§1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr -...

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U , r¯nI:zlr§1 Mr¯n §2 I:zlr§3 r §4 ¨KYrŒ §5 I:lr§6 I_r -WrŒ

Transcript of §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr -...

Page 1: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

îU

,�à r�Ån�I:özør'

§1 �âMr�Ån

§2 I:�zôør'

§3 ��r�

§4 ÈK�Yr�ê

§5 I:�öôør'

§6 �I_r� Õ�Ì-ÀWr�ê

Page 2: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.1�âMr�Ån

§5.1.1�âMr�Ån

r�Ån/�ÇKÏr�a¹�r�a¹�9Ø�°r�¡Ï�Ån��(¹Õ$Í��Í/ú�ÂßMn�pr�a¹�*p�æ�Í/ý*ú��Чa¹�KÏ�û¨�Ý»�

:�°r�Ån��H�·�ørI��

În�I�·�ørI��¹Õ�

�¹�Ñú�Iâ��:���vÏ ����Í°Íà�

�âMÕ�Î��âb�ú$è���è����Ù�è��Pâørà ��/EÕ��_I��0�_h��IýA�è�Í���è������Ù$_IÑ�¤à�

Page 3: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.1�âMr�Ån

§5.1.1�âMr�Ån

�âMr���,Ó�þ

S1,S2�+:$è�âMùIfûßI,II��Ï�àd�¤à:�r�:ïIH0�\/�ùør¹�S1,S2§���h�ÌTr�:{<�

Page 4: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.1�âMr�Ån

§5.1.1�âMr�Ån

ò�3Ìb\

a¹ôÝ ∆x =(B+C)λ

2αB

Page 5: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

Page 6: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.1�âMr�Ån

§5.1.1�âMr�Ån

�Ã\

a¹ôÝ ∆x =Dλ

2a

Page 7: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.1�âMr�Ån

§5.1.1�âMr�Ån

�iÅn:ò�3Ìb\��Ã\

Page 8: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.1�âMr�Ån

§5.1.1�âMr�Ån

vÖ�âMr�Ån�Ô/V��\

�¯��Ô/V��\�$J /¿*��/¿t�É��*Ý»�S1,S2/M�It�$*¹�

Page 9: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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��

Page 10: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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)

Page 11: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

Page 12: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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)

Page 13: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ

§5.1.3I�½¦ùr�:lÔ¦�qÍ

�EI� ïý/¹I��;/��àU¿¦�bï�ð:iUI��

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�¦

Page 14: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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)

Page 15: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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�

Page 16: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ

§5.1.3I�½¦ùr�:lÔ¦�qÍ

^ør¿I�g���è�ør:

Ö¿Cx0− x0 +dx0,äf = 1∆x = d

Dλ, f0 = d

Rλ,�

Page 17: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

Page 18: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ

§5.1.3I�½¦ùr�:lÔ¦�qÍ

γýpò¿

Page 19: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ

§5.1.3I�½¦ùr�:lÔ¦�qÍ

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�

Page 20: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.1�âMr�Ån 5.1.3I�½¦ùr�:lÔ¦�qÍ

§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

Page 21: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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�

Page 22: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

Page 23: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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'�}�

Page 24: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.2I:�zôør' 5.2.1zôør'�õ

§5.2.1zôør'�õ

lÔ¦

γ = |sinπf0bπf0b

|= |sinπ

∆θ

∆θ0

π∆θ

∆θ0

|

Page 25: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.2I:�zôør' 5.2.1zôør'�õ

§5.2.1zôør'�õ

ørbï��%�b�bï

∆S0 ≈π

4(R ·∆θ0)2 ≈ (

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

Page 26: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.2I:�zôør' 5.2.2ÈK�YK�r�ê

§5.2.2ÈK�YK�r�ê

)(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�

ÈK�YK�r�êç�0ã³�Ù*î��1920t12�ÙWÅn�!(�KÏ�7§α��Òô��h∼ 121in = 3.07mör�a¹�1�àdå�Òô�

∆θ′ ≈ λ

h≈ 570nm

3.07m≈ 2×10−7rad

Page 27: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.2I:�zôør' 5.2.2ÈK�YK�r�ê

§5.2.2ÈK�YK�r�ê

Page 28: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.3��r� 5.3.1��r��ð

§5.3.1��r��ð

��r�/�Í8Áê6°a�

¥�á�4b¹B�;�Å��Ñ^hb'��· · · · · ·

Page 29: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.3��r� 5.3.1��r��ð

§5.3.1��r��ð

�*¹I�Ñ���bâ�g�����B�Ï�B�hbÍ��e�I«�ã:$_I�(zô¤à:(�B�¹��Bhb��B¹�∞Ü)b�r�:�

Page 30: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.3��r� 5.3.1��r��ð

§5.3.1��r��ð

�ßî�

¹I�g�–^�ß

iUI�g�–�ß

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§5.3��r� 5.3.1��r��ð

§5.3.1��r��ð

�ì͹sè$��r�:

��hb�–I�a¹�BG�ö∞Ü��–I>a¹

à:Ù$Í:���r�:�º���U����(�Û�

Page 32: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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�}

Page 33: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.3��r� §5.3.2��hb�r�:

§5.3.2��hb�r�:

�E�I�î∆L�∆L0ïý±λ02�:+�Ö³�n�n1,n2�

'�sû�

Page 34: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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�

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§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�

Page 36: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.3��r� §5.3.3I�a¹

§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��r� §5.3.3I�a¹

§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

TÒ���a¹ôÝ�'�KÏ∆lïå¾n�ú�Ò¦α�

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§5.3��r� §5.3.3I�a¹

§5.3.3I�a¹

Tb����(�KÏÆ�ô�

�Æ�9($sL»����ï��'»���æ�ï�$»��Kô1b��*Tbz����(sLIce��vhb���ÄsLôa¹�ùñ¹��¹0Æ�ôa¹pîNï�ú

d = N · λ2

(+12· λ

2) ����9a¹/®¹Ø/�¹

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§5.3��r� §5.3.3I�a¹

§5.3.3I�a¹

Tb����(�Kåöhbst¦

(�Kö��Æöb��*Tbz����9nr�a¹�b�ïå�å�Köhbw��ŵ�

Tb����(�r�¨À¡(I�a¹�Ø�KÏ�¦�Ø��

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§5.3��r� §5.3.4[�¯

§5.3.4[�¯

[�¯/�ÍI�r�a¹�

�WsL»��>�*sø�\�øb����\�»��ôb�z����

��88Ç(UrI�ôe��(z�B$hbÍ��§�I�r��

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§5.3��r� §5.3.4[�¯

§5.3.4[�¯

I�¿:åO:-Ã��Ã��àdI�a¹:�Ã��

∆l = 2nt− λ0

2=⇒ O¹z���¦:0,:�¹�

,m§�¯{

2ntm = mλ0r2

m = (2R− tm)tm ≈ 2Rtm

∴ rm =

√mRλ0

n=√

mRλ

Page 42: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.3��r� §5.3.4[�¯

§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

(UrIZ[�¯��ö�_ï�0��[�¯�r�a¹���[�¯�Í�[�¯/�e��

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§5.3��r� §5.3.4[�¯

§5.3.4[�¯

(If· åfô�8)([�¯Êvبë�ÀK�\hbò�/&�<

��Kö>(�Æö�Âß[�¯��p���ô�Oî�'�������I������èåö-.�I��)���èåö¹��

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§5.3��r� §5.3.5:ÀH/����

§5.3.5:ÀH/����

��hba¹O»I�¿

�§a¹$¹P,P′á³II�

2ntP cos iP = 2nt′P′ cos i′P′

iP′ > iP =⇒ cos i′P′ < cos iP =⇒ t′P′ > tPr�a¹ø�ñ¹�àdSI�a¹(�¾ÆKÏ�ö��KϾ¦�×6�ÙÍr�a¹ùI�¿�O»�

Page 45: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.3��r� §5.3.5:ÀH/����

§5.3.5:ÀH/����

�§a¹�¹II��s

2nt cos i1 = const

∴ d(2nt cos i1) = 0 =⇒−2nt sin i1di1 +2ncos i1dt = 0

∴dtdi1

= t · tan i1

àd�>Ò'���B��üôb�Ù*üp'�a¹/ò�ô%Í��B���r�a¹ùI�¿�O»1���KÏ�¾¦1�Ø�

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§5.3��r� §5.3.5:ÀH/����

§5.3.5:ÀH/����

�EI�;/iUI���¹�����Wa¹^ørà ��MNhba¹�lÔ¦γ�

ù��:¹P�eê �¹��r�a¹ ��I�î�ÖiUI�¹�$¹A,B�SI�îKî:λ0öγ ∼ 0

−2nt sin i1δ i1 = λ0 =⇒ δ i1 =λ

2t sin i1∝

1t

����A¸�I�¿¦�'�

Page 47: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.3��r� §5.3.6����r ����ØÍ�

§5.3.6����r ����ØÍ�

����r

å8�;-�0���r�ý/>r��–�r��I�

}Ig��hb ���åÊÎ �¹MèÆ���(iUI�)�ý� �r��(}Ice��¦G���B���hb�rG��r�Ö³��B��¦�ïå)(Ù�'(KÏ���

H�6�û��Æ�¦�����((vÖ¹ÕK���ðÍ)���K�(ø�g�aö���Æ�Ôù�1ïË;$­v�¦�¾¦ï¾10nm���r��I��*Í��/�1/6�����ØÍ���

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§5.3��r� §5.3.6����r ����ØÍ�

§5.3.6����r ����ØÍ�

����ØÍ�

(�ÏIfêh-�:ëc�ÍÏî���Ç( ��\�Ù&e�O�/� �I ­öG0�hb�*p��Ï*hb;�àÍ�_1'¦5%�Iý�Shb��ö�ÙÍ_1/ ï¹Í�����Í�I\:BcI�qÍ�Ï(Ï�

�H��@����

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§5.3��r� §5.3.6����r ����ØÍ�

§5.3.6����r ����ØÍ�

����,Ç(MgF2(n = 1.38),n1 < n1 < ng�$_ørI¡D øMî�:��Í�

2n2t =λ0

2=⇒ t =

λ0

4n2

æ���:���B�Ø�Í�����@ØÍ���

�,P�n1 < n2 > ng�$_ørIλ02�D øMî�àd

:����

2n2t =λ0

2=⇒ t =

λ0

4n2

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§5.3��r� §5.3.6����r ����ØÍ�

§5.3.6����r ����ØÍ�

���:��h�Í��Ø{$_ørI/EøI�1ò�3l��ï�

n2 =√

n1ng =√

1.5 = 1.22 Ù7�P��*~0�

ùMgF2�I:Í��¦:1.2%�@�;/ùÐ�y�â����ƾ¡��³��ùê*â�����Í�

å�¨ºùa:UB��H��� ýá³���ïå�(�B�¾0ôØ�åz�B�

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§5.3��r� §5.3.7I>r�

§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��r� §5.3.7I>r�

§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

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§5.3��r� §5.3.7I>r�

§5.3.7I>r�

�(iUI�)�ÂßI>a¹

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§5.4ÈK�Yr�ê §5.4.1Ó��'ý

§5.4.1Ó��'ý

ÈK�Yr�ê/Michelson(1881t:�v�å*�/&X(�¾¡��

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§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@�

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§5.4ÈK�Yr�ê §5.4.1Ó��'ý

§5.4.1Ó��'ý

i���(ÈK�Yr�ê

Page 57: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§5.4ÈK�Yr�ê §5.4.1Ó��'ý

§5.4.1Ó��'ý

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§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��-$­z��sL�&������ÒØ'Ø/Ø����BØ��Ø/Ø����� /(�<�K�ôÉ��Å{�`a¹�b��Ø�Zúcn�$­�

Page 59: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

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§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

)

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§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�

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§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 =

∆k,γ = 1

r�:lÔ¦�I�îZh�'Ø��

Jh�=π

∆k=

12· λ1 ·λ2

λ2−λ1≈ λ 2

2∆λ

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§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ

§5.4.3I��^Ur'ùr�:lÔ¦�qÍ

Page 64: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

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§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�

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§5.4ÈK�Yr�ê §5.4.3I��^Ur'ùr�:lÔ¦�qÍ

§5.4.3I��^Ur'ùr�:lÔ¦�qÍ

Page 67: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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'�

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§5.4ÈK�Yr�ê §5.4.4�ËöØbI1ê

§5.4.4�ËöØbI1ê

FTS

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§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)

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§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

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§5.4ÈK�Yr�ê §5.4.5¾ÆK���¦�ê6úÆ

§5.4.5¾ÆK���¦�ê6úÆ

�¦��iúÆ–ýEs�h

Âñ�Ñ6��X>�ôÎýE¦Ïa@�:¹� 3�� ï`�

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§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�

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§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��

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§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�

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§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�

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§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

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§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�

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§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

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§5.5I:�öôør' §5.5.3öôør¦ÍÔ�l�

§5.5.3öôør¦ÍÔ�l�

ïÁ�áX(I�î�öî�:��Å6X(I:öôør'î��

ÍÔ�l�b ·∆θ0 ≈ λ L0 ·∆λ

λ≈ λ τ0∆ν ≈ 1

8(/í�ørT�Ò�ørbï�øröô�ør�¦�ørSï

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§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

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§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�

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§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�

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§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

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§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

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§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 ≈ ·· ·

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§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�

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§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

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§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�

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§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

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§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

Page 91: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

Page 92: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

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£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�

Page 93: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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�

Page 94: §1 âMr n I zôłr K Y Œ I öôłr ˆ r ÀWr - USTChome.ustc.edu.cn/~linhan09/09011/dldsource/physics/3b.pdf · Dx dx =2p d Rl x 0 =2pf 0x 0)dI(x)_(1+cos(2pfx+2pf 0x 0))dx 0 eÔ‰8pB

§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

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