %ear you (sho#% i% +i"ure 261)
co%$er"e%t 1ea as sho#% i% +i"ure 26c
&igure #.4b&igure #.4b
&igure #.4c&igure #.4c
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seco%dary #a$efro%t
states thatevery point on a wavefront can be considered asevery point on a wavefront can be considered as
a source of secondary wavelets that spread out in thea source of secondary wavelets that spread out in the
forward direction at the speed of the wave. 'he newforward direction at the speed of the wave. 'he new
wavefront is the envelope of all the secondary wavelets wavefront is the envelope of all the secondary wavelets
i.e. the tangent to all of the"i.e. the tangent to all of the"
#.$.# Huygens principle
&igure #.5&igure #.5
#a$elets
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PHYSICS CHAPTER 2
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P&
P2
P3
P4
A
.
A'
.'
7&
72
73
74s
Application of Huygens principleApplication of Huygens principle
a Co%structio% of %e# #a$efro%t for a pla%e #a$e
&igure #.6&igure #.6
If the #a$e speed is v- he%ce i%tie t the dista%ce tra$els 1y the
#a$elet iss = vt.
+ro Huy"e%s' Pri%ciple- poi%ts
P&- P2- P3a%d P4o% the#a$efro%t A. are the sources of
seco%dary #a$elets
+ro the poi%ts- dra# cur$es of
radiuss
The% dra# a strai"ht li%e A'.'
#hich is ta%"e%t to the cur$es at
poi%ts 7&-72-73a%d 74
He%ce- li%e A'.' is the %e#
#a$efro%t after tseco%d
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PHYSICS CHAPTER 2
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A
A'
.
.'
sP&
P2
P3
P4
7&
72
73
74
source
ray
1 Co%structio% of %e# #a$efro%t for a circular #a$e
&igure #.7&igure #.7
E8pla%atio% as i% theco%structio% of %e# #a$efro%t
for a pla%e #a$efro%t
.ut the #a$efro%t A'.' is a
cur$e touchi%" poi%ts
7&-72-73a%d 74
The cur$e A'.' is the %e#
(circular) #a$efro%t after tseco%d
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c /iffractio% of #a$e at a si%"le slit
&igure #.$8&igure #.$8
Huy"e%s' pri%ciple ca% 1e used to e8plai% the
diffractio% of #a$e
Each of the poi%t i% +i"ure 2&- acts as a
seco%dary source of #a$elets (red circular
arc)
The ta%"e%t to the #a$elets fro poi%ts 2- 3a%d 4 is a pla%e #a$efro%t
.ut at the ed"es- poi%ts & a%d 5 are the last
poi%ts that produce #a$elets
Huy"e%s' pri%ciple su""est that i% co%fori%"to the cur$ed shape of the #a$elets %ear the
ed"es- the %e# #a$efro%t 1e%ds or diffracts
arou%d the ed"es applied to all i%ds of
#a$es
Stiulatio% 2&
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PHYSICS CHAPTER 2
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At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
/efine/efinecoherence.coherence.
)tate)tatethe conditions to observe interference of light.the conditions to observe interference of light.
)tate)tatethe conditions of constructive and destructivethe conditions of constructive and destructive
interference.interference.
earning !utco"e:
22 Co%structi$e i%terfere%ce a%d destructi$ei%terfere%ce (& hour)
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#.#.$ Interference of light !i"ht #a$e is a% electroa"%et #a$es (e#)
It co%sists of varying electric fieldvarying electric fieldEEa%d varying "agneticvarying "agneticfieldfieldBB#hich are perpendicular to each otherperpendicular to each otheras sho#% i%+i"ure 2&&
#.# (onstructive interference and
destructive interference
&igure #.$$&igure #.$$
Electric field: E = E0sin (t-kx)
a"%etic field: B = B0sin (t-kx)
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InterferenceInterferenceis defi%ed as the effect of interaction betweenthe effect of interaction betweentwo or "ore waves which overlaps or superposed at a pointtwo or "ore waves which overlaps or superposed at a point
and at a particular ti"e fro" the sourcesand at a particular ti"e fro" the sources &or light&or lightthe I%terfere%ce is occurred #he% t#o li"ht #a$es eet
at a poi%t- a bright or a dar9 regionbright or a dar9 region#ill 1e producedproducedi%accorda%ce to the Pri%ciple of superpositio%
+rinciple of superposition+rinciple of superpositionstates the resultant displace"entthe resultant displace"entat any point is the vector su" of the displace"ents due toat any point is the vector su" of the displace"ents due to
the two light wavesthe two light waves (onstructive interference(onstructive interferenceis defi%ed as a reinforce"ent ofa reinforce"ent of
a"plitudes of light waves that will produce a bright fringea"plitudes of light waves that will produce a bright fringe
-"axi"u"0-"axi"u"0
/estructive interference/estructive interferenceis defi%ed as a total cancellation ofa total cancellation of
a"plitudes of light waves that will produce a dar9 fringea"plitudes of light waves that will produce a dar9 fringe-"ini"u"0-"ini"u"0
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Pera%e%t i%terfere%ce 1et#ee% t#o sources of li"ht o%ly taeplace if they are coherentcoherentsources It ea%s
the sources ust ha$e the sa"e wavelength or freuencysa"e wavelength or freuency
(o%ochroatic)
the sources ust ha$e a constant phase differenceconstant phase difference
1et#ee% the The li"ht #a$es that are i%terferi%" ust ha$e the sa"e orsa"e or
approxi"ately of a"plitudeapproxi"ately of a"plitudeto o1tai% total cancellationtotal cancellationat
i%iu or to o1tai% a good contrastgood contrastat a8iu
The distance between the coherent sourcesdistance between the coherent sources should 1e as
s"alls"all as possi1leof the light wavelength -of the light wavelength - 00
#.#.# (onditions for per"anent interference
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x2
x1
is defi%ed as the difference in distance fro" each sourcethe difference in distance fro" each source
to a particular point to a particular point
#.#.* +ath difference, L
Path difference, L = |S2PS1P|
= |x2x1|
&igure #.$#&igure #.$#
S1
S2 scree%
P
L
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PHYSICS CHAPTER 2
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Interference of two coherent sources in phaseInterference of two coherent sources in phase
+ath difference for constructive interference+ath difference for constructive interference
S&a%d S2are t#o cohere%t sources i% phaseS1
S2
x1
x2
P (maximum)
&igure #.$*&igure #.$*
+ =
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+ath difference for destructive interference+ath difference for destructive interference
S&a%d S
2are t#o cohere%t sources i% phase
S1
S2
x1
x2
(minimum)
&igure #.$&igure #.$
+ =
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A dar fri%"e is o1ser$ed at 7 thus
At P-
the%
therefore
;ote :
( )m 12 += #here ,...2,1,0 =m)sin( 10P1 kxtEE = )sin( 20P2 kxtEE =
)()( 12 kxtkxt =
)( 21 xxk =L=
2
( ) Lm =+
212
,.....2,1,0 =m
+=
2
1mL
#here
&st dar fri%"e (
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PHYSICS CHAPTER 2
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Interference of two coherent sources in antiphaseInterference of two coherent sources in antiphase
+ath difference for constructive interference+ath difference for constructive interference
S&a%d S2are t#o cohere%t sources i% a%tiphase
S1
S2
x1
x2
P (maximum)
&igure #.$4&igure #.$4
+ =
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A 1ri"ht fri%"e is o1ser$ed at P thus
At P-
the%
therefore
;ote :
m2 = #here ,...2,1 =m)sin( 10P1 kxtEE =
)sin( 20P2 = kxtEE)()( 12 kxtkxt =
= )( 21 xxk
= L2
= Lm2
2
,.....2,1,0 =m#here0he%
+=
2
1mL
&st 1ri"ht fri%"e (
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PHYSICS CHAPTER 2
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+ath difference for destructive interference+ath difference for destructive interference
S&a%d S
2are t#o cohere%t sources i% a%tiphase
S1
S2
x1
x2
(minimum)
&igure #.$5&igure #.$5
+ =
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A dar fri%"e is o1ser$ed at 7 thus
At P-
the%
therefore
;ote :
( )m 12 += #here ,...2,1,0 =m
)sin( 10P1 kxtEE = )sin( 20P2 += kxtEE
)()( 12 kxtkxt += += )( 21 xxk
+
= L2
( )
+
=+ Lm2
12
,.....2,1,0 =m#hereCe%tral dar fri%"e (
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+ri%"e m L
Interference pattern for two coherent sources in antiphaseInterference pattern for two coherent sources in antiphase
&igure #.$6&igure #.$6
#"!"
$"
2"
2
00
11
2
2
1
0Ce%tral dar
&st 1ri"ht
2" 0 21 &st 1ri"ht
&st dar
!" 1 &st dar
2
! 2%d 1ri"ht
#" 1 2! 2%d 1ri"ht
2%d dar
$" 2 22%d dar
S1
S2
scree%
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'wo (oherent
sources
2right fringe2right fringe /ar9 fringe/ar9 fringe
In phaseIn phase
AntiphaseAntiphase
Ta1le 2& sho#s the suary of chapter 223
'able #.$'able #.$
,...2,1,0 =mmL=
,...2,1,0 =m
+=
2
1mL
m2 = ,...2,1,0=m m )12( += ,...2,1,0=m
,...2,1,0 =m
+=2
1mL
,...2,1,0 =m
mL=
m2 =,...2,1=m
m )12( +=,...2,1,0=m
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PHYSICS CHAPTER 2
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At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
/erive/erivewith the aid of a diagra" andwith the aid of a diagra" and useuse
for bright fringes -"axi"a0for bright fringes -"axi"a0
for dar9 fringes -"ini"a0,for dar9 fringes -"ini"a0,
wherewhere mm; 8,
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#.*.$ ?ethods of obtaining two coherent sources
/ivision of wavefront/ivision of wavefront
#.* Interference of trans"itted light
through doubleslits
&igure #.$7&igure #.$7
A slit S is placed at e=ual
dista%ce fro slits S&a%d S2assho#% i% fi"ure
!i"ht #a$es fro S that arri$ed
at S&a%d S2are i% phase
Therefore- 1oth slits S&a%d S2are t#o %e# cohere%t sources-
e" i% You%"'s dou1le slit
e8perie%t
o%ochroatic
li"ht source
S
si%"le
slit
S&
dou1le
slits
S2
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air
fil
air
t
/ivision of a"plitude/ivision of a"plitude
&igure #.#8&igure #.#8
The i%cide%t #a$efro%t is di$idedi%to t#o #a$es 1y partial
reflectio% a%d partial
tra%sissio%
.oth reflected #a$es & a%d 2 are
cohere%t a%d #ill result i%i%terfere%ce #he% they
superpose
e" ;e#to%'s ri%"- air #ed"e
fri%"es a%d thi% fil i%terfere%ce
i%cide%t ray $$ ##
partial reflectio%
partial
tra%sissio%
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+i"ure 22& sho#s the scheatic dia"ra of You%"'s dou1leslit
e8perie%t
#.*.# @oungs doubleslit experi"ent
&igure #.#$&igure #.#$
?ax?ax
?ax?ax
?ax?ax
?ax?ax
?ax?ax
?in?in
?in?in
?in?in
?in?in
scree%
Intensity
i%terfere%ce
patter%
o%ochroatic
li"ht 1ea
S
si%"le
slit
S&
dou1le
slits
S2
m= 2
m= 1
m= 0
m= 1
m= 2
Picture 2&
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Explanation of @oungs doubleslit experi"ent by usingExplanation of @oungs doubleslit experi"ent by using
Huygens principleHuygens principle
0a$efro%t fro li"ht source falls o% a %arro# slit S a%ddiffractio% occurs
E$ery poi%t o% the #a$efro%t that falls o% S acts as sources of
seco%dary #a$elets that #ill produce a %e# #a$efro%t that
propa"ate to slits S&a%d S
2
S&a%d S
2are produced t#o %e# sources of cohere%t #a$es i%
phase 1ecause they ori"i%ate fro the sae #a$efro%t a%d their
dista%ce fro S are e=ual
A% i%terfere%ce patter% co%sisti%" of 1ri"ht a%d dar fri%"es is
fored o% the scree% as sho#% i% +i"ure 22& The 1ri"ht fri%"es are occurred #he% the li"ht fro slits S
&a%d S
2
superposes co%structi$ely
The dar fri%"es are occurred #he% the li"ht fro slits S&a%d S
2
superposes destructi$ely
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/erivation of @oungs doubleslit euations/erivation of @oungs doubleslit euations
Euation for separation betweenEuation for separation between central bright fringecentral bright fringeandand ""thth
bright fringebright fringe
&igure #.##&igure #.##
S&
S2
P
m
7
;>
d
D
my
y
1+my
dou1leslit scree%
(entral(entral1ri"ht
""thth 1ri"ht
-"$0-"$0thth 1ri"ht
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Suppose P i% +i"ure 222 is the thorder 1ri"ht fri%"e- thus
!et >P ?ym? dista%ce fro P to >
I% practice dis $ery sall (@&) a%d D>>d- the% S&;
eets P7 at ri"ht a%"le He%ce
;P= S&P the% S
2;= S
2P;P= m
a%"le P7> ? a%"le S2S&; ? +ro the fi"ure-
S2S
&;
P7>
Si%ce is sall- thus
m= PSPS 12
d
m ==
12
2
SS
%Ssin
D
ym
== &P&
tan
tansin =
D
y
d
m m=
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Therefore- the separatio% 1et#ee% ce%tral 1ri"ht a%d th
1ri"ht fri%"es-ymis "i$e% 1y
;ote: +or brightbrightfri%"es
d
Dmym
=
,...2,1,0'rder: =m#herewavelength:
screentheandslitsd'uleetweendistance:Dslitsd'uleetweense*arati'n:d
0=m (entral(entral1ri"ht fri%"e (Beroth orderBeroth ordera8iu)$$stst 1ri"ht fri%"e ($$stst orderordera8iu)
##ndnd 1ri"ht fri%"e (##ndnd orderordera8iu)
**rdrd 1ri"ht fri%"e (**rdrd orderordera8iu)
1=m2=m!=m
-#.$0-#.$0
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Euation for separation betweenEuation for separation between central bright fringecentral bright fringeandand ""thth
dar9 fringedar9 fringe
&igure #.#*&igure #.#*
S&
S2
R
7
;>
d
D
mx
y
dou1leslit scree%
+ 21m
(entral(entral1ri"ht
""thth orderorder dar
-"-"$0$0thth orderorder dar
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Suppose R i% +i"ure 223 is the thorder dar fri%"e- thus
!et >R ?xm? dista%ce fro R to >
I% practice dis $ery sall (@&) a%d D>>d- the% S&;
eets R7 at ri"ht a%"le He%ce-
;R= S&R the%
a%"le R7> ? a%"le S2S
&; ?
+ro the fi"ure-
S2S
&;
R7>
Si%ce is sall- thus
+=2
1+S+S
12
m
dm
+==
2
1
SS
%Ssin
12
2
D
xm==&
+&tan
tansin =
D
x
d
m m=
+
2
1
+== 21
%++S%S 22 m
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Therefore- the separatio% 1et#ee% ce%tral 1ri"ht a%d thorder
dar fri%"es-xmis "i$e% 1y
;ote: +or dar9dar9fri%"es
d
Dmxm
+=
2
1
,...2,1,0'rder: =m#here
0=m $$stst dar fri%"e (Beroth orderBeroth orderi%iu)##ndnd dar fri%"e ($$stst orderorderi%iu)
**rdrd dar fri%"e (##ndnd orderorderi%iu)
thth dar fri%"e (**rdrd orderorderi%iu)
1=m2=m
!=m
-#.#0-#.#0
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Euation for separation between successive -consecutive0Euation for separation between successive -consecutive0
bright or dar9 fringes,bright or dar9 fringes, yy (+i"ure 222) is "i$e% 1y
mm yyy = +1 dDm
ym
=#here a%d ( )d
Dmym
11 +=+
d
Dy =
( )
d
Dm
d
Dmy
+= 1
#here
wavelength:
screentheandslitsd'uleetweendistance:Dslitsd'uleetweense*arati'n:d
rightec'nsecutivetweense*arati'n:yfringesdar'r
-#.*0-#.*0
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Appearance of @oungs doubleslit experi"entAppearance of @oungs doubleslit experi"ent
+ro the e=uatio% -#.*0-#.*0-
ydepe%ds o% : the #a$ele%"th of li"ht-
the dista%ce apart- dof the dou1le slits- dista%ce 1et#ee% slits a%d the scree%-D
Explanation for the above factors:Explanation for the above factors:
if is short a%d thus ydecreasesfor fi8edDa%dd. The
i%terfere%ce fri%"es are closer to each other a%d $ice$ersa if the dista%ce apart d of the slits dii%ished- yi%creased
for fi8edDa%d a%d $ice$ersa ifDi%creases yalso i%creases for fi8ed a%d $ice$ersa
dDy =
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if a source slit S (+i"ure 22&) is #ide%ed the fri%"es
"radually disappear The slit S the% e=ui$ale%t to lar"e
%u1er of %arro# slits- each produci%" its o#% fri%"e systeat differe%t places The 1ri"ht a%d dar fri%"es of differe%t
systes therefore o$erlap- "i$i%" rise to a differe%t
illui%atio%
if o%e of the slit- S&or S
2is co$ered up- the fri%"es disappear
if the source slit S is o$ed %earer the dou1le slits- yisu%affected 1ut their i%te%sity i%creases
if the e8perie%t is carried out i% a differe%t ediu- for
e8aple #ater- the fri%"e separatio% ydecreased or
i%creased depe%di%" o% the #a$ele%"th- of the ediu
if #hite li"ht is used the ce%tral 1ri"ht fri%"e is #hite- a%d the
fri%"es o% either side are coloured Biolet is the colour %earer
to the ce%tral fri%"e a%d red is farther a#ay as sho#% i%
+i"ure 224
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Ta1le 22 sho#s the ra%"e of #a$ele%"th for colours of $isi1le
li"ht
&igure #.#&igure #.#
'able #.#'able #.#
(olour 1ange ofC n"
Biolet 4 45
.lue 45 52
Dree% 52 56
Yello# 56 6
>ra%"e 6 625
Red 625
Stiulatio% 22
Stiulatio% 23
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A dou1leslits patter% is $ie# o% a scree% & fro the slits If
the third order i%ia are 25 c apart- deteri%ea the ratio of #a$ele%"th a%d separatio% 1et#ee% the slits-
1 the dista%ce 1et#ee% the first order i%iu a%d fourth order
a8iu o% the scree%
)olution :)olution :
a
+ro the fi"ure-
E8aple & :
!m-2$.0m-00.1 ! === mxD
S&
S2
DD
d
33rdrd order i%iuorder i%iu
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)olution :)olution :
a .y usi%" the e=uatio% of separatio% 1et#ee% ce%tral 1ri"ht a%d
thorder dar fri%"es- thus
1 The separatio% 1et#ee% ce%tral a8 a%d the &storder i% is
!m-2$.0m-00.1 ! === mxD
d
Dmxm
+=
2
1
d
Dx
+=
2
1!!
( )
d
00.1
2
1!12$.0
+=
210$.! =d
dDx += 2
111
d
Dx
$.11=
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)olution :)olution :
1 a%d the separatio% 1et#ee% ce%tral a8 a%d the 4thorder a8
(m? 4) is "i$e% 1y
Therefore the dista%ce 1et#ee% the first order i%iu a%d
fourth order a8iu o% the scree% is
d
Dmym
=
d
Dy
##=
1# xyd =
=
d
D
d
Dd
$.1#
dDd $.2=
( )( )00.110$.!$.2 2=dm10/!. 2=d
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a Ho# #ould you e8pect the i%terfere%ce patter% of a dou1leslit
e8perie%t to cha%"e if #hite li"ht is used i%stead ofo%ochroatic li"htF
1 /escri1e the cha%"es that #ould 1e o1ser$ed i% a dou1leslit
i%terfere%ce patter% if the e%tire e8perie%t #ere su1er"ed i%
#ater
-+hysics, *-+hysics, *rdrdedition, D. ). %al9er, F4, p.74*0edition, D. ). %al9er, F4, p.74*0
)olution :)olution :
a The locatio%s of 1ri"ht a%d dar fri%"es depends on thedepends on the
wavelength of lightwavelength of light Therefore- if #hite li"ht is used i% a
dou1leslit e8perie%t- each bright fringe will show so"ebright fringe will show so"e
separation into coloursseparation into colours- "i$i%" a Grainbow effectGrainbow effect
E8aple 2 :
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48
)olution :)olution :
1 Su1er"i%" the dou1leslit e8perie%t i% #ater would reducewould reduce
the wavelength of the light fro"the wavelength of the light fro" toto /n/n- #here n? &33is
the refractio% i%de8 of #ater Therefore- the 1ri"ht or dar
fringe separation would be reducedfringe separation would be reduced- accordi%" to the
e=uatio% 1elo#:
It follo#s that the i%terfere%ce patter% fringes get closer to eachfringes get closer to each
otherother
d
Dy
=
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I% a You%"'s dou1leslit e8perie%t- #he% a o%ochroatic li"ht
of #a$ele%"th 6 % shi%es o% the dou1le slits- the fri%"e
separatio% of the i%terfere%ce patter% produced is 0he%
a%other o%ochroatic li"ht source is used- the fri%"e separatio%
is 5 Calculate the #a$ele%"th of the seco%d li"ht
)olution :)olution :
&stcase:
.y applyi%" the fri%"e separatio% e=uatio%- thus
E8aple 3 :
m-100.m-1000 !1/
1
== y
m100.$!
2
=y
S&
S2
DD
d Ce%tral of i%terfere%ce patter%Ce%tral of i%terfere%ce patter%
1y1y
d
Dy 11
= ( )
d
D/! 1000100.
= -$0-$0
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)olution :)olution :
2%d
case:
(2) (&):
m-100.m-10$00 !1/
1
== ym100.$ !2
=y
d
Dy 22
=
d
D2!100.$
= -#0-#0
/
2
!
!
1000100.
100.$
=
m10#2/ /2= nm2/#>R
S&
S2
DD
d Ce%tral of i%terfere%ce patter%Ce%tral of i%terfere%ce patter%
2y2y
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+i"ure 225 sho#s t#o cohere%t sources (S&a%d S2) of li"ht i%phase The separatio% of S&a%d S2is &2 a%d the scree% is
25 fro the sources
a The fre=ue%cy of the li"ht is 5 &&4 H
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52
)olution :)olution :
a i Di$e%
.y applyi%" the #a$e speed e=uatio%- thus
ii .y usi%" the e=uatio% of fri%"e separatio%- thus
m$.2m-102.1 ! == Dd310.$ 1#=f
fc =( )1# 10.$1000.! =
m10$20 /= nm20$>R
d
Dy =
m100.1 !=y
( )( )!/
102.1$.210$20
=y
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)olution :)olution :
1 Di$e%
The #a$ele%"th of li"ht i% #ater is "i$e% 1y
Therefore the dar fri%"es separatio% is
m$.2m-102.1 ! == Dd
w
=n
w
/10$20!!.1
=
m10/1.! w=
d
Dx =
m101$. #=x
( )( )!
102.1$.210/1.!
=x
!!.1=n
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E8ercise 2& :& You%"'s dou1leslit e8perie%t is perfored #ith 5G9% li"ht
a%d a dista%ce of 2 1et#ee% the slits a%d the scree%The te%th i%terfere%ce i%iu is o1ser$ed 26 fro
the ce%tral a8iu /eteri%e the spaci%" of the slits
-+hysics for scientists and engineers,4-+hysics for scientists and engineers,4 ththedition,)erwayFDewett,edition,)erwayFDewett,
*5.3, p.$$760*5.3, p.$$760
A). :A). : $.3 ""$.3 ""2 A You%"'s i%terfere%ce e8perie%t is perfored #ith
o%ochroatic li"ht The separatio% 1et#ee% the slits is
5 - a%d the i%terfere%ce patter% o% a scree% 33
a#ay sho#s the first side a8iu 34 fro the ce%tre
of the patter% 0hat is the #a$ele%"thF
-+hysics for scientists and engineers,4-+hysics for scientists and engineers,4 ththedition,)erwayFDewett,edition,)erwayFDewett,
*5.#, p.$$750*5.#, p.$$750
A). :A). : 3$3 n"3$3 n"
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E8ercise 2& :3 A cohere%t li"ht that co%tai%s t#o #a$ele%"th- 66 % (red)
a%d 4 % (1lue) passes throu"h t#o %arro# slits separated1y 3 a%d the i%terfere%ce patter% is o1ser$ed o% a
scree% 5 fro the slits /eteri%e the dista%ce
1et#ee% the first order 1ri"ht fri%"es for each #a$ele%"th
->niversity physics,$$->niversity physics,$$ththedition, @oungF&reed"an, *3.$,edition, @oungF&reed"an, *3.$,
p.$*4#0p.$*4#0
A). :A). : *.$5 ""*.$5 ""
4 A o%ochroatic li"ht of #a$ele%"th 56 % passes throu"h
a You%"'s dou1leslit syste of u%%o#% slit separatio% After
that- the slits is illui%ated 1y a o%ochroatic li"ht of
u%%o#% #a$ele%"th It #as o1ser$ed that the 4thorder
i%iu of the %o#% #a$ele%"th li"ht o$erlapped #ith the
5thorder a8iu of the u%%o#% #a$ele%"th li"ht o% a
scree% Calculate the #a$ele%"th of the u%%o#% #a$ele%"th
li"ht
A). :A). : 38 n"38 n"
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56
At the end of this chapter, students should be able to:At the end of this chapter, students should be able to: ExplainExplainwith the aid of a diagra" the interference of lightwith the aid of a diagra" the interference of light
in thin fil"s for nor"al incidence.in thin fil"s for nor"al incidence.
&or nonreflective coating:&or nonreflective coating:(onstructive interference : #(onstructive interference : #ntnt;; mm/estructive interference : #/estructive interference : #ntnt; -; -mm J 0 J 0
&or reflective coating:&or reflective coating:
(onstructive interference : #(onstructive interference : #ntnt; -; -
mm J 0 J 0
/estructive interference : #/estructive interference : #ntnt;; mmwherewhere mm; 8,
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57
I%terfere%ce due to reflected #a$es is o1ser$ed i% a%ye$eryday circusta%ces such as 1ri"ht colours reflected fro oilfil o% #ater a%d soap 1u11le
The reflected #a$es ca% cha%"e their phase i% t#o #ays:
The phase changes in proportion to the distance of thephase changes in proportion to the distance of the
waves travelwaves travel The phase cha%"es as a result of the reflectiona result of the reflectionprocess
itself
!ptical path!ptical pathis defi%ed as the product between a distancethe product between a distance
travelled by light and the refractive index of the "ediu"travelled by light and the refractive index of the "ediu"
>R
#. Interference of reflected light in
thin fil"s
nlL=#here
mediumin thelight4travelleddistance:l
*ath'*tical:Lmediuma'findexrefractive:n
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A li"ht #a$e tra$elli%" i% a "ediu" of lower refractive index -"ediu" of lower refractive index -nn1100
#he% reflected fro" a "ediu"s surface of higher refractivereflected fro" a "ediu"s surface of higher refractiveindex -index -nn
2200u%der"oes a radian phase changeradian phase changeas sho#% i%
+i"ure 226a
#..$ +hase changes due to reflection
&igure #.#4a&igure #.#4a
1n 2n
i%cide%t #a$e
1n 2n
reflected #a$e tra%sitted #a$e
i%cide%t pulse
reflected pulse
tra%sitted pulse
radian phase changeradian phase change
&igure #.#4b: string analogous&igure #.#4b: string analogous
ote:ote:
rad=
2
=L
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59
A li"ht #a$e tra$elli%" i% a "ediu" of higher refractive index"ediu" of higher refractive index
--nn2200#he% reflected fro" a "ediu"s surface of lowerreflected fro" a "ediu"s surface of lower
refractive index -refractive index -nn1100u%der"oes no phase changeno phase changeas sho#% i%+i"ure 22a
&igure #.#5a&igure #.#5a
1n2n
i%cide%t #a$e
1n2n
reflected #a$e tra%sitted #a$e
i%cide%t pulse
no phase changeno phase change
&igure #.#5b: string analogous&igure #.#5b: string analogous
ote:ote:
0=0=L
reflected pulse
tra%sitted pulse
Stiulatio% 24
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+i"ure 22G sho#s the li"ht #a$es reflected fro the upper a%dlo#er surfaces of a thi% fil (refracti$e i%de8- n) o% a de%serediu
#..# Interference fro" thin fil"s on a denser
"ediu"
0.11=n
$.1=n
$.!2=n
A
.
E
C
/
+
##$$
'fthicness:tfilmthin
&igure #.#6&igure #.#6
rad phaserad phasechangechange
rad phaserad phasechangechange
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0he% a% i%cide%t ray falls o% a thi% fil surface alost %oral to thesurface (poi%t .)
di$isio% of aplitude occurs-
part of ray are reflected (ray &ray A.E)-
part of ray are refracted a%d reflected (ray 2ray A.C/+)-
poi%t / $ery close to . (.C a%d C/ 1ecoe strai"ht li%e)
At .-
the reflected ray (ray &) u%der"oes radian phase changeradian phase change 1ecause the ray & reflected fro a surface of higher refractivesurface of higher refractive
index -denser "ediu"0index -denser "ediu"0
At C-
the reflected ray (ray 2) u%der"oes radian phase changeradian phase change
Therefore 1oth rays & a%d 2 are t#o cohere%t sources i% phase
1ecause the phase differe%ce- is
a%d eet at a poi%t produces i%terfere%ce patter%0==
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The optical path differe%ce 1et#ee% rays & a%d 2 is "i$e% 1y
(onstructive interference:(onstructive interference:
/estructive interference:/estructive interference:
E8aple of thi% fil o% a de%ser ediu: ;o%reflecti$e (a%tireflecti$e) coati%"
>il fil o% #ater a%d etc
5675689=L
8968+=L ntntL += ntL 2=
mnt=2
,...2,1,0 =m
#here
+=
2
12 mnt
,...2,1,0 =m#here
Picture 23 Picture 24
in vacuumlight'fwavelength:
Picture 22
PHYSICS CHAPTER 2
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0.1air=n
!!.1=n
0.1air=n
'fthicness:tfilmthin
+i"ure 229 sho#s the li"ht #a$es reflected fro the upper a%dlo#er surfaces of a thi% fil (refracti$e i%de8- n) i% a less de%seediu
#..* Interference fro" thin fil"s on a less dense
"ediu"
A
.
E
C
/
+
##$$
&igure #.#7&igure #.#7
rad phaserad phasechangechange
nonophasephase
changechange
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0he% a% i%cide%t ray falls o% a thi% fil surface alost %oralto the surface (poi%t .)
di$isio% of aplitude occurs- part of ray are reflected (ray &ray A.E)- part of ray are refracted a%d reflected (ray 2ray A.C/+)- poi%t / $ery close to . (.C a%d C/ 1ecoe strai"ht li%e)
At .-
the reflected ray (ray &) u%der"oes radian phaseradian phase
changechange
1ecause the ray & reflected fro a surface of highersurface of higher
refractive index -denser "ediu"0refractive index -denser "ediu"0
At C-
the reflected ray (ray 2) u%der"oes no phase changeno phase change
Therefore 1oth rays & a%d 2 are t#o cohere%t sources a%tiphase
1ecause the phase differe%ce- is
a%d eet at a poi%t produces i%terfere%ce patter%
rad0 ==
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The optical path differe%ce 1et#ee% rays & a%d 2 is "i$e% 1y
(onstructive interference:(onstructive interference:
/estructive interference:/estructive interference:
E8aple of a thi% fil o% a less de%se ediu:
Soap 1u11les
Reflecti$e coati%" a%d etc
5675689=L
28968
++=L
2
++= ntntL
22
+= ntL
mnt=2,...2,1,0 =m
#here
+=
212 mnt ,...2,1,0 =m
#here
mnt =+2
2
+=+ 2
1
22 mnt
Picture 25 Picture 26
PHYSICS CHAPTER 2
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66
A %o%reflecti$e coati%" of a"%esiu fluoride of refracti$e i%de8
&3G co$ers the caera le%s of refracti$e i%de8 &52 The coati%"
pre$e%ts reflectio% of yello#"ree% li"ht of #a$ele%"th i% $acuu
565 % /eteri%e the i%iu %o%
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67
)olution :)olution :
.y usi%" the co%ditio% of destructi$e i%terfere%ce for %o%reflecti$e
coati%"- thus
+or i%iu thic%ess of "+2-
+=
2
12 mnt
+=
2102 minnt
( ) ( )/min 10$$2
1!.12
=t
m1002.1 min=t
m10$$ /=
0=m
>R
nm102
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68
0hite li"ht is i%cide%t o% a soap fil of refracti$e i%de8 &3 i% air
The reflected li"ht loos 1luish 1ecause the red li"ht of #a$ele%"th
6 % is a1se%t i% the reflectio%
a State the co%ditio% for destructi$e i%terfere%ce
1 0hat is the i%iu thic%ess of the soap filF
-+hysics,*-+hysics,*rdrd edition, D.).%al9er, #4, p.7440edition, D.).%al9er, #4, p.7440
)olution :)olution :
E8aple 6 :
0.11=n
!0.1=n
0.11=n
##$$
mint
rad phaserad phasechangechange
nonophasephase
changechange
# coherent sources# coherent sources
antiphaseantiphase
m100/
=
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69
)olution :)olution :
a The co%ditio% of destructi$e i%terfere%ce is "i$e% 1y
1 +or i%iu thic%ess of soap fil-mnt=2
( )12 min=nt
( ) ( )/
min 100!0.12
=tm10$.2
min
=t
m100 /=
1=m
>R
nm$2
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70
At the end of this chapter, students should be able to:At the end of this chapter, students should be able to: ExplainExplainwith the aid of a diagra" the interference in airwith the aid of a diagra" the interference in air
wedge.wedge. ExplainExplainwith the aid of a diagra" the for"ation ofwith the aid of a diagra" the for"ation of
ewtons rings.ewtons rings. >se>se
##tt; -; -mm++ J0J0 for bright fringes -"axi"a0for bright fringes -"axi"a0 ##tt ;; mm for dar9 fringes -"ini"a0,for dar9 fringes -"ini"a0,
wherewhere mm== 8, $, #, *, =8, $, #, *, =
earning !utco"e:
25 I%terfere%ce of reflected li"ht i% air #ed"e a%d
;e#to%'s ri%"s (& hour)
###
()p
h)
atri(
ed
u)
y*ph
ysic
s
###
()p
h)
atri(
ed
u)
y*ph
ysic
s
PHYSICS CHAPTER 2#.3 Interference of reflected light in air
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71
#.3.$ Air wedge
#.3 Interference of reflected light in air
wedge and ewtons ring
&igure #.*8: Apparatus setup&igure #.*8: Apparatus setup
travelling
"icroscope
glass plate
glass slide
thin foil
"onochro"atic
light source
KK @@
air
T
L
!!22
++ t
l
))
x
&st dar
fri%"e
m= & & 2 2 3 3 4 4 5
&igure #.*#&igure #.*#
&igure #.*$&igure #.*$
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Ray S falls alost %oral to the surface of a "lass slide
At poi%t >- Ray S is
partially reflected (ray >!) partially refracted (>.) a%d the% reflected at . (ray P7)
The t#o refracted rays (>! a%d P7) are cohere%t si%ce 1othha$e ori"i%ated fro the sae source >
>! a%d P7 produces i%terfere%ce patter% if it is 1rou"ht
to"ether as sho#% i% +i"ure 232 Si%ce the i%cide%ce is %early %oral (poi%t P $ery close to >)-
the path differe%ce 1et#ee% the rays at > (ray >! a%d ray>.P7) is "i$e% 1y-
path differe%ce- L? >. .P ? nt+ nt ? 2nt
#here nis refracti$e i%de8 of air ? & At J-t? a%d thus the path differe%ce ? a%d a 1ri"ht fri%"e
is e8pected- 1ut a dar fri%"e is o1ser$ed at J This is due to
the phase cha%"e of radia% for ray P7 (reflected o% ade%ser ediu at .)
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He%ce- ray P7 is i% a%tiphase #ith ray >! a%d #he% 1rou"htto"ether (1y the reti%a or le%s) to i%terfere- a dar fri%"e iso1tai%ed
(onstructive interference -bright fringe0:(onstructive interference -bright fringe0:
/estructive interference -dar9 fringe0:/estructive interference -dar9 fringe0:
2
12 +=mt
A phase cha%"e of radianradianis e=ui$ale%t to a path
differe%ce of
+= 21
2 mt
,...2,1,0=m#here
mt=2,...2,1,0=m#hereote:ote:
-#.30-#.30
-#.0-#.0
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+ro e=uatio% (24)-
0he%
+ro e=uatio% (25)-
0he%
#1
0-m == t
,.......,,film,air
'fthicnesswhen thef'rmedarefringesrighti.e.
#$
#!
#1 =t
#!1-m == t
#$2-m == t
$$stst
brightbrightfri%"e (Beroth orderBeroth ordera8iu)
##ndnd brightbrightfri%"e ($$stst orderordera8iu)
**rdrd brightbrightfri%"e (##ndnd orderordera8iu)
00-m == t
,.......,,,0film,air
'fthicnesswhen thef'rmedarefringesdari.e.
2
!
2
1
=t
211-m == t== 2-m t
$$stst dar9dar9fri%"e (Beroth orderBeroth orderi%iu)
##ndnd dar9dar9fri%"e ($$stst orderorderi%iu)
**rdrd dar9dar9fri%"e (##ndnd orderorderi%iu)
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Euation for separation between the $Euation for separation between the $ststdar9 fringe and thedar9 fringe and the
""ththorder dar9 fringe,order dar9 fringe,ll
+ro +i"ure 23&-
Rearra%"e e= (25):
l
t
L
T==tan
tan
tl=
2
m
t=su1stitute i%to e= (26)
-#.40-#.40
tan2
ml=
,...2,1,0'rder: =m#here
in vacuumlight'fwavelength:
slideglass'fninclinati''fangle:;
-#.50-#.50
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Euation for separation between the $Euation for separation between the $ststdar9 fringe and thedar9 fringe and the
""ththorder bright fringe,order bright fringe,ll
Rearra%"e e= (24):
Euation for separation between adLacent dar9 fringes orEuation for separation between adLacent dar9 fringes or
bright fringes,bright fringes, xx Put m? & i%to e= (2)-
( )2
21 += mt su1stitute i%to e= (26)
( )
tan2
21+
= m
l
,...2,1,0'rder: =m#here
-#.60-#.60
tan2=x -#.70-#.70
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#.3.# ewtons ring
&igure #.**:&igure #.**:
Apparatus setupApparatus setup
travelling
"icroscope
glass plate
"onochro"atic
light source
planoconvex
lens
glass bloc9
))
t22
!! ++
t
d
&igure #.*3:&igure #.*3:
ewtons ringewtons ring
&igure #.*&igure #.*
KK
@@
((
AA
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Ray S falls alost %oral to the surface of a pla%oco%$e8
At poi%t >- Ray S is
partially reflected (ray >!) partially refracted (>.) a%d the% reflected at . (ray P7)
The t#o refracted rays (>! a%d P7) are cohere%t si%ce 1othha$e ori"i%ated fro the sae source >
>! a%d P7 produces i%terfere%ce patter% if it is 1rou"ht
to"ether as sho#% i% +i"ure 235 The patter% is a series of circular i%terfere%ce fri%"es called
;e#to%'s ri%" This 1ecause of a cur$ed piece of "lass #ith aspherical cross sectio%
Si%ce the i%cide%ce is %early %oral (poi%t P $ery close to >)-
the path differe%ce 1et#ee% the rays at > (ray >! a%d ray>.P7) is "i$e% 1y-
path differe%ce- L? >. .P ? nt+ nt ? 2nt
#here nis refracti$e i%de8 of air ? &
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At J-t? a%d thus the path differe%ce ? a%d a 1ri"ht spot ise8pected- 1ut a dar spot is o1ser$ed at J This is due to the
phase cha%"e of radia% for ray P7 (reflected o% a de%serediu at .)
He%ce- ray P7 is i% a%tiphase #ith ray >! a%d #he% 1rou"htto"ether (1y the reti%a or le%s) to i%terfere- a dar spot iso1tai%ed
(onstructive interference -bright ring0:(onstructive interference -bright ring0:
/estructive interference -dar9 ring0:/estructive interference -dar9 ring0:
212 +=mt
+=2
12 mt
,...2,1,0=m#here
mt=2
,...2,1,0=m#here
-#.70-#.70
-#.60-#.60
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1elationship between dia"eter of ring,1elationship between dia"eter of ring, ddand thic9ness ofand thic9ness of
air gap,air gap, tt
+ro +i"ure 234-
t
2d
@@
((
AA
.y usi%" the Phyto"orea% theore-
thus the dista%ce AY is
Si%ce tis $ery thi% thus t2
222
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Euation for dia"eter of dar9 ringEuation for dia"eter of dar9 ring
Rearra%"e e= (29):
0he%
2
m
t=su1stitute i%to e= (2&)
md #2 =
,...2,1,0'rder: =m#here
-#.$$0-#.$$0
=
22
#
2 m
d
0-0 == tm (entral dar9 spot(entral dar9 spot
21-1 == tm $$stst dar ri%" ($$stst orderorder i%iu)== tm -2 ##ndnd dar ri%" (##ndnd orderorder i%iu)
2!-! == tm **rdrd dar ri%" (**rdrd orderorder i%iu)
(zeroth orderzeroth orderi%iu)- d?
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Euation for dia"eter of bright ringEuation for dia"eter of bright ring
Rearra%"e e= (29):
0he%
( )
2
21 +
=
m
tsu1stitute i%to e=
(2&)
( )212
# += md,...2,1,0'rder: =m#here
-#.$#0-#.$#0
( )
+=
22
#
212 m
d
#1-0 == tm $$stst bright ringbright ring (zeroth orderzeroth order
a8iu)
#!-1 == tm ##ndnd 1ri"ht ri%" ($$stst orderorder a8iu)
#$-2 == tm **rdrd 1ri"ht ri%" (##ndnd orderorder a8iu)
#-! == tm thth 1ri"ht ri%" (**rdrd orderorder a8iu)
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+ro +i"ure 235-
The ri%"s 1ecoe "ore closely spaced"ore closely spacedas o%e o$es
farther fro the ce%tre of the ;e#to%'s ri%" The reaso% is that the convex surface of the lens "ovesconvex surface of the lens "oves
away fro" the lower glass bloc9 at a progressivelyaway fro" the lower glass bloc9 at a progressively
fasterfasterrate therefore the thic9ness of air fil" increasesthic9ness of air fil" increases
rapidlyrapidly
;e#to%'s ri%" ca% 1e used to test the accuracy with which atest the accuracy with which a
lens has been groundlens has been ground
'he rings are not circular if the surface is not spherical'he rings are not circular if the surface is not spherical
-or the glass bloc9 is not flat0-or the glass bloc9 is not flat0
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A% air #ed"e is fored 1y placi%" a hua% hair 1et#ee% t#o "lass
slides of le%"th 44 o% o%e e%d- a%d allo#i%" the to touch o%
the other e%d 0he% this #ed"e is illui%ated 1y a red li"ht of#a$ele%"th & %- it is o1ser$ed to ha$e 265 1ri"ht fri%"es
/eteri%e
a the diaeter of hair-
1 the a%"le of air #ed"e-
c the thic%ess of the air fil for 99thdar fri%"e to 1e o1ser$ed-
d the separatio% 1et#ee% t#o co%secuti$e 1ri"ht fri%"es
)olution :)olution :
E8aple :
m10##m-101 !/ == L
d
L #43#43thth bright fringebright fringe
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)olution :)olution :
a Assui%" the diaeter of the hair- d? the thic%ess of air fil- t
at 265th
1ri"ht fri%"e Therefore the diaeter of the hair is "i$e% 1y
1 The a%"le of air #ed"e is
+=
2
12 mt
m1002.1 #=d
a%d
m10##m-101 !/ == L
2#=m
( )/101
212#2
+=d
L
d=tan!
#
10##
1002.1tan
=
1!.0=
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a E8plai% #hy the ce%tral spot i% ;e#to%'s ri%" is dar
1 I% a ;e#to%'s ri%" e8perie%t- the radius of the =th1ri"ht ri%"
is 32 c a%d the radius of the (=&9)thdar ri%" is 6 c
/eteri%e the radius of cur$ature of the pla%oco%$e8 used i%
the e8perie%t if the #a$ele%"th of li"ht used is 5G9 %
)olution :)olution :
a
E8aple G :
A ray of li"ht reflected fro the lo#er surface of the co%$e8
surface has %o phase cha%"e
ea%#hile- a ray of li"ht reflected fro the top surface of
"lass 1loc u%der"oes a radia% phase cha%"e Thus thet#o reflected rays are t#o cohere%t sources i% a%tiphase
At the ce%tre of the i%terfere%ce patter%- the thic%ess of the
air fil is
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)olution :)olution :
1 +or =th
1ri"ht ri%"-
+or (=&9)thdar ri%"-
m10$/ /=( ) m10.0m-10!2.0
2
1/=
2
=
+
== !!
1="m( )212 # += md a%d =2!d=
( ) ( )[ ]212
= 1=#2 += !
-$0-$0
1/+= "m
md #2 = a%d ( )1/=2 += !d
( )( ) ( )1/=#22
1/= +=+ !-#0-#0
( )( ) ( )1/=#22
1/= +=+ !
( ) ( )$.0=#22
= = !
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)olution :)olution :
1 (2) (&) :
.y su1stituti%" = ? 62 i%to e= (&) thus
m10$/ /=( ) m10.0m-10!2.0
2
1/=
2
=
+
== !!
( )
$.0=
1/=
2
=
1/=
+=
+!
!
$.0=1/=
10!2.010.0
2
2
2
+=
2.="
( )( ) ( ) ( )/22 10$/$.02.#10!2.02 = m01.!=
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E8ercise 22 :& A thi% fil of "asoli%e floats o% a puddle of #ater Su%li"ht falls
alost perpe%dicularly o% the fil a%d reflects i%to your eyes
Althou"h the su%li"ht is #hite- si%ce it co%tai%s all colours- thefil has a yello# hue- 1ecause destructi$e i%terfere%ce hasoccurred elii%ati%" the colour of 1lue ( ?469 %) fro thereflected li"ht If the refracti$e i%dices for "asoli%e a%d #aterare &4 a%d &33 respecti$ely- Calculate the i%iu
thic%ess of the filA). :A). : $46 n"$46 n"
2 0hite li"ht is i%cide%t %orally o% a thi% soap fil (% ?&33)suspe%ded i% air
a 0hat are the t#o i%iu thic%ess that #ill co%structi$ely
reflect yello# li"ht of #a$ele%"th 59 %F1 0hat are the t#o i%iu thic%ess that #ill destructi$ely
reflect yello# li"ht of #a$ele%"th 59 %F
-+hysics,*-+hysics,*rdrd edition, D.).%al9er, *, p.7440edition, D.).%al9er, *, p.7440
A). :A). : $$8 n", **8 n" M ##8 n", 8 n" M$$8 n", **8 n" M ##8 n", 8 n" M
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3 T#o pla%e "lass plates #hich are i% co%tact at o%e ed"e areseparated 1y a piece of etal foil &25 c fro that ed"eI%terfere%ce fri%"es parallel to the li%e of co%tact are o1ser$ed
i% reflected li"ht of #a$ele%"th 546 % a%d are fou%d to 1e &5 apart /eteri%e the thic%ess of the foil
A). :A). : #.#5#.#5 $8$833""4 ;e#to%'s ri%"s are fored 1y reflectio% 1et#ee% a% 1ico%$e8
le%s of focal le%"th & c ade of "lass of refracti$e i%de8&5 a%d i% co%tact #ith a "lass 1loc of refracti$e i%de8 &6
Calculate the diaeter a%d thic%ess of air fil for fifth 1ri"htri%" usi%" li"ht of #a$ele%"th 6
Di$e% & a%"stro () ? &&9
A). :A). : *.#6 ""M $.*3*.#6 ""M $.*3 ""5 ;e#to%'s ri%"s are fored #ith li"ht of #a$ele%"th 5G9 %
1et#ee% the pla%oco%$e8 le%s of radius of cur$ature & ca%d a "lass 1loc- i% perfect co%tact
a /eteri%e the radius of the 2thdar ri%" fro the ce%tre
1 Ho# #ill this ri%" o$e a%d #hat #ill its radius 1ecoe ifthe le%s a%d the 1loc are slo#ly separated to a dista%ceapart 5 &4cF
A). :A). : *.* ""M inwards, $.#4 c"*.* ""M inwards, $.#4 c"
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At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
ExplainExplainwith the aid of a diagra" the diffraction of awith the aid of a diagra" the diffraction of a
single slit.single slit.
/erive and use/erive and usefor"ulafor"ula
for dar9 fringes -"ini"a0for dar9 fringes -"ini"a0
for bright fringes -"axi"a0,for bright fringes -"axi"a0,
wherewhere nn;
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#.4.$ /iffraction of light is defi%ed as the bending of light waves as they travel aroundthe bending of light waves as they travel around
obstacles or pass through an aperture or slit co"parable toobstacles or pass through an aperture or slit co"parable to
the wavelength of the light wavesthe wavelength of the light waves
+i"ures 236a- 2361 a%d 236c sho# the 1e%di%" of pla%e
#a$efro%t
#.4 /iffraction by a single slit
&igure #.*4a:&igure #.*4a:
obstacleobstacle
&igure #.*4b:&igure #.*4b:
slit,slit, aa NN
&igure #.*4c:&igure #.*4c:
slit,slit, aa
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+i"ure 23 sho#s a% apparatus setup of diffractio% 1y a si%"leslit
#.4.# /iffraction by a single silt
&igure #.*5&igure #.*5
intensityintensity
scree%si%"le slit
Ce%tral
a8iu
&st i%iu
2%d i%iu
3rdi%iu
&st a8iu
2%d a8iu
&st i%iu
2%d i%iu
3rdi%iu
&st a8iu
2%d a8iu
2
1
2
1
A%iatio% 2&
Picture 2
Picture 2G
S
ndiffracti''fangle:#here
PHYSICS CHAPTER 2
http://opt/scribd/conversion/tmp/scratch2492/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://opt/scribd/conversion/tmp/scratch2492/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://opt/scribd/conversion/tmp/scratch2492/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://opt/scribd/conversion/tmp/scratch2492/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://opt/scribd/conversion/tmp/scratch2492/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://opt/scribd/conversion/tmp/scratch2492/G:/P&P/Semester1/Latest/p11_01_01_01a.swfhttp://rectangular.jpg/http://circular.jpg/http://single_slit.rm/ -
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Explanation of single slit diffraction experi"entExplanation of single slit diffraction experi"ent
0a$efro%t fro li"ht source falls o% a %arro# slit S a%d
diffractio% occurs E$ery poi%t o% the #a$efro%t that falls o% S acts as sources of
seco%dary #a$elets a%d superposed each a%other to for a%
i%terfere%ce patter% o% the scree% as sho#% i% +i"ure 23
The central fringe is bright -"axi"u"0central fringe is bright -"axi"u"0a%d widenwidencopare to
other 1ri"ht fri%"es The ce%tral fri%"e has the highest intensityhighest intensitycopare to the
other 1ri"ht fri%"es
The intensity of bright fringes reduceintensity of bright fringes reduceas the distancedistance
increaseincreasefro the ce%tral 1ri"ht fri%"e
>ther rays #ith a%"le 2a%d
1#ill produce i%iu a%d
a8iu o% 1oth sides of the ce%tral a8iu
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/erivation of single slit diffraction euations/erivation of single slit diffraction euations
Euation for separation betweenEuation for separation between central "axi"u" -bright0central "axi"u" -bright0
andand nnthth"ini"u" -dar90 fringes"ini"u" -dar90 fringes
&igure #.*6&igure #.*6
slit width:##herescreenandslitsingleetweendistance:D
2%d st
rip&st strip
(entral(entral
"axi"u""axi"u"
++
D
yynn
1
1AA
2
##
2
#
1sin2
#
1sin2
#
((
22
screenscreen
EE
nnthth
"ini"u""ini"u"
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A si%"le slit is split i%to t#o e=ual parts- AC a%d C. A-C a%d. are %e# sources of seco%dary #a$elets (Huy"e%'spri%ciple)
0he% the #a$elets fro A- C a%d . superpose- i%terfere%ce#ill occur at P
As A2 is very s"allA2 is very s"all- thus
AE is perpendicular to (+ and A+ ; E+AE is perpendicular to (+ and A+ ; E+-
the out"oi%" rays are considered parallelconsidered parallel-
a%d therefore the path differe%ce at P 1et#ee% ray APa%d CP is :
Co%sider t#o %arro# strips as sho#% i% +i"ure 23G- for the
two strips superposed destructivelytwo strips superposed destructivelythus 1oth strip of li"ht
ust i% antiphaseantiphaseto each a%other #hich is e=ui$ale%ce to a
path difference ofpath difference of If the $$stst"ini"u" -$"ini"u" -$ststorder "ini"u"0order "ini"u"0is at P- he%ce :
1sin2
87 #
L ==
2
sin
21
==
#L =1sin#
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+or the ##ndnd"ini"u""ini"u"a%d **rdrd"ini"u""ini"u"- A. is split i%to
eual parts, 4 eual partseual parts, 4 eual partsa%d so o% as sho#% i% +i"ures239 a%d 24
2sin#
a2
= 2sina 2=
2sin
a!
= !sina !=
2
2
##
#
!
!
#
#
2%d i%iu
(2%d orderi%iu)
3rdi%iu
(3rdorder
i%iu)
&igure #.*7&igure #.*7 &igure #.8&igure #.8
&st str
ip
2%d str
ip
3rd str
ip
4th str
ip
&st s
trip
2%d s
trip
5th st
rip3rd st
rip
4th st
rip
6th st
rip
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I% "e%eral- for "ini"a -dar9 fringes0"ini"a -dar9 fringes0
If the dista%ce of si%"le slit to the scree% isD- a%dD>>aD>>athe%:
Therefore the distance of ndistance of nthth"ini"u" fro" central"axi"u" is:
0he%
nn=sina!,..2,1,'rder: =n#here
D
ynnn == tansin
nD
y# n =
#
Dnyn
=
1=n $$stst i%iu fri%"e--$$stst orderorder i%iu)2=n ##ndnd i%iu fri%"e (##ndnd orderorder i%iu)!=n **rdrd i%iu fri%"e (**rdrd orderorder i%iu)
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2%d st
rip&st strip
3rd st
rip
Euation for separation betweenEuation for separation between central "axi"u" -bright0central "axi"u" -bright0
andand nnthth"axi"u" -bright0 fringes"axi"u" -bright0 fringes
&igure #.$&igure #.$
(entral(entral
"axi"u""axi"u"
11
D
yynn
1
1AA
!
##
!
#
((
22
screenscreen
EE
nnthth "axi"u""axi"u"
!
#1sin
!
#
1sin#
//
PHYSICS CHAPTER 2
C C
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A si%"le slit is split i%to three e=ual parts- AC-C/ a%d /.A-C-/ a%d . are %e# sources of seco%dary #a$elets(Huy"e%'s pri%ciple)
0he% the #a$elets fro A-C-/ a%d . superpose-i%terfere%ce #ill occur at R
As A. is $ery sall- thus
AE is perpe%dicular to CP a%d AP ? EP-
the out"oi%" rays are co%sidered parallel-
a%d therefore the path differe%ce at P 1et#ee% ray APa%d CP is :
Co%sider three %arro# strips as sho#% i% +i"ure 24&- thefirst t#o strips (pair) superposed destructi$ely at #hich the
path differe%ce is > a%d leave the third stripleave the third strip The **rdrdstrip produces the "axi"u" -bright0 fringe at 1.strip produces the "axi"u" -bright0 fringe at 1.
If the $$stst"axi"u" -$"axi"u" -$ststorder "axi"u"0order "axi"u"0is at R- he%ce :
1sin!
87 #
L ==
2
sin
!
1
==
#L
2
!sin 1
=#
PHYSICS CHAPTER 2
+ th # dd i d * dd i A. i lit i t 3
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+or the ##ndnd"axi"u""axi"u"a%d **rdrd"axi"u""axi"u"- A. is split i%to 33
eual parts, 5 eual partseual parts, 5 eual partsa%d so o% as sho#% i% +i"ures242 a%d 243
2sin$
a2
=
2
$sina 2
=
2sin
a
!
=
2
sina !
=
2
$
2
2
!
2%d a8iu
(2%d ordera8iu)
3rda8iu
(3rdorder
i%iu)
&igure #.#&igure #.# &igure #.*&igure #.*
2%d str
ip
3rd str
ip
4th str
ip
5th str
ip
&st str
ip
$#
#
#
#
&st strip
2%d s
trip
5th st
rip3rd st
rip
4th st
rip
6th st
rip
Eth st
rip
PHYSICS CHAPTER 2
I l f i -b i h f i 0
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103
( )
#
Dnyn
21+
=
I% "e%eral- for "axi"a -bright fringes0"axi"a -bright fringes0
If the dista%ce of si%"le slit to the scree% isD- a%dD>>aD>>athe%:
Therefore the distance of ndistance of nthth"axi"u" fro" central"axi"u" is:
0he%
+= 21
sina nn !,..2,1, =n#here
D
ynnn == tansin
+=
2
1n
D
y# n
1=n $$stst a8iu fri%"e--$$stst orderorder a8iu)2=n ##ndnd a8iu fri%"e (##ndnd orderorder a8iu)!=n **rdrd a8iu fri%"e (**rdrd orderorder a8iu)
PHYSICS CHAPTER 2 E ti fE ti f t l i -b i ht0 f it l i -b i ht0 f i
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Euation forEuation for central "axi"u" -bright0 fringecentral "axi"u" -bright0 fringe
&igure #.&igure #.
1
1
(entral(entral
"axi"u""axi"u"
$$stst "ini"u""ini"u"
$$stst "ini"u""ini"u"
y1
y1
&igure #.3&igure #.3
AA((
22
//
EE
D
#
screenscreen
single slitsingle slit
PHYSICS CHAPTER 2 +i 2 45 h fi f H ' l t d th
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105
=
#
1w sin2
+i"ure 245 sho#s fi$e sources of Huy"e%'s #a$elets a%d the
screen is to be so far fro" the slit -screen is to be so far fro" the slit -D>>aD>>a) thus the raysraysfro" each source are nearly parallelfro" each source are nearly parallel
All the #a$elets fro each source tra$el the sa"e distancesa"e distance
to the point to the point (+i"ure 244) a%d arri$i%" there in phasein phase
Therefore- the constructive interference is occurred at theconstructive interference is occurred at the
central of the single slit diffraction patterncentral of the single slit diffraction pattern
The angular width of central "axi"u",angular width of central "axi"u", wwis "i$e% 1y
1w 2 = anglendiffracti'minimum1:st
1a%d
a
sin 11
=
PHYSICS CHAPTER 2
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106
=#
D$
2
The width of central "axi"u",width of central "axi"u", wwis "i$e% 1y
;ote:
To calculate the "axi"u" nu"ber of orders observed"axi"u" nu"ber of orders observed- tae
the diffraction angle,diffraction angle, ;;7878 +ro 1oth e=uatio%s for i%ia a%d a8ia- #e o1tai%
.y usi%" this t#o relatio%s- the cha%"es of si%"le slit diffractio%patter% ca% 1e e8plai%ed
12y$ = a%d andminimum1'fse*arati'n:st
1y
maximumcentral
a1
Dy
=
nsin a%d ny
PHYSICS CHAPTER 2
E8aple 9 :
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107
A sodiu li"ht of #a$ele%"th 5G % shi%es throu"h a slit a%d
produces a diffractio% patter% o% a scree% 6 a#ay The #idth
of the ce%tral a8iu fri%"e o% the scree% is 5 c /eteri%e
a the #idth of the slit-
1 the a%"ular #idth of the ce%tral a8iu fri%"e-
c the %u1er of i%iu that ca% 1e o1ser$ed o% the scree%
)olution :)olution :
a Si%ce
E8aple 9 :
m100.$m,0.0m-10$0
2/
=== $D(entral(entral
"axi"u""axi"u"
$$stst "ini"u""ini"u"
$$stst "ini"u""ini"u"
$#
12y$ = a%da
1Dy =
=#
D$
2
( )( )#
0.010$02100.$
/2
=
m10!/.1$
=#
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PHYSICS CHAPTER 2
E8aple & :
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109
a State the siilarities a%d differe%ces of dou1leslit i%terfere%ce
a%d si%"le slit diffractio% patter%s
1 Ho# a%y 1ri"ht fri%"es #ill 1e produced o% the scree% if a
"ree% li"ht of #a$ele%"th 553 % is i%cide%t o% a slit of #idth
G F
)olution :)olution :
a The siilarities are
E8aple & :
/ou1leslit i%terfere%ce patter% Si%"le slit diffractio% patter%
2oth patterns consist of alternating dar9 and bright2oth patterns consist of alternating dar9 and bright
fringes.fringes.
'he central for both patterns is bright fringe.'he central for both patterns is bright fringe.
PHYSICS CHAPTER 2
a The differe%ces are
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110
a The differe%ces are
1 Di$e%
.y applyi%" the e=uatio% for 1ri"ht (a8iu) fri%"e-
+or the a8iu %o of order for 1ri"ht fri%"e-
Therefore the %u1er of 1ri"ht that ca% 1e o1ser$ed is
-$*-$* #0$ ; #5 fringes#0$ ; #5 fringes
/ou1leslit i%terfere%ce patter% Si%"le slit diffractio% patter%
'he width of each fringe is'he width of each fringe isthe sa"e.the sa"e. 'he central fringe is wider'he central fringe is widerthan the other fringes.than the other fringes.
'he intensity of each bright'he intensity of each bright
fringe is constant.fringe is constant.'he intensity of bright'he intensity of bright
fringes reduce as a distancefringes reduce as a distance
increase fro" the centralincrease fro" the central
bright.bright.
m1000.m-10$$! / == #
+=2
1sin n#
/0=( ) ( ) ( )/max
10$$!$.0/0sin1000. += n
/.1!max=n 1!
(entral bright(entral bright
fringefringe
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PHYSICS CHAPTER 2
earning !utco"e:
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112
At the end of this chapter, students should be able to:At the end of this chapter, students should be able to:
ExplainExplainwith the aid of a diagra" the for"ation ofwith the aid of a diagra" the for"ation of
diffraction.diffraction.
ApplyApply
for"ula,for"ula,
wherewhere
/escribe/escribewith the aid of diagra" the for"ation ofwith the aid of diagra" the for"ation of
spectru" by using white light.spectru" by using white light.
earning !utco"e:
2 /iffractio% "rati%" (2 hours)
###
()
ph
)a
tri(
ed
u)
y*ph
ysics
###
()
ph
)a
tri(
ed
u)
y*ph
ysi
cs
nd n =sin%
d1
=
PHYSICS CHAPTER 2
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113
is defi%ed as a large nu"ber of eually spaced parallel slitsa large nu"ber of eually spaced parallel slits /iffractio% "rati%" ca% 1e ade 1y ruling very fine parallelruling very fine parallel
lines on glass or "etal by a very precise "achinelines on glass or "etal by a very precise "achine
The untouched spaces between the linesuntouched spaces between the linesser$e as the slitsslitsas
sho#% i% +i"ure 246
#.5 /iffraction grating
&igure #.4&igure #.4
li%es slit
d !i"ht passes throu"h the slit 1ecause it istra%spare%t
The spaces 1et#ee% the li%es are the slits-
for e8aple : if there are four li%es the% #e
ha$e 3 slits
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PHYSICS CHAPTER 2
# 5 $ Explanation of diffraction by using Huygens
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115
+i"ure 24 sho#s a% i%cide%t li"hts fall o% the tra%sissio%diffractio% "rati%"
#.5.$ Explanation of diffraction by using Huygen s
principle for diffraction grating
&igure #.5&igure #.5
((
//
first order #a$efro%t
&&
EEseco%d order #a$efro%t
third order #a$efro%t
AA
22
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116
Ksi%" Huy"e%s' pri%ciple- each a8iu is located 1y tai%"
the ta%"e%t of the #a$elets fro the slits
If the #a$elets fro each of the slits are dra#% a%d a ta%"e%t A2A2is dra#%- a pla%e #a$efro%t parallel to the diffractio% "rati%" is
o1tai%ed This represe%ts the
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117
+i"ure 24G illustrates li"ht tra$els to a dista%t $ie#i%" scree%fro fi$e slits of the "rati%"
g g
&igure #.6&igure #.6
ce%tral or
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118
The a8iu (1ri"ht) fri%"es are soeties called the pri%cipal
a8ia or pri%cipal fri%"es si%ce they are placed #here the li"ht
i%te%sity is a a8iu
Si%ce the scree% is far so that the rays %early parallel #hile the
li"ht tra$els to#ard the scree% as sho#% i% +i"ure 249
I% reachi%" the place o% the scree% #hile the &storder a8iu
is located- li"ht fro o%e slit tra$els a dista%ce of o%e
#a$ele%"th farther tha% li"ht fro ad,ace%t slit
Therefore the path differe%ce for a8iu fri%"e (co%structi$e
i%terfere%ce) is "i$e% 1y
0he%
nd n =sin
!,..2,1,,0'rder:
=n#here
anglendiffracti''f'rder: thnn
0=n (entral(entral a8iu fri%"e--88thth orderorder a8iu)1=n $$stst a8iu fri%"e ($$stst orderorder a8iu)
2=n ##ndnd
a8iu fri%"e (##ndnd
orderorder a8iu)
PHYSICS CHAPTER 2 The a8iu fri%"es produce 1y a "rati%" are uch %arro#er
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119
The a8iu fri%"es produce 1y a "rati%" are uch %arro#er
a%d sharper tha% those fro a dou1leslit as the i%te%sity "raph
i% +i"ures 25a a%d 251
0=n 1 212
0=n 1 212
&igure #.38a&igure #.38a
&igure #.38b&igure #.38b
PHYSICS CHAPTER 2 +i"ures 2 5& sho#s the diffractio% "rati%" patter%
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120
+i"ures 25& sho#s the diffractio% "rati%" patter%
&igure #.3$&igure #.3$
2
1
"rati%"
Parallel 1ea of
o%ochroatic li"ht
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121
If the #hite li"ht is falls o% the "rati%"- a rai%1o# colours #ould
1e o1ser$ed to either side of the ce%tral fri%"e o% the scree%
#hich is #hite as sho#% i% +i"ure 25& This 1ecause the whitewhite
light contains wavelengths between violet and redlight contains wavelengths between violet and red
Rai%1o# Rai%1o# Rai%1o#Rai%1o# #hite
0=n 1 212
0hite
li"ht
&igure #.3$&igure #.3$
PHYSICS CHAPTER 2 ;ote:
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122
;ote:
To calculate the "axi"u" nu"ber of orders for bright"axi"u" nu"ber of orders for bright
fringes observedfringes observed- tae the diffraction angle,diffraction angle, ;;7878Therefore
+ro the e=uatio% for a8ia- #e o1tai%
.y usi%" this t#o relatio%s- the cha%"es of diffractio% "rati%"patter% ca% 1e e8plai%ed
max/0sin nd =
dn =max
#herenmax : a8iu %u1er of orders that ca% 1e
o1ser$ed
nsin a%dd
n
1sin
PHYSICS CHAPTER 2
E8aple && :
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123
A o%ochroatic li"ht of u%%o#% #a$ele%"th falls %orally o% a
diffractio% "rati%" The diffractio% "rati%" has 3 li%es per c
If the a%"ular separatio% 1et#ee% the first order a8ia is 35Calculate
a the #a$ele%"th of the li"ht-
1 the a%"ular separatio% 1et#ee% the seco%dorder a%d third
order a8ia)olution :)olution :
p
1-!$2-cm!000 11 === n%
!$
$$stst order "axorder "ax
$$stst order "axorder "ax
1
PHYSICS CHAPTER 2
)olution :)olution : 1-!$2-cm!000 11 === n%
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124
)olution :)olution :
a The diffractio% a%"le for &storder a8iu is
A%d the slit separatio%- dis "i$e% 1y
Therefore the #a$ele%"th of the li"ht is
%d
1=
$.11=
cm10!!.! #=d
1cm!000
1=d
1-!$2-cm!000 1 n%
>R m10!!.!
!$21
=
nd n=sin( ) =
1
sin10!!.!
( ) = $.1sin10!!.!
m1000.1 =
PHYSICS CHAPTER 2
)olution :)olution : 3rd d
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125
)olution :)olution :
1
.y usi%" the e=uatio% of diffractio% "rati%" for a8ia-
2 thorder
a8iu0=n
2%d order
a8iu
2%d order
a8iu
2=n
2=n
3rdorder
a8iu
3rdorder
a8iu!=n
!=n
3
!2
nd n=sin
PHYSICS CHAPTER 2
)olution :)olution :
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126
)olution :)olution :
1 +or 2%dorder a8iu-
+or 3rdorder a8iu-
Therefore the a%"ular separatio%-
2sin
2=d
2=n
( ) ( )2 1000.12sin10!!.! =
/.!2=
!sin !=d!=n
( ) ( )! 1000.1!sin10!!.! =
!.#!=
2!2! =#.22!=
/.!!.#2! =
PHYSICS CHAPTER 2
E8aple &2 :
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127
The seco%dorder a8iu produced 1y a diffractio% "rati%" #ith
56 li%es per ce%tieter is at a% a%"le of 3&
a 0hat is the #a$ele%"th of the li"ht that illui%ates the "rati%"F
1 /eteri%e the %u1er of a8iu ca% 1e o1ser$ed o% a
scree%
c State a%d "i$i%" reaso%- #hat you #ould e8pect to o1ser$e if a
"rati%" #ith a lar"er %u1er of li%es per ce%tieter is used)olution :)olution :
a.y applyi%" the e=uatio% of diffractio% "rati%" for 2%dorder
a8iu- thus
p
2-!.1-m10$ 21! === n%
2sin 2=d %2sin 2=
a%d
%
d1
=
( )!10$21.!sin =
m10!.# =
PHYSICS CHAPTER 2
)olution :)olution :
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128
)olution :1 .y applyi%" the e=uatio% of "rati%" for a8iu-
+or the a8iu %o of order for a8iu fri%"e-
Therefore the %u1er of a8iu ca% 1e o1ser$ed is
-*4-*4 #0$ ; 5* fringes#0$ ; 5* fringesc The fringes beco"e farther to each anotherfringes beco"e farther to each another
Reaso% : si%ce
a larger nu"ber of lines per c" results in a largerlarger nu"ber of lines per c" results in a larger
diffraction angle diffraction anglethus the dista%ce 1et#ee% t#o
co%secuti$e a8iu fri%"es #ill i%crease
nd n=sin a%d %d1
= n%n=sin/0=n
( )( )!max 10!.#10$/0sin =n
/.!max=n !
d
1
sin a%d %d1
= %sin
PHYSICS CHAPTER 2E8ercise 24 :
f f f ff
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129
& The firstorder a8iu li%e of 5G9 % li"ht falli%" o% a diffractio"rati%" is o1ser$ed at a% a%"le of &55 /eteri%e
a the slit separatio% o% the "rati%"1 the a%"le of diffractio% for thirdorder a8iu li%e
-+hysics for scientist F engineers ,*-+hysics for scientist F engineers ,*rdrd edition, Oiancoli, *#, p.7$0edition, Oiancoli, *#, p.7$0
A). :A). : #.#8#.#8 "M 3*."M 3*.2 A diffractio% "rati%" has 6 li%es per c Calculate the a%"ular
separatio% 1et#ee% #a$ele%"ths 5G96 % a%d 546& %respecti$ely after tra%sissio% throu"h it at %oral i%cide%ce- i%the firstorder spectru (a8iu li%e)
A). :A). : $.48$.483 0he% 1lue li"ht of #a$ele%"th 465 % illui%ates a diffractio%
"rati%"- it produces a &st order a8iu 1ut %o 2%d ordera8iu
a E8plai% the a1se%ce of 2%d order a8iu
1 0hat is the a8iu spaci%" 1et#ee% li%es o% this "rati%"F
-+hysics,*-+hysics,*rdrd edition, D.).%al9er, 43, p.7460edition, D.).%al9er, 43, p.7460
A). :A). : 7*8 n"7*8 n"
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Electrostatics