matriculation physics physical optics

8/12/2019 Matriculation Physics Physical Optics

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1

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

2

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

4

'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

5

)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

6

+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

7

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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PHYSICS CHAPTER 2

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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


#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


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


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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PHYSICS CHAPTER 2

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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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/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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PHYSICS CHAPTER 2

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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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PHYSICS CHAPTER 2

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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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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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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% phase

S1

S2

x1

x2

(minimum)


+ =


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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)


+ =


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PHYSICS CHAPTER 2

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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)


+ =


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PHYSICS CHAPTER 2

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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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PHYSICS CHAPTER 2

27

+ri%"e m L

Interference pattern for two coherent sources in antiphaseInterference pattern for two coherent sources in antiphase


#"!"

$"

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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28

'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

29


/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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PHYSICS CHAPTER 2

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#.*.$ ?ethods of obtaining two coherent sources

/ivision of wavefront/ivision of wavefront

#.* Interference of trans"itted light

through doubleslits


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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PHYSICS CHAPTER 2

31

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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PHYSICS CHAPTER 2

32

+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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PHYSICS CHAPTER 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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PHYSICS CHAPTER 2

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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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PHYSICS CHAPTER 2

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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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PHYSICS CHAPTER 2

36

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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

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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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

38

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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

39

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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

40

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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

41

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 =

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

42

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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

43

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

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://p02_01_05_01s.html/http://af_3702.html/


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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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PHYSICS CHAPTER 2

45


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=

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

46


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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

47

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


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 :

PHYSICS CHAPTER 2


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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

=

PHYSICS CHAPTER 2


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49

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


&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

PHYSICS CHAPTER 2


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50


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

PHYSICS CHAPTER 2


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51

+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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PHYSICS CHAPTER 2

52


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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

53


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

PHYSICS CHAPTER 2


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PHYSICS CHAPTER 2

54

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"

PHYSICS CHAPTER 2


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55

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"

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: 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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PHYSICS CHAPTER 2

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

PHYSICS CHAPTER 2


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58

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

PHYSICS CHAPTER 2


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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

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://af_1617.html/


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PHYSICS CHAPTER 2

60

+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


rad phaserad phasechangechange


PHYSICS CHAPTER 2


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61

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==

PHYSICS CHAPTER 2


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62

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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63

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

/

+

##$$



nonophasephase

changechange

PHYSICS CHAPTER 2


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64

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 ==

PHYSICS CHAPTER 2


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65

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
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://dichroics_filters.jpg/http://soap_bubble.jpg/


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PHYSICS CHAPTER 2

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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PHYSICS CHAPTER 2

67


.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

PHYSICS CHAPTER 2


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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


E8aple 6 :

0.11=n

!0.1=n

0.11=n

##$$

mint


nonophasephase

changechange

# coherent sources# coherent sources

antiphaseantiphase

m100/

=

PHYSICS CHAPTER 2


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69


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

PHYSICS CHAPTER 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 #.*$&igure #.*$

PHYSICS CHAPTER 2


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72

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 .)

PHYSICS CHAPTER 2


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73

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

PHYSICS CHAPTER 2


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74

+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)

PHYSICS CHAPTER 2


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75

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

PHYSICS CHAPTER 2


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76

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

PHYSICS CHAPTER 2


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77

#.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

PHYSICS CHAPTER 2


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78

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 ? &

PHYSICS CHAPTER 2


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79

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

PHYSICS CHAPTER 2


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80

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


81/130

81

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?

PHYSICS CHAPTER 2


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82

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)

PHYSICS CHAPTER 2


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83

+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

PHYSICS CHAPTER 2


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84

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


E8aple :

m10##m-101 !/ == L

d

L #43#43thth bright fringebright fringe

PHYSICS CHAPTER 2


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85


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=


86/130

PHYSICS CHAPTER 2


87/130

87

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 %


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


88/130

88


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

= = !

PHYSICS CHAPTER 2


89/130

89


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.!=

PHYSICS CHAPTER 2


90/130

90

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

PHYSICS CHAPTER 2


91/130

91

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"

PHYSICS CHAPTER 2


92/130

92


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;


93/130

93

#.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

PHYSICS CHAPTER 2


94/130

94

+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/


95/130

95

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

PHYSICS CHAPTER 2


96/130

96

/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"

PHYSICS CHAPTER 2


97/130

97

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#

PHYSICS CHAPTER 2


98/130

98

+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

PHYSICS CHAPTER 2


99/130

99

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)

PHYSICS CHAPTER 2


100/130

100

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


(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


101/130

101

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


102/130

102

+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


103/130

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


104/130

104

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"


y1

y1


AA((

22

//

EE

D

#

screenscreen

single slitsingle slit

PHYSICS CHAPTER 2 +i 2 45 h fi f H ' l t d th


105/130

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


106/130

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 :


107/130

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%


a Si%ce

E8aple 9 :

m100.$m,0.0m-10$0

2/

=== $D(entral(entral

"axi"u""axi"u"



$#

12y$ = a%da

1Dy =

=#

D$

2

( )( )#

0.010$02100.$

/2

=

m10!/.1$

=#


108/130

PHYSICS CHAPTER 2

E8aple & :


109/130

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


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


111/130

PHYSICS CHAPTER 2

earning !utco"e:


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112


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


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


114/130

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


((

//

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


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%


124/130

124


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


125/130

125


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



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126


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



128/130

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"

PHYSICS CHAPTER 2


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