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§1 �âMr�Ån
§2 I:�zôør'
§3 ��r�
§4 ÈK�Yr�ê
§5 I:�öôør'
§6 �I_r� Õ�Ì-ÀWr�ê
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§5.1�âMr�Ån 5.1.1�âMr�Ån
§5.1.1�âMr�Ån
ò�3Ìb\
a¹ôÝ ∆x =(B+C)λ
2αB
§5.1�âMr�Ån 5.1.1�âMr�Ån
§5.1.1�âMr�Ån
ò�3Ìñ\
a¹ôÝ ∆x =(B+C)λ
2(n−1)αB
§5.1�âMr�Ån 5.1.1�âMr�Ån
§5.1.1�âMr�Ån
�Ã\
a¹ôÝ ∆x =Dλ
2a
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vÖ�âMr�Ån�Ô/V��\
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§5.1�âMr�Ån 5.1.1�âMr�Ån
§5.1.1�âMr�Ån
�âMr����q�¹�
ù�âMÌI_r��r�a¹($I_�¤à:��ïÁ�/�Í^�ßr��(Ù�Ån-�:��0�p�r�a¹�ýP6I_�í����T�àdr�a¹:¦�1�¾�(�E�(�}6�'I�½¦ïåÐØ:¦�Fr�:lÔ¦��M�¾0��½¦ör�a¹�1�®¹��¹Mn�a¹ôÝý�I��â�øs�àd}Ie��d�0§-.®¹Í:}r�vÖ�§b�ira¹�Î���0�gGï�0®¹ /I®¦���/×M�àP�6��
§5.1�âMr�Ån 5.1.2r�a¹�û¨
§5.1.2r�a¹�û¨
r�a¹�¨�Ø�88Tû@¸��E��(–r�¡Ï�
∆L(P)→a¹��I(P) ∆L(P)Ø�→a¹Ø¨
Íà �ÅnÓ�Ø��Ë(Ø��I�û¨
�Ïsû�
åI�îØ�δ (∆L) = Nλ�d�I:I(P)Ø�N!�ûÇN*a¹�
$a¹Ø¨��,¹Õ�
ú�zô¹��I�î∆L(P)�Ø�ú�I�î�<��zô¹�Ø�(�8ý*0§a¹)
§5.1�âMr�Ån 5.1.2r�a¹�û¨
§5.1.2r�a¹�û¨
¹�Mû
0§a¹∆L = (R1 + r1)− (R2 + r2) = (R1−R2)+(r1− r2) = 0
R1−R2 ≈dδ sR
, r2− r1 ≈dδxD
∴ δx =DR
δ s
§5.1�âMr�Ån 5.1.2r�a¹�û¨
§5.1.2r�a¹�û¨
���ìú�ÂßP0¹�ûÇà9a¹�
N =δx∆x
=dδ sRλ
è�dö∆x Ø�r�a¹¿y¹�U��¹I�¿d¹�û¨ �üôr�a¹�û¨
ùvÖ�âMr�Ån�ônM�Ó��r�a¹�ôÝ�Ö��b�ýïýÑ�Ø��1 /�*�U�a¹û¨�î���
Ë(Ø�üôa¹û¨��P
^)r�ê�(�K��S���(`�4.9)
§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ
§5.1.3I�½¦ùr�:lÔ¦�qÍ
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iUI�ïåÆ\'Ï^ør�¹I��Æ��Ï�¹�b��Är�a¹��ìÂß0�r�:�E/�ÄÄr�a¹�^ørà !�,ŵ��Ù�ÄÄa¹v �ô�|d�M�^ørà üôr�:lÔ¦�M�
*+ŵ��Ù�ÄÄa¹|dà��0à (�w�^ørà �Ó���®¹ô®�Í�)�ÂK¡Ï�
�ì:ÀHsÃr�:�lÔ¦γ?�¹b��wÂK��I�ê·���'��lÔ¦�r�:M��ÛLr�¡Ï�
æ�¹b�Î�ºØ¦���Í �r�:�ør�¦
§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ
§5.1.3I�½¦ùr�:lÔ¦�qÍ
lÔ¦Í �r�:�ør�¦γ = 1 �hør
0 < γ < 1 è�ør
γ = 0 �h^ør
$*�»¹�g���è�ør:
¹�A,§�IA(x,y) = I0(1+ cos(2π
∆x · x),γA = 1
¹�B,§�IB(x,y) = I0(1+ cos(2π
∆x x+ϕ0),γB = 1øûϕ0Ö³�Mûδx:
ϕ0 =2π
∆xδx = 2π
dRλ
x0()(δx =DR
x0)
§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ
§5.1.3I�½¦ùr�:lÔ¦�qÍ
�öX(A,B�r�:�:¦��
I(x,y) = IA(x,y)+ IB(x,y) ^ørà
= I0(1+ cos2πfx+ I0(1+ cos(2πfx+ϕ0))
= 2I0(1+ cos ϕ02 · cos(2πfx+ ϕ0
2 ))
Íl¦
γ = |cosϕ0
2| ≤ 1
γ�δx�x0���h��Ø��
δx = ∆x2 ,ϕ0 = π,γ = 0; δx = ∆x,ϕ0 = 2π,γ = 1
s�a¹��12a�r�a¹�1�
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§5.1.3I�½¦ùr�:lÔ¦�qÍ
^ør¿I�g���è�ør:
Ö¿Cx0− x0 +dx0,äf = 1∆x = d
Dλ, f0 = d
Rλ,�
§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ
§5.1.3I�½¦ùr�:lÔ¦�qÍ
øû
ϕ(x0) =2π
∆xδx = 2π
dRλ
x0 = 2πf0x0
∴ dI(x)∝ (1+ cos(2πfx+2πf0x0))dx0
�eÔ�8pB
I(x) =∫ b
2
− b2
dI(x) =∫ b
2
− b2
B(1+ cos(2πfx+2πf0x0))dx0
ï�Ó�
I(x) = I0(1+sinπf0b
πf0b· cos2πfx)
,�yBb = I0(ôA��)
,�y:¤A���ïÁlÔ¦
γ = |cossinπf0b
πf0b|= |sinu
u|, u = πf0b = π
dRλ
b
§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ
§5.1.3I�½¦ùr�:lÔ¦�qÍ
γýpò¿
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I��P½¦
SdÙ��ïÙúI��P½¦
b0 =Rλ
d
���SI�½¦b���ïÙúÌT�Pô�
d0 =Rλ
b
è�Ô�å$Íŵ
å¿I�$ï¹Ý»:b0��döÙ$*ï¹�a¹|d��N = d
Rλb0 = 1a��tS�γ = 0�
å¿I�$ï¹Ý»:b02�$Wa¹|d��
12a��t
Sγ = 0.64�
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§5.1.3I�½¦ùr�:lÔ¦�qÍ
1d�ìïå�0Ù7�$n�
�(^øriUI��S¹�¹�ù��I�î:�*â�λ0ö�Âß:ßr�:�γ = 0
δ (∆L) = ∆LA(P)−∆LB(P) =±λ0ö
γ(PDÑ)≈ 0
§5.2I:�zôør' 5.2.1zôør'�õ
§5.2.1zôør'�õ
î��Ðú��ß(g�zô-*��$*!â��øs'
S1¹�;p¨U1(t) = (uA + · · ·+uO + · · ·+uB) = ∑ui(t)S2¹�;p¨U2(t) = (u′A + · · ·+u′O + · · ·+u′B) = ∑u′i(t)
v-�+{�hør�ý�uA,u′A; uo,u′o; · · ·�h^ør�ý�uA,u′o,u
′B, · · · uB,u′A,u′o, · · ·
;H��â^�hør�_^�h ør��/è�ør�
§5.2I:�zôør' 5.2.1zôør'�õ
§5.2.1zôør'�õ
I�/�h^ør�I��F�@I� �ør�¦Ñ��Ø��
�UϦ(S1,S2�ør�¦�
(Ù$*!â�ZÌT���r�:�lÔ¦γ��ì�ør�¦ô¥øs�
Í I:zôør'�ÍÔl�
SI�¿¦bÙ��ÌT��P½¦d0 = Rλ
b
sb · d0
R= λ
�eÒÏ∆θ0 =d0
R(�PÒ�ô��ðørT�Ò)
b ·∆θ0 ≈ λ
§5.2I:�zôør' 5.2.1zôør'�õ
§5.2.1zôør'�õ
zôør'ÍÔl���I
�EÌTùI�-Ã� Ò
∆θ ≈ ∆θ0,�γ ≈ 0;∆θ < ∆θ0,�γ > 0,è�ørI�¿¦b����ørT�Ò∆θ0�'1ÍÔl�����*Ò�ô�(S1,S2)(Ù*T�K��àN ør�����T���è�ør����(∆θ0 ��ñ�ør'�}�
§5.2I:�zôør' 5.2.1zôør'�õ
§5.2.1zôør'�õ
lÔ¦
γ = |sinπf0bπf0b
|= |sinπ
∆θ
∆θ0
π∆θ
∆θ0
|
§5.2I:�zôør' 5.2.1zôør'�õ
§5.2.1zôør'�õ
ørbï��%�b�bï
∆S0 ≈π
4(R ·∆θ0)2 ≈ (
Rλ
b)2
(*3IZÌTr�����'Ý»d0 =?
òå*3ù0bÂK�@ �Ò¦∆θ ′0 ≈ 30′ ≈ 10−2rad
d0 =λ
∆θ ′0=
550nm10−2 = 55µm
å�TôÝd ≈ 30µmZr����ïå·�γ ≈ 0.5�r�a¹�ø��ørbï
∆S0 ≈ d20 ≈ 3×10−3mm2
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)(γ��M�ïå¾nKÏeÜ�S�Òô�
Sd→ d0,�γ → 0�r�a¹�1�d0 ≈ 1m ∆θ ′ ≈ 5.5×10−7rad�/��°î��
ï��ô(m�ϧ�ÌT����� ¿ÙH'�d�a¹ôÝ*��a¹Çƾå�¨�àÕ(e$γ�Ø�
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∆θ′ ≈ λ
h≈ 570nm
3.07m≈ 2×10−7rad
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à:Ù$Í:���r�:�º���U����(�Û�
§5.3��r� §5.3.2��hb�r�:
§5.3.2��hb�r�:
:n���hbr�:�H¡�I�î
����∆θ1���Ñ<aö�∆θ��
∆L0(P)≈ L(ABP)−L(CP)≈ 2ntcos i1
−2t tan i1 ·n1 sin i
= 2nt cos i1 ����Ñ<�¦1�}
§5.3��r� §5.3.2��hb�r�:
§5.3.2��hb�r�:
�E�I�î∆L�∆L0ïý±λ02�:+�Ö³�n�n1,n2�
'�sû�
§5.3��r� §5.3.2��hb�r�:
§5.3.2��hb�r�:
Sn1 < n2 > n3��n1 > n2 < n3ö�Â���r��$_I;X(ÙÍπ�øM�Ø�
dö∆L = ∆L0± λ02 ,�EI�î�àUI�îøîJ*â��
�Jâ_1(�M){<�Sn1 < n2 < n3��n1 > n2 > n3ö�Â���r��$_I X(ÙÍπ�øM�Ø�
dö∆L = ∆L0,�EI�î�àUI�îøI�
§5.3��r� §5.3.2��hb�r�:
§5.3.2��hb�r�:
qÍ��hbr�:I�î�$*à �
�¦ t�>Òi1
:�ú�¦�à ���ïå(sLIÑN�ôg������i1���
cos i1 ≈ 1 =⇒ ∆L = 2nt +λ0
2
ô�dö��hb�a¹wI�'–I�a¹�å��ú>Ò�à �ïåÇ(I�¦���(s�hbsL���)�§��a¹1/I>a¹�
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§5.3.3I�a¹
I�a¹�y�
hba¹b����I�¿�ô(�§r�a¹���I�¿ù�)á³aö2nt + λ0
2 = mλ0�0¹ú°®¹(��¹)á³aö2nt + λ0
2 = (m+ 12)λ0�0¹ú°�¹(�®¹)
ø»a¹Kôù��B��¦î:λ
2
δ (∆L) = δ (2nt) = λ0 =⇒ 2nδ t = λ0 =⇒ δ t =λ0
2n=
λ
2
ÙùûUb��hba¹G�(�
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§5.3.3I�a¹
Tb����ù sL��s�Kôb��Tbz�B�×ð���
I�¿:�ÄsL�ñ¹�ô¿�àdI�a¹:�ÄsLôa¹�¾TÒ:α��ù��¦î∆t�hb*�Ý»∆l = ∆t
sinα≈ ∆t
α
∴ ∆l =∆tα
=λ
2α
TÒ���a¹ôÝ�'�KÏ∆lïå¾n�ú�Ò¦α�
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d = N · λ2
(+12· λ
2) ����9a¹/®¹Ø/�¹
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∆l = 2nt− λ0
2=⇒ O¹z���¦:0,:�¹�
,m§�¯{
2ntm = mλ0r2
m = (2R− tm)tm ≈ 2Rtm
∴ rm =
√mRλ0
n=√
mRλ
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§5.3.4[�¯
åär1 =√
Rλ ,�rm =√
mr1,[�¯1Ì��J��!:r1,
√2r1,√
3r1, · · · ,ø»ôÝ�e���sa¹�e�Æ[�¯88(eK�sø�\�ò�J�R1�X(�Ã�vÖÆ®i�O�$hbv ��Æ¥�-Ãïýú°®��àdï`�¾nKϹÕ/�
KÐ�¯J�rm����p,N*¯�J�rm+N
r2m+N− r2
m = NRλ =⇒ R =r2
m+N− r2m
Nλ
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2nt cos i1 = const
∴ d(2nt cos i1) = 0 =⇒−2nt sin i1di1 +2ncos i1dt = 0
∴dtdi1
= t · tan i1
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2t sin i1∝
1t
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2=⇒ t =
λ0
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λ0
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n1ng =√
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§5.3.7I>r�
�B�¦G��¹I�g��àwÜ��r�:
∆L0 = 2nt cos i1 ��Mb�¨º�ÙÌ/%<�
∆L = ∆L0 (+λ0
2)
nt���∆Lê�i1s�I�î/�0³��>Òi1�I>Ò�:¹hù(�%b)¿/a¹b¶�àdr�a¹/�¯�
-ç+Ø���§+N
2nt cos i1 +λ0
2= mλ0 (®¯) =⇒ m =
12
+2ntλ0
cos i1
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§5.3.7I>r�
-.ï®ï�
a¹-.��¹�Æ{,m§2nt cos im = mλ0,m+1§2nt cos im+1 = (m+1)λ0
=⇒ cos im+1−cos im =λ0
2nt
∴−2sinik+1 + ik
2sin
ik+1− ik2
≈−sin ik(ik+1− ik) =λ0
2nt
∆r = rk+1− rk ∝ ik+1− ik =−λ
2t sin ik��Ø��H°a¹����
t↘���–�-Ã6)t↗���–Î-Ã�úÏ�����!���9Øδ t = λ/2
§5.3��r� §5.3.7I>r�
§5.3.7I>r�
�(iUI�)�ÂßI>a¹
§5.4ÈK�Yr�ê §5.4.1Ó��'ý
§5.4.1Ó��'ý
ÈK�Yr�ê/Michelson(1881t:�v�å*�/&X(�¾¡��
§5.4ÈK�Yr�ê §5.4.1Ó��'ý
§5.4.1Ó��'ý
1887tW �Michelson-Morley��û~ÝùÂgû�å*���þ1%��Ïxi�fVåúË�ÝùözÂ×0%Í���:íIøùº�úËÐ����ú@�
§5.4ÈK�Yr�ê §5.4.1Ó��'ý
§5.4.1Ó��'ý
i���(ÈK�Yr�ê
§5.4ÈK�Yr�ê §5.4.1Ó��'ý
§5.4.1Ó��'ý
�
§5.4ÈK�Yr�ê §5.4.2(�Âß��r�a¹Êvû¨
§5.4.2(�Âß��r�a¹Êvû¨
r�a¹�b�Ö³�r�:I�î����ÈK�Yr�ê¥6�r�:�IH�M1�M′2\bb��z�BÍ�@b��r�:�
�Ír�a¹Êø�M1,M′2�MnÁP.121��-$z��sL�&������ÒØ'Ø/Ø����BØ��Ø/Ø����� /(�<�K�ôÉ��Å{�`a¹�b��Ø�Zúcn�$�
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
^Ur'�$Íx�
(1)Ì¿Ó�
�NaÄrÌ¿589nm,589.6nmI�∆λ � λ1,λ2
(2)Ur¿½–ÆUr
∆λ � λ0
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
(1)I1�Ì¿Ó�üôγ(∆L)Hh�'Ø�
λ11¿−→�Wr�a¹
I1(∆L) = I0(1+ cos2π
λ1∆L)
λ21¿−→�Wr�a¹
I1(∆L) = I0(1+ cos2π
λ2∆L)
$Wr�a¹^ørà
I(∆L) = I1(∆L)+ I2(∆L) = 2I0(1+ cos k∆L · cos∆k2
)
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
ÙÌ∆k� k,à�cos(∆k2 ∆L)�h�'�bØ��cos(k∆L)h�
��ëØ�
r�:H°1N�àP�6�Í°a�
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
lÔ¦1/Ù*bØ��6àP
γ(∆L) = |cos(∆k2·∆L)|
∆L = 0,γ = 1 ∆L =π
∆k,γ ≈ 0 ∆L =
2π
∆k,γ = 1
r�:lÔ¦�I�îZh�'Ø��
Jh�=π
∆k=
12· λ1 ·λ2
λ2−λ1≈ λ 2
2∆λ
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
(2)ÆUrüôlÔ¦�M
ùI1�Ö�*��!�
i(k) ={
i0, |k− k0|< ∆k2
0, |k− k0|> ∆k2
�/r�:�(k− k +∆k)1C�!.:
dI = dI0(1+ cosk∆L) = i(k)(1+ cosk∆L)dk
∴ I(∆L) =∫
∞
0i(k)(1+ cosk∆L)dk = i0∆k + i0
∫ k2
k1
cosk∆Ldk
= I0(1+sinv
vcosk0∆L), v-I0 = i0∆k,v =
∆k2
∆L
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
lÔ¦
γ(∆L) = |sinvv|= |
sin ∆k2 ∆L
∆k2 ∆L
|= |sinπ
∆L∆LM
π∆L
∆LM
|
∆k2
∆L = π =⇒ ∆LM =2π
∆k=
λ 2
∆λ
∆LM��I/
�EI�î∆L < ∆LM, γ > 0∆L≥ ∆LM, γ ≈ 0ð:�'ørI�î�
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ
§5.4.3I��^Ur'ùr�:lÔ¦�qÍ
��ÍÔb�
∆LM ·∆k = 2π =⇒ ∆LM ·∆λ
λ= λ (
∆λ
λ=
∆kk
=∆ω
ω)
∆LM = λ · λ
∆λ
(m+1)(λ − ∆λ
2) = m(λ +
∆λ
2) =⇒ m≈ λ
∆λ=⇒ ∆L = λ · λ
∆λ
Ù*Óºùh�r����r�(ÌI_r�)G�(�∆λ�∆ký/ϦI�^Ur'�i�Ï�àd∆LM×6�I��Ur'�
§5.4ÈK�Yr�ê §5.4.4�ËöØbI1ê
§5.4.4�ËöØbI1ê
FTS
§5.4ÈK�Yr�ê §5.4.4�ËöØbI1ê
§5.4.4�ËöØbI1ê
FTSå\����òåI��1��i(k)�ïå(ÈK�Yr�êKÏ�0I(∆L)��ù�òåI(∆L) (�Ç��K�)��7_ïåB�I1i(k)�
I(∆L)− I0 =1π
∫∞
0i(k)cos(k∆L)dk
���Øb
i(k) = 2∫
∞
0(I(∆L)− I0)cos(k∆L)d(∆L)
FTIRI1ê(�ËöØb¢�I1ê)
§5.4ÈK�Yr�ê §5.4.5¾ÆK���¦�ê6úÆ
§5.4.5¾ÆK���¦�ê6úÆ
r�K��¾¦
δ l =λ
2δN,Ö³�a¹�¡p¾¦
Ç(I5²¡p�δNïå¾01/10,àd�¦�KÏïå¾n0λ/20∼ 10−2µmÏ�×P�I�Ur'
lM ≤12
∆LM =λ 2
2∆λ
�∆λ ∼ 10−3nm,λ ∼ 600nm, lM ∼ 18cm
§5.4ÈK�Yr�ê §5.4.5¾ÆK���¦�ê6úÆ
§5.4.5¾ÆK���¦�ê6úÆ
�¦��iúÆ–ýEs�h
Âñ�Ñ6��X>�ôÎýE¦Ïa@�:¹� 3�� ï`�
§5.4ÈK�Yr�ê §5.4.5¾ÆK���¦�ê6úÆ
§5.4.5¾ÆK���¦�ê6úÆ
�¦�ê6úÆ
1892t�Michelson(I¢¿�â�\:�¦�úÆ1960t�ýE¦ÏaÔX�(86Kr��ay�Yr1¿\:�¦�°úÆ
λKr = 605.7802102nm,1m = 1650763.73λKr
1983t�,17JýE¡Ï'�c�yÆ�1s:��z-I(1/299792458Ò�öô�LÛ�ï���¦�
Ù7��z-I�Ø��Ä��<�_�d�)�f¶���æ|�l = c · t∆l∼ 10−7,∆t ∼ 10−13���^8¬��üôc<Å{ 9Û�
§5.5I:�öôør' §5.5.1î��Ðú
§5.5.1î��Ðú
zôør'/1iUI��w����/¹I����ÀÑ�âb��¹;/ør��
6�����ßI:µ�$¹�ør'��Ñ°s�/¹I�g����¦^��høs��
§5.5I:�öôør' §5.5.1î��Ðú
§5.5.1î��Ðú
ÆUrI��êÑ����:Ç��íÑI
®Â���íÑIöôτ0P�à�â��¦(I�)P L0 ≈ cτ0�/p¨S1�p¨S2v ;ý����*â�K���ì�øs�¦Ö³�I�î∆L12�L0�øù'��
∆L > L0�S1,S2^ør;∆L < L0�S1,S2è�ør∆L���S1,S2ør�¦1�Ø�
§5.5I:�öôør' §5.5.2øröô�ør�¦
§5.5.2øröô�ør�¦
I��öôør'}O�/åøröô�ør�¦eaÏ��
øröôτ0ør�¦L0 ≈ cτ0
öôør'î�(��r�(��(ÈK�Yr�êK�)-y+�ú�$ïÂ�r��I��'I�î∆L′M×ør�¦�P6����^��*�õ�ó��ì/�pϧ��
â��¦�1¿½¦/�:hÌ��
∆LM��1¿½¦−→ ∆LM ≈λ 2
∆λ
∆L′M��â��¦−→ ∆L′M ≈ L0
��/&�ô�
§5.5I:�öôør' §5.5.2øröô�ør�¦
§5.5.2øröô�ør�¦
�óUrâ /EU(x) = A · eikx��Q^Urâ�(k− k +∆k1C
dU(x) = dA · eikxv-dA = a(k)dk,:/E1Ʀ
∴zôâýpU(x) =∫
dU =∫
∞
0a(k)eikxdk
�*��!�
a(k) ={
a0, |k− k0|< ∆k2
0, |k− k0|> ∆k2
∴ U(x) = A0eik0x sinvv
,A0 = a0∆k,v =∆k2
x
§5.5I:�öôør' §5.5.2øröô�ør�¦
§5.5.2øröô�ør�¦
∆k� k0,àdsincýp:N��6àPö¹Mnv = π,=⇒ ∆k
2 x = π
∴ x =2π
∆k≈ λ 2
∆λ=⇒ L0 ≈
λ 2
∆λ
�Mb�0�∆LM�Ó��ô�
§5.5I:�öôør' §5.5.3öôør¦ÍÔ�l�
§5.5.3öôør¦ÍÔ�l�
ør�¦L0�^Ur'∆λ�sû
L0 ·∆λ
λ≈ λ
øröôτ0�^Ur'∆ν�sû
τ0 ·∆ν ≈ 1
9�lÔ¦γ(∆L)l�
γ(∆L) = |sin(π ∆L
∆LM)
π∆L
∆LM
|
γ(∆L) = |sin(π ∆L
L0)
π∆LL0
| �γ(τ) = |sin(π τ
τ0)
πτ
τ0
|,τ = ∆L/c
§5.5I:�öôør' §5.5.3öôør¦ÍÔ�l�
§5.5.3öôør¦ÍÔ�l�
ïÁ�áX(I�î�öî�:��Å6X(I:öôør'î��
;Ó
ÍÔ�l�b ·∆θ0 ≈ λ L0 ·∆λ
λ≈ λ τ0∆ν ≈ 1
8(/í�ørT�Ò�ørbï�øröô�ør�¦�ørSï
§5.5I:�öôør' §5.5.3öôør¦ÍÔ�l�
§5.5.3öôør¦ÍÔ�l�
�E�r�Ån-���/vX��à:�EI�;/^Ur�iUI��
¥6:¹Pà ���ö'��s@!â�S1,S2Ñ���^�ö'��
τ =∆Lc
, t1 = t, t2 = t− τ
§5.5I:�öôør' §5.5.3öôør¦ÍÔ�l�
§5.5.3öôør¦ÍÔ�l�
ùr�:�özør'�ß�Ïð�R9��vU1(t)�U2(t− τ)�ør'�1dU��/�è�ørI� �º��
(h�M�:ãh��âMr�Ån-��úh°�/zôør'�à:ÙÌ�r�/í�îr��
�(ÈK�Yr�êÙ{r�Ån-��úh°�/öôør'�à:ÙÌ/��îr���(iUI�Í�)�Âßr�°a�
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.1�I_r�
§5.6.1�I_r�
Í����b�ør�I_
ù��r��¨º�têP�1,2$_ørI�:ÀH�
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.1�I_r�
§5.6.1�I_r�
��I_
�Q0(n1 = n2)�r =−r′,r2 + tt′ = 1(Strokes��sû)
U1 = Ar =−Ar′ U2 = Artt′eiδ U3 = Ar′3tt′ei2δ U4 = Ar′5tt′ei3δ
v-δ =2π
λ02nt cosθ
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.1�I_r�
§5.6.1�I_r�
���I_
U′1 = Att′ U′2 = Ar′2tt′eiδ U′3 = Ar′4tt′ei2δ U4 = Ar′6tt′ei3δ
v-δ =2π
λ02nt cosθ
�r�:���r�:
UR = ∑ Uj, UT = ∑ U′j
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.1�I_r�
§5.6.1�I_r�
NÍ��Åbr� 1, tt′ ∼ 1Í��I_-4$y'�Ô�¥ÑA1 ≈ A2� A3� A4 · · ·döÍ��I_ïÑ<Æ:1,2$_I�ÌI_r��Mb¨º���r��c/ú�d����I_A′1� A′2� A′3� ·· ·dör�:�lÔ¦Ô�N�à�¨º��r�v ÍÆ��¹�r�°a�
ØÍ��Åbr ∼ 1, tt′ ∼ 0�ŵ�øÍ����I_/E�Ï�tøî '
A′1 > A′2 > A′3 > · · ·�A′1 ≈ A′2 ≈ A′3 ≈ ·· ·
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.2I:��
§5.6.2I:��
��r�:
UT =(1−R)A0
1−Reiδ, U∗T =
(1−R)A0
1−Re−iδ
∴ IT(δ ) = UTU∗T =I0
1+ 4R(1−R)2 sin2 δ
2
=I0
1+F sin2 δ
2
Fð:¾Æ¦ûp��a¹¾Æ�¦s�
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.2I:��
§5.6.2I:��
�r�:
IR(δ ) = I0− IT =I0
1+ (1−R)2
4Rsin2 δ
2
=I0
1+ 1F sin2 δ
2
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.2I:��
§5.6.2I:��
ù��r�:�
Sδ = 2mπöÖ�'<ITmax = I0�
Sδ = (2m+1)πöÖ��<ITmin = I0(1−R1+R
)2
øMîδ
δ =2π
λ0·2nt cosθÖ³�*i�Ï: t,λ ,θ
��(UrIZI���úθ�qÍ��Âß0I>a¹��a¹^8Æ��ï(��¨�¾Æ1¿Ó���(^UrsLIg���úλ�qÍ��9ØI1�ý�ú°�H��ï(Zäâhå�â�
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.2I:��
§5.6.2I:��
:¦ð�J<½¦
J<øM½¦ ∆δ ≈ 2(1−R)√R
=4√F
R→ 1,∆δ → 0,a¹�Ø��Æ
J<Ò½¦∆θm ≈λ
2πnt sinθm
1−R√R
J<1½¦∆λm ≈λ 2
m2πnt
1−R√R
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.3Õ�Ì-ÀWr�ê
§5.6.3 Fabry-Pérot Interferometer
�°�I_r��Í�êh1/Õ�Ì-ÀWr�ê�
G1,G2Kôb��*�¦G��z�T(�EáË()��¦�,0.1−10cm
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.3Õ�Ì-ÀWr�ê
§5.6.3 Fabry-Pérot Interferometer
F-Pr�ê(��vI1¿�¾ÆÓ�(Ì¿Ó�!�)
9n^)$n�S$1¿m§$*®¯�Òô�δθ�Ï*®¯ê«�JÒ½∆θmøIöpï�¨�
δθ =mδλ
2nt sinθm= ∆θm =
λ
2πnt sinθm· 1−R√
R
∴ δλmin =λ
mπ· 1−R√
R
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.3Õ�Ì-ÀWr�ê
§5.6.3 Fabry-Pérot Interferometer
r�¨,�
R≡ λ
δλ= mπ
√R
1−R
F-Pr�êt�'�üôr�§m�Ø�ïå·��Ø�r�¨,��Ùù��vI1��¾ÆÓ�/)��
£HT�/&���}�1�I�Ur'�P6(ÆUr!�)�Sλmax�,m§®¯�λmin�,(m+1)§®¯Í��γ ∼ 0
mλmax = (m+1)λmin =⇒ λmax−λmin ≈λ
m
sT��'�ê1I1�ô(sÏ�)�MN�
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.3Õ�Ì-ÀWr�ê
§5.6.3 Fabry-Pérot Interferometer
F-P�/T�ÞíI1Ø�Æ�ËI1
��ør�:�â�aö
2nt = mλm =⇒ λm =2ntm
��ør�:���aö
νm =c
λm= m
c2nt
=⇒ø»1���ô�
∆ν = νm+1−νm =c
2nt,I��ô�–µ!ô�
§5.6�I_r�Õ�Ì-ÀWr�ê §5.6.3Õ�Ì-ÀWr�ê
§5.6.3 Fabry-Pérot Interferometer
Ï*��â�λm�νmØêñ�1¿½¦∆λm�∆νm
∆λm =λ 2
m2πnt
· 1−R√R
,∆νm =c
2πnt· 1−R√
R
–U!¿½¨º�I_r�ö�:ÀH �Qør�¦�P6�c/1�X(ÙÍ�H��
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