sin θ 0 ~ = B A ′ C ′ B = B A ′ C P = B A ′ 2 d tan θ {\displaystyle \sin {\widetilde {\theta _{0}}}={\frac {BA'}{C'B}}={\frac {BA'}{CP}}={\frac {BA'}{2d\tan \theta }}}
B A ′ = 2 d tan θ sin θ 0 ~ {\displaystyle BA'=2d\tan \theta \sin {\widetilde {\theta _{0}}}}
Δ Λ = 2 d cos θ n t − 2 d tan θ sin θ 0 n i {\displaystyle \Delta \Lambda ={\frac {2d}{\cos \theta }}nt-2d\tan \theta \sin \theta _{0}ni}
= 2 d cos θ n t [ 1 − sin θ sin θ 0 n i n t ] {\displaystyle ={\frac {2d}{\cos \theta }}nt\left[1-\sin \theta \sin \theta _{0}{\frac {ni}{nt}}\right]}
= 2 d cos θ n t [ 1 − sin 2 θ ] {\displaystyle ={\frac {2d}{\cos \theta }}nt\left[1-\sin ^{2}\theta \right]}
Δ Λ = 2 d n t cos θ {\displaystyle \Delta \Lambda =2dnt\cos \theta }
δ = 2 π λ 0 Δ Λ = 4 π λ 0 n t d cos θ {\displaystyle \delta ={\frac {2\pi }{\lambda _{0}}}\Delta \Lambda ={\frac {4\pi }{\lambda _{0}}}ntd\cos \theta }
E 1 r = E 0 r e i ω t {\displaystyle E_{1r}=E_{0}re^{i\omega t}}
E 2 r = E 0 t t ′ r ′ e i ( ω t − δ ) {\displaystyle E_{2r}=E_{0}tt'r'e^{i\left(\omega t-\delta \right)}}
E 3 r = E 0 t t ′ r ′ 3 e i ( ω t − 2 δ ) {\displaystyle E_{3r}=E_{0}tt'r'^{3}e^{i\left(\omega t-2\delta \right)}}
E N r = E 0 t t ′ r ′ ( 2 N − 3 ) e i ( ω t − ( N − 1 ) δ ) {\displaystyle E_{Nr}=E_{0}tt'r'^{(2N-3)}e^{i\left(\omega t-\left(N-1\right)\delta \right)}}
E r T = ∑ E i r = E 0 r e i ω t + ∑ j = 2 N E 0 t r ′ ( 2 j − 3 ) t ′ e i ( ω t − ( j − 1 ) δ ) {\displaystyle E_{rT}=\sum E_{ir}=E_{0}re^{i\omega t}+\sum _{j=2}^{N}E_{0}tr'^{(2j-3)}t'e^{i\left(\omega t-\left(j-1\right)\delta \right)}}
= E 0 e i ω t [ r + { ∑ j = 2 N ( r ′ 2 e i δ ) j − 2 } r ′ t t ′ e − i δ ] {\displaystyle =E_{0}e^{i\omega t}\left[r+\left\{\sum _{j=2}^{N}\left(r'^{2}e^{i\delta }\right)^{j-2}\right\}r'tt'e^{-i\delta }\right]}
E r = E 0 e i ω t [ r + r ′ t t ′ e − i δ 1 − r ′ 2 e − i δ ] {\displaystyle E_{r}=E_{0}e^{i\omega t}\left[r+{\frac {r'tt'e^{-i\delta }}{1-r'^{2}e^{-i\delta }}}\right]}
E r = E 0 e i ω t [ r ( 1 − e − i δ ) 1 − r 2 e − i δ ] {\displaystyle E_{r}=E_{0}e^{i\omega t}\left[{\frac {r\left(1-e^{-i\delta }\right)}{1-r^{2}e^{-i\delta }}}\right]}
t t ′ + r 2 = 1 {\displaystyle tt'+r^{2}=1}
![=\frac{2d}{\cos\theta}nt\left[1-\sin\theta\sin\theta_{0}\frac{ni}{nt}\right]](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/455f0e5a74986b38c484df10149376ef5a5758e5)
![=\frac{2d}{\cos\theta}nt\left[1-\sin^{2}\theta\right]](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/6667616d800b603ab8780cdd1b4a221593ffdaee)
![=E_{0}e^{i\omega t}\left[r+\left\{ \sum_{j=2}^{N}\left(r'^{2}e^{i\delta}\right)^{j-2}\right\} r'tt'e^{-i\delta}\right]](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/77f5111ec03dc7932464dee83e2042a6c54b2617)
![E_{r}=E_{0}e^{i\omega t}\left[r+\frac{r'tt'e^{-i\delta}}{1-r'^{2}e^{-i\delta}}\right]](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/19dd2c845b6001b96f205892d97b98d4adc1a6b5)
![E_{r}=E_{0}e^{i\omega t}\left[\frac{r\left(1-e^{-i\delta}\right)}{1-r^{2}e^{-i\delta}}\right]](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/815ea5f9cde5ec44b5ffefea2e11d98704c77643)
