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Department of Physics
위조지폐 방지 장치
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Chapters 35 & 36
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p. 1183
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간섭; interference
간섭 현상
(interference)
회절 현상
(diffraction)
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• 기하광학 • 파동광학
빛살 파동면 (wavefront)
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Huygens 원리 (1678)
빛살 파면
Huygens 원리 (1678)
파동면(wavefront)
새로운 파동면
Huygens 원리에 따라 진공중에서 평면파가 전파하는 모습
광선
파(동)면
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cvn
2
1 2
1 ; n
n
nv
vnv cv c
1 1 2 2sin sinn n
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n n
c fcv fn
n
nv
nc
1
2
2
1 ;
1 n
n
v
v
v
c f
a, b, c 중에 광속이가장 빠른 영역은?
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11
1
vc n
1
2
1 2
주어진 거리 L을 지나는 데 포함된 파장 수
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Young의 2중 슬릿 간섭실험 p. 1189
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보기문제 p. 1192
질문: 서로 이웃한 두 극대점 사이의 거리?
1
: m
(
;
, sin = 1),
tan
mm m
m
m m
y
md
y
m D m Dy yd
D
d
:간섭무늬중앙으로부터 번째
= =
극대점까지의수직거리
풀
한편
이
1 2.5 mmm mDy y yd
- =
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Coherence 결 맞음:
Incoherence 결 어긋남
constant in time
p. 1194
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1 0 2 0
indep. of tim e," bu dsin , sin( )
t
sin
epends
o "n
2
E E t E E t
d
2( )
위상차 경로차
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2 20 0
0 1 2 12 00 0
/ 2 ; 2cos cosE EI I I I Ic c
0 02 2 (1 cos ) co ( )4 s
2II If
f= + =
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2 10 2
1 0 2
0
2
0sin , sin( )
4
2 cs
cosin
o
s
E
E E
E t
I
E t
I
E
d
p. 1195
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p. 1199
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Fig. 35-16
n1 n2
n1 > n2
n1 n2
n1 < n2
Reflection Reflection Phase ShiftOff lower index : 0Off higher index: 0.5 wavelength
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2 1n n
2
2
12 ( ) 2
2
, for m=0, 1, 2, :
, for m=0, 1 , 2, :
밝은 필름
어두운 필름
L mn
L mn
반사 위상차 주의!!
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Film Thickness Much Less Than
r2r1
If L << , for example L < 0.1, then phase difference due to the path difference 2L can be neglected.
Phase difference between r1 and r2 will always be ½ destructive interference film will appear dark
when viewed from illuminated side.
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For multilayer systems, this is not always the case and these equations are not appropriate.
2
2
12 ( ) 2
2
, for m=0, 1, 2, :
, for m=0, 1 , 2, :
밝은 필름
어두운 필름
L mn
L mn
For the special case of a higher index film flanked by air on both sides
주의!
n1=1 n2=1.38 n3=1.50
r1
r2
L
보기문제p.1203
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빛의 파장
Michelson’s Interferometer
박막
= 1,533 ,163 m .1 5 L 빨강=ml l
(Michelson:1907 Nobel Prize in Physics)
2 ( 1)LN N n
공기박막
박막의 두께
박막의 굴절률
통과 파장 갯수
shift in fringes
For each change in path by 1, the interference pattern shifts by one fringe at T. By counting the fringe change, one determines N박막- N공기
and can then solve for L in terms of and n.
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36장 회절, 에돌이, diffraction
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Diffraction Pattern from a single narrow slit
Diffraction and the Wave Theory of Light
36-
Centralmaximum
Side or secondarymaxima
Light
Fresnel Bright Spot
Brightspot
Light
These patterns cannot be explained using geometrical optics (Ch. 34)!
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에워싸고돌아서(에돌이)
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회절무늬:
Centralmaximum
Side or secondarymaxima
Light
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“Poisson” 광점
Fresnel Bright Spot
• Newtonian group (1819): 빛의 입자성
• Huygens(1678):
wave optics
원반 뒤쪽에 형성되는 회절무늬
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회절; diffraction
물결파의 회절현상. 장벽에 난 작은 틈을통과한 물결파가 틈의 끝을 돌아서 장벽의뒷쪽으로 퍼져나간다.
작은 틈작은 틈
p. 1220
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1sina
a D a
What do you expect if ?al =
p. 1221
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a s in ;
1, 2 ,
m ma
m
~D a
:2 m = 인경우
2 22 s is i m =n
2
42n :a
a
m번째 극소무늬
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a 일 때
~D a
:2 m = 인경우
2 22 s is i m =n
2
42n :a
a
복습
s in ;
1, 2 ,
m ma
m
m번째 소멸(극소)
어두운 띠의 일반적인 위치:
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Intensity in Single-Slit Diffraction2( )( s )inx
: 이웃영역에서 오는
빛의 위상차
이웃 영역에서 오는빛의 경로차
p. 1225
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2sin( ) ( )
si
1, sin2
; n minima-dark fring for 1, 2,3 es
ma
m m
I I
a m
(p. 1227-1229 참고)
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sin , 0,1, 2, : maxima1sin ( ) , 0,1,2, : minima2
d m m
d m m
Young의 2중 슬릿 간섭무늬 (p.1190-1197)
• 슬릿의 폭을무시한 경우임
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(p.1234-1236)
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22
sicos
n( ) mI I
aq b
aæ ö÷ç ÷ç ÷çè ø
=
간섭인자
회절인자
sin
sin
d
apa
pb
l
ql
q
=
=
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2중 슬릿 무늬
단일 슬릿 무늬
2중슬릿의 밝은
간섭무늬가 지워짐
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• m= order, 차수
회절격자, gratings : 간격이 고른 여러 개의 슬릿
(p.1237-1240)
• 격자(발)의 수 N이 클수록 예리한 회절선
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중앙선의 반너비 각;half width
sin for 0,1, 2 (maxima-lines)d m m
1 si
: sin 1
:
sin
n 1
H WWW HH
a
N N
N
Nd d
d
d
회단일슬 자릿 절: 격
회절격
제
중앙극대의폭
극
자
소
의
의
위치
:
•격자(발)의 수 N 이 클수록예리한 회절선
•밝은 띠의 밝기:
슬릿의 개수의 제곱에 비례
1차 극소반너비 각
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Grating Spectroscope; 회절 분광기
• 수소의 방출 스펙트럼 (회절무늬)
회절격자
(p.1213)
• separates different wavelengths for a given m
sin for 0,1, 2 (maxima-lines)d m m
광원
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X선 회절: 결정구조 분석에 활용 (p.1244-1245)
1sin 0.0019 for 0.1nm, 3000nmm dd
300 slits/mm
광학용회절격자X-선 파장
Too small to be distinguished from the central maximum !!
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, =0, 2 1, 2, sin md m
Diffraction of x-rays by crystal: spacing d of the order of 0.1 nm
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36-
Fig. 36-29
inter-planar spacing d is related to the unit cell dimension a0
X-Ray Diffraction, cont’d
2 050 045 or 0.2236
20ad a d a
Not only can
1) crystals be used to separate different x-ray wavelengths, but
2) x-rays, in turn, can be used to study crystals, for example determine the type crystal ordering and a0
, =0, 2 1, 2, sin md m
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양자장 이론- Pauli Adrien Maurice Dirac(1902. 8. 8-1984. 10. 20),- Wolfgang Pauli(1900. 4. 25-1958. 12. 15),- Julian Seymour Schwinger(1918. 2. 12 - ),- Richard Phillips Feynman(1918. 5. 11-1988. 2. 15),
상대론적 역학- Albert Einstein(1879. 3. 14-1955. 4. 18), - Hermann Minkowski(1864. 6. 22-1909. 1. 12),
.
.
.
양자역학- Niels Hendrik David Bohr(1885. 10. 7-1962. 11. 18),- Erwin Schrödinger(1887. 8. 12-1961. 1. 4),- Werner Heisenberg(1901. 12. 5-1976. 2. 1),..
고전역학- Galileo Galilei(1564. 2. 15-1642. 1. 8),- Isaac Newton(1642. 12. 25-1727. 3. 20),- Joseph Louis Lagrange(1736. 1. 25-1813. 4. 10),- Pierre Simon de Laplace(1749. 3. 23-1827. 3. 5),
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