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7/30/2019 nhiu x nh sng
1/21
Nhiu xa nh sng
1Hin tng nhiu x - Nguyn l Huygens-Fresnel1.1 Hin tng nhiu x nh sng1.2 Nguyn l Huygens-Fresnel1.3 Nhiu x Fresnel v nhiu x Fraunhofer
2 Nhiu x Fresnel2.1 Phng php i cu Fresnel.2.2 Nhiu x nh sng qua l trn v a trn nh
3 Nhiu x Fraunhofer3.1 Nhiu x qua mt khe hp3.2 Nhiu x qua mt l trn3.3 Nhiu x qua 2 khe3.4 Nhiu x qua nhiu khe3.5 Cch t nhiu x- my quang ph cch t3.6 Nhiu x tia X
TS. Hong Ch Hiu
1
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 2
1. Hin tng nhiu x-Nguyn l Huygens-Fresnel
Cac vi du v nhiu xa:
Nc chay qua mt khe p nho.
1.1 Hin tng nhiu xa anh sang.
Khi song anh sang truyn quamt l hep hoc mep man chn,anh sang khng truyn thng ma
bi lch i va c goi la hintng nhiu xa anh sang.
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 3
Mi im khng bi che khut cua mt mt song mt thi im cho trcc dung nhmt ngun phat song cu th cp vi cung tn s nh songscp. Bin cua trng quang hoc tai mt im bt ky bn ngoai la schng cht cua tt ca nhng song thcp nay khi tinh n bin vaphatng quan cua chung.
1.1 Nguyn ly Huygen-Fresnel.
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 4
1.2 Nhiu xa Fresnel va nhiu xa Fraunhofer.
Nhiu x Fresnel (Nhiu x trng gn): Nu ngun sngv mn quan st t gn vt gy nhi x Fresnel. C thxem nhiu x Fresnel l nhiu x vi sng cu.
Nhiu x Fraunhofer (Nhiu x trng xa): Nu ngunsng v mn quan st kh xa vt gy nhiu x ta c nhiux Fraunhofer. Co th thy l chng no sng n v ikhi vt gy nhiu x c xem l sng phng th ta cnhiu x Fraunhofer.
Quy tc l: R> a2
/
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 5
2. Nhiu xa Fresnel
2.1 Phng phap i cu FresnelLy B lm tm dng cc mt cubn knh ln lt b, b+/2, b+ ,b+ 3/2, b+j /2.
Cc mt cu ny ct mt sng thnh cc i cu. ng truynca cc sng th cp t cc ilin tip gi n B chnh nhau /2nn sng t hai i lin tip sngc pha nhau khi n B.
nB SSSSSSS +++= ...54321
y Sj vi j=1,2,3, l bin sng gi t i cu Fresnel th j n B.
j l din tch i th j, kj l tha s xin ca i th j.
jjj
jba
aKS
+
=
2
0
Nh vy, bin sng tng hp ti B l:
B
b
b+/2
b+b+3/2
A
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 6
Din tich i thu j la hiu din tich 2 chom cu lin tip:
Nh vy khi j tng, h s xin Kj giam dn va do o bin Sj giam dn va tin n 0 khi BMj tip tuyn vi mt song .
Coi gn ung Sj bng trung binh cng cua hai s hang bn canh:
ba
abj
+=
nSSSS >>>> ...321
( )11
2
1+ += jjj SSS
2
2...
22222
1
5
4
33
2
11
nB
nB
SSS
SSSSSSSSS
+
++
++=
Du + khi n le va du khi n chn
Khi gia A va B khng co man chn: Sn 0,
vi I1 la cng sang do mt i
cu Fresnel u tin gi n4822
1
22
1 1ISS
IS
S bBB ====
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 8
2.2 Nhiu x nh sng qua l trn v a trn
a. Nhiu xa qua l tron.
Gia s l tron m ra q i Fresnel u tin. Khi o bin dao ng song tng hp tai B la:
Nu kinh thc l nho, s i q khng ln lm (q
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+ Nu s i q nguyn, chn th
Nu s i q khng nguyn th bng phng php th ta c th xc nhc bin sng tng hp OP v so snh n vi OI.
Bi ging Nhiu x nh sng TS. Hong Ch Hiu 9
002
21
= BB ISS
Si roi tai B xp xi bng0 nn se thy ti tai B.
+ Nu khng co man chn:
+ Nu l cha ung 1 i:422
2
1 ISIS
S oo
B
BoB===
1
2
12
IS
ISS BBB ===
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 10
b. Nhiu xa qua mt l tron chn sang
BA
Gi s a mt p i u tin, bin
dao ng tng hp s l:
V n , nn Sn 0. Do
Nu l c knh thc nh, p nh th:
2
1 np
B
SSS
=
+
2
1+
=p
B
S
S
2
111
SSSSBp +
roi tai B khng khac nhiu so vi khi khng co man chn D va cho ta mt im sang,goi la im sang Poison.Khi kich thc ia chn ln, thi B se ti, vi: 001 == + BpB ISS
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 11
3. Nhiu xa Fraunhofer
3.1 Nhiu xa qua mt khe hep
Chia mt song gii han bi khe thanh Nphn bng nhau rng x=a/N.Xet song phng th cp theo goc gpnhau tai P. hiu quang trinh gi t hai i
lin tip la:
Song tai P la chng cht cua N song thcp gi t khe n P. H s xin la nhnhau, nn bin cac song th cp la nhnhau.
x
sin22
sinsin.
N
aL
N
axL
==
==
N
oN
EEEEE
EEEEErrrrr
++++=
=====
...
..
321
321
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 12
+ Ti O trn mn. Khi N sngth cp ti O l ng pha =0, sin=0 =0. Cng sng ti Ol cc i.
+ Ti phng 0, cc sng thcp lch pha nhau mt lngkhng i. Tng ca N vector lmt vector di Er
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 13
M
H
C
R
Khi N tin ti v hn, chui vector cc sng th cp s tin ti m
t cung trn tm C v bin sng tng hp l di dy trngcung :
sin22 ROHOME ===
2/=
sin
2. aN ==
Mt khac theo inh nghia:
22 maxmax
ER
R
E
R
OM===
2
2222
sin
sin
sinsinsin
22
=
=
==
a
a
IIEEI mmm
+ Tai O, =0; =0 ta co vn sang trung tmmax01
sinII == =
O
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 14
+ Cc tiu cng sang xut hin khi sin=0 va 0 ng vi:
+ Khi m=1 ta c cc tiu u tin vi gc 1 tha mn
ma
mma
=
===
sin
,...3,2,1,sin
a
=1sin
Nu khe rt hp; a sin1=11=/2. iu ny cos ngha l cci chnh gia m v hn, nh
sng chiu khp mn. Khi a tngdn, cc i chnh hp li, xuthin cc cc i th xen k.
Cc ai th cp
+=2
1sin ma
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 15
3.2. Nhiu xa qua mt l tron
Cc tiu u tin:
phn ly theo tiu chun Rayleigh:
Cc ai cua anh thnht trungung vicc tiu au tin cuaanh th2 la gii han phn ly.
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 16
3.3. Nhiu xa qua 2 khe hp
2
sin
sinsin
=
a
a
II mP
=
2cos4
2 oP II
sin
22b==
Cng sng phn b theo hin tng giao thoa:
Do hin tng nhiu x trn khe c rng a nncng sng qua mi khe l:
Cc tiu nhiu x:,...3,2,1sin == m
am
Cc i giao thoa:
,...3,2,1;sin == mb
m
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 17
3.4. Nhiu xa qua nhiu khe hp
( )
[ ]
=
=
=
)1(
2
1
.
................
.
Nti
N
ti
ti
eES
eES
eES
( )[ ]
=
=+++== i
iNtiNiiti
N
i
iPe
eeEeeeESS
1
1...1
1
1
Bin ca sng pht ra t mi khe theo phng l:
lch pha ca 2 khe lin tip l:
sin2
b=
sin,
sin aEE m ==
Cc khe c th xem l mt ngun sng gi ti P nh sau
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 18
==
2sin
2sin
2 2
2
2*
N
ESS
I PPP
( )22
sin
sinsin
=
NII oP
Gia 2 cc i chnh lin tip s c (N-1)cc tiu, c (N-2) cc i ph
Vi2
20
0
EI =
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 19
3.5 Cach t nhiu xa
Cc ai nhiu xa
d: chu ky cua cach t
md =sin
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 20
tn sc gc ca cch t:
bn rng gc ca mt vch nhiu x:
Khong cch gc gia hai vn sng cng bc:
Nng sut phn gii ca cch t :
Vng ph t do ti bc m:
m
m
b
m
d
dD
cos
==
m
mNb
cos=
m
mdmddDd
cos==
mNR =
=
min
)(
( )m
td
=
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Bi ging Nhiu x nh sng TS. Hong Ch Hiu 21
3.6 Nhiu xa tia X
Cng thc Bragg:
2dsin = m
d = Khong cch gia cc mt phng nguyn t = Gc gia chm tia X vi mt phng nguyn tm = Bc giao thoa= bc sng
Mt phng trn
Mt phng di
Chm tia ti Chm phn x