2,薄膜干涉（ Thin-Film Interference）
Color of oil slick Color of soap bubble
a broad
source
transparent
thin-film
S1
S2
a b
n1
n2
n1
B
C
A
D
n2> n1
AD可看作同相面
)(2 CBACn ???
r
eCBAC
c o s
???
i
re
iABDB s in?
2
2 12 ?? ??? DBnACn
ie t g rn
r
en s in2
c o s
2 12 ??
2
?? rnin s ins in 21 ??
)
2
( 1 ??? DBn
ie tg r s in2?
i
r
ren
r
en s in
c o s
s in2
c o s
2 12 ??
2
)s in1(
c o s
2 22 ???? r
r
en
2
c o s2 2 ??? ren
2
??
i
a b
n1
n2
n1
B
C
A
D
n2> n1
i
re rnin s ins in
21 ??
2
)s in1(
c o s
2 22 ?? ??? r
r
en
2
c o s2 2 ??? ren
2
s in2 22122 ?? ??? inne
or,
2
s in2 22122 ?? ??? inne
2
)12( ??k
?k{ = ?.3.2.1?k
?.3.2.1.0?k
(max)
(min)
The conditions for a
minimum or a maximum
intensity,
Equal inclination interference
iii i
（等倾干涉）
Shown as the fig,
r
thin
film
lens
e
a broad
source
,1”
,2”, 3”, 4”
two rays“1”、,2”
are not coherent light!
i
screen
i
'ii 'i
r
Conclusion,
1） the same i-angle
corresponds to same
grade of interference
(equal inclination
interference等倾干涉 ) 。
2） the smaller i-angle is,the greater optical path
difference is,and the higher k is,
k
1?k
Discuss,1）
1)when thin film thickness increases,
frings extend outwardly
2
s in2 22122 ?? ??? inne ?k? ?.3.2.1?k (max)
i'ii 'i
when thin film thickness
frings extend outwardly
e increases,i
,
2)when thin film thickness decreases,
i'ii 'i
2
s in2 22122 ?? ??? inne ?k? ?.3.2.1?k 明纹
frings extend outwardly
frings contract inwardly
e decreases,i
frings contract inwardly
e
3) if white light falls on,
colour fringes appear
from red to violet,
2
s in2 22122 ?? ??? inne ?k?
?.3.2.1?k (max)
ke,一定,? 大,? 大,inn 22122 s in?
大
i 小，条纹靠中心
3）等倾干涉定域在无限远，只能通过透镜或将
眼调到聚焦无限远才能看到,
iii i
薄膜
透镜
屏
e
扩展
光源
,1”
,2”, 3”, 4”
4）扩展 光源成为观察等倾干涉条纹的有利条件。
,1”、,2”、
,3”
“4”光线之间虽
非相干光，但
在同一倾角下,
加强则同时加
强。减弱则都
减弱
Equal thickness interference (等厚干涉 )
?
Suppose:the thickness corresponding each fringes are respectively,
?? keeee 321,.
2
2 2 ?? ?? en
2
)12( ??k
?k{ = ?.3.2.1.?k
?.3.2.1.0?k
(max)
(min)
……(1)
1?n
6.wedge(劈尖干涉 )
2
s in2 22122 ?? ??? inne
2
)12( ??k
?k{ =
0s in ?i?
ke
1?ke
?
l
Distances of any two
adjacent maxma are:l
l
Any two adjacent maxima are given by,
kk eel ?? ? 1s in ?
…(2)
?? )1(
2
2 21 ???? kne k
…(4)
?? kne k ??
2
2 2 …(3) {
2
1 2 nee kk
?
??? …(5)
(4)-(3),
Substituting into（ 2）,
?
?
s in2 2n
l ?
?
chceked body
chceked body
The
standard
angle
The
standard
angle
Check angle
d
?
?
l
L
dtg ?? ??s in
?
?
s in2 2n
l ?
L
?L tgd ??
用测微显微镜测出 L,l,即可得到 d
paper n2=1
l
L
2
???sinL?
测量微小厚度变化,
薄膜厚度增加时，条纹下移，厚度减小时
条纹上移。
薄膜的 增加时，条纹下移,减小时
条纹上移。
? ?
??
显然，从视场中移动了 m个条纹，薄膜厚度改
变了,
2
?me ??
条纹
从上
向棱
边移
动！
条纹
从棱
边向
上移
动！
?
上
移
?
下
移
C
Interference expansion instrument
M
C：铟钢作成的，热
膨胀极小；
M：被检体。
We count the number
of passing fringes m
when the temperature
Increase ?t,
M heighten,
2
?ml ??
Thermal expansion coefficient,
tl
l
??
???
checked body
checked body
checked body
checked body
check surface,
Color of oil slick Color of soap bubble
a broad
source
transparent
thin-film
S1
S2
a b
n1
n2
n1
B
C
A
D
n2> n1
AD可看作同相面
)(2 CBACn ???
r
eCBAC
c o s
???
i
re
iABDB s in?
2
2 12 ?? ??? DBnACn
ie t g rn
r
en s in2
c o s
2 12 ??
2
?? rnin s ins in 21 ??
)
2
( 1 ??? DBn
ie tg r s in2?
i
r
ren
r
en s in
c o s
s in2
c o s
2 12 ??
2
)s in1(
c o s
2 22 ???? r
r
en
2
c o s2 2 ??? ren
2
??
i
a b
n1
n2
n1
B
C
A
D
n2> n1
i
re rnin s ins in
21 ??
2
)s in1(
c o s
2 22 ?? ??? r
r
en
2
c o s2 2 ??? ren
2
s in2 22122 ?? ??? inne
or,
2
s in2 22122 ?? ??? inne
2
)12( ??k
?k{ = ?.3.2.1?k
?.3.2.1.0?k
(max)
(min)
The conditions for a
minimum or a maximum
intensity,
Equal inclination interference
iii i
（等倾干涉）
Shown as the fig,
r
thin
film
lens
e
a broad
source
,1”
,2”, 3”, 4”
two rays“1”、,2”
are not coherent light!
i
screen
i
'ii 'i
r
Conclusion,
1） the same i-angle
corresponds to same
grade of interference
(equal inclination
interference等倾干涉 ) 。
2） the smaller i-angle is,the greater optical path
difference is,and the higher k is,
k
1?k
Discuss,1）
1)when thin film thickness increases,
frings extend outwardly
2
s in2 22122 ?? ??? inne ?k? ?.3.2.1?k (max)
i'ii 'i
when thin film thickness
frings extend outwardly
e increases,i
,
2)when thin film thickness decreases,
i'ii 'i
2
s in2 22122 ?? ??? inne ?k? ?.3.2.1?k 明纹
frings extend outwardly
frings contract inwardly
e decreases,i
frings contract inwardly
e
3) if white light falls on,
colour fringes appear
from red to violet,
2
s in2 22122 ?? ??? inne ?k?
?.3.2.1?k (max)
ke,一定,? 大,? 大,inn 22122 s in?
大
i 小，条纹靠中心
3）等倾干涉定域在无限远，只能通过透镜或将
眼调到聚焦无限远才能看到,
iii i
薄膜
透镜
屏
e
扩展
光源
,1”
,2”, 3”, 4”
4）扩展 光源成为观察等倾干涉条纹的有利条件。
,1”、,2”、
,3”
“4”光线之间虽
非相干光，但
在同一倾角下,
加强则同时加
强。减弱则都
减弱
Equal thickness interference (等厚干涉 )
?
Suppose:the thickness corresponding each fringes are respectively,
?? keeee 321,.
2
2 2 ?? ?? en
2
)12( ??k
?k{ = ?.3.2.1.?k
?.3.2.1.0?k
(max)
(min)
……(1)
1?n
6.wedge(劈尖干涉 )
2
s in2 22122 ?? ??? inne
2
)12( ??k
?k{ =
0s in ?i?
ke
1?ke
?
l
Distances of any two
adjacent maxma are:l
l
Any two adjacent maxima are given by,
kk eel ?? ? 1s in ?
…(2)
?? )1(
2
2 21 ???? kne k
…(4)
?? kne k ??
2
2 2 …(3) {
2
1 2 nee kk
?
??? …(5)
(4)-(3),
Substituting into（ 2）,
?
?
s in2 2n
l ?
?
chceked body
chceked body
The
standard
angle
The
standard
angle
Check angle
d
?
?
l
L
dtg ?? ??s in
?
?
s in2 2n
l ?
L
?L tgd ??
用测微显微镜测出 L,l,即可得到 d
paper n2=1
l
L
2
???sinL?
测量微小厚度变化,
薄膜厚度增加时，条纹下移，厚度减小时
条纹上移。
薄膜的 增加时，条纹下移,减小时
条纹上移。
? ?
??
显然，从视场中移动了 m个条纹，薄膜厚度改
变了,
2
?me ??
条纹
从上
向棱
边移
动！
条纹
从棱
边向
上移
动！
?
上
移
?
下
移
C
Interference expansion instrument
M
C：铟钢作成的，热
膨胀极小；
M：被检体。
We count the number
of passing fringes m
when the temperature
Increase ?t,
M heighten,
2
?ml ??
Thermal expansion coefficient,
tl
l
??
???
checked body
checked body
checked body
checked body
check surface,
