Tātai Whakararuraru Mārama
Ko te whakararuraru mārama he āhuatanga e puta ana ina tūtaki ngā ngaru mārama e rua, neke atu rānei, ka taunekeneke tetahi ki tetahi, ka puta he tauira tohatoha kaha mārama ka taea te whakarei, te whakaiti rānei tetahi i tetahi. Ka kitea tēnei āhuatanga i roto i ngā āhuatanga maha, pērā i te whakamātautau rua-kōhatu, te whakamātautau kiriata angiangi, me te whakamātautau whakararuraru Michelson. Ka matapakihia e tēnei tuhinga te ariā taketake o te whakararuraru mārama, ngā tātai e pā ana ki te whakararuraru, me ētahi tono mahi i roto i te oranga o ia rā.
Ariā Taketake o te Whakararuraru Mārama
Ka puta te whakararuraru mārama ina tūtaki ngā ngaru mārama e rua. Ka kiia he whakararuraru ngā ngaru mārama mēnā he rerekētanga āhua pumau, ā, he rite tonu te roangaru. Ina tūtaki ngā ngaru e rua, ko te whānuitanga katoa i ia pūwāhi ko te tapeke whārite o ngā whānuitanga o ngā ngaru e rua. E rua ngā momo matua o te whakararuraru:
1. Te Whakararuraru Hanga: Ka puta ina tūtaki te tihi o tētahi ngaru ki te tihi o tētahi atu ngaru, ā, ka nui haere te whānui katoa. Ka puta he wāhi kanapa i roto i te tauira whakararuraru i te whakararuraru hanga.
2. Te Whakararuraru Whakangaro: Ka puta ina tūtaki te tihi o tētahi ngaru ki te raro o tētahi atu ngaru, ka hua ake he iti ake, he kore rānei te whānuitanga katoa. Ka puta he wāhi pōuri i roto i te tauira whakararuraru nā te whakararuraru whakangaro.
Tātai Whakararuraru Takirua
Ko tētahi o ngā whakamātautau matarohia e whakaatu ana i te pokanoa mārama ko te whakamātautau āputa-rua i whakahaerehia e Thomas Young i te tīmatanga o te rautau 19. I roto i tēnei whakamātautau, ka tukuna te mārama mā roto i ngā āputa whaiti e rua e tata ana, ka puta he tauira pokanoa i runga i te mata i muri i ngā āputa. Ko te tātai i whakamahia hei tatau i ngā tūranga o ngā whitiki mārama me te pōuri i roto i te tauira pokanoa ko:
\[ d \sin \theta = n \lambda \] (mō ngā awhi kanapa)
\[ d \sin \theta = (n + \frac{1}{2}) \lambda \] (mō ngā awhi pōuri)
Kei hea:
– ko d te tawhiti i waenganui i ngā āputa e rua.
– Ko θ te koki i hangaia e te rārangi mai i te kōhao ki te pūwāhi i runga i te mata.
– ko n te raupapa o ngā awhi mārama, pōuri rānei (n = 0, 1, 2, …).
– Ko λ te roangaru o te mārama e whakamahia ana.
Tātai Whakararuraru i roto i ngā Papa Angiangi
Ka taea hoki te whakararuraru i roto i ngā kiriata angiangi, pērā i ngā kiriata hinu i runga i ngā kiriata wai, i ngā kiriata hopi rānei. I ēnei wā, ka puta te whakararuraru i te whakaata o te mārama mai i ngā mata o mua me muri o te kiriata. Ko te matotoru o te kiriata me te taupū whakaata o te rauemi e whakatau ana i ngā āhuatanga mō te whakararuraru hanga me te whakararuraru whakangaro. Ko te tātai whānui mō te whakararuraru i roto i ngā kiriata angiangi ko:
\[ 2t = (m + \frac{1}{2}) \frac{\lambda}{n} \] (mō te pokanoa hanga)
\[ 2t = m \frac{\lambda}{n} \] (mō te pokanoa whakangaro)
Kei hea:
– ko t te matotoru o te kiriata.
– he tauoti a m (0, 1, 2, …).
– Ko λ te roangaru o te mārama.
– ko n te taupū whakaata o te kiriata angiangi.
Inenga Whakawhitiwhiti Michelson
He taputapu te ine whakawhiti Michelson e whakamahi ana i te kaupapa o te whakararuraru hei ine i ngā roangaru mārama, i ngā huringa taupū whakaata, i ngā roa whatu rānei me te tino tika. Kei roto i te ine whakawhiti he pūtake mārama, he whakaata āhua-mārama (he wehewehe hihi), me ngā whakaata whakaata e rua. Ka wehea te mārama mai i te pūtake kia rua ngā hihi e te wehewehe hihi, ka whakaatahia e ngā whakaata e rua, kātahi ka honoa anō e te wehewehe hihi hei hanga i tētahi tauira whakararuraru.
Ko te tātai taketake i whakamahia i roto i te ine whakawhiti Michelson ko:
\[ \Delta L = m \lambda \]
Kei hea:
– Ko te ΔL te rerekētanga o te roa o te ara whatu i waenga i ngā hihi mārama e rua.
– ko m te maha o ngā roopu pokanoa i kitea.
– Ko λ te roangaru o te mārama.
Ngā Taupānga Whakararuraru Mārama
He maha ngā whakamahinga o te pokanoa mārama i roto i te oranga o ia rā me ngā hangarau hou:
1. Ngā Tirohanga Matatika: Ka whakamahia te whakararuraru i roto i ngā taputapu ine tino tika, pērā i te inenga Michelson, hei ine i te roangaru o te mārama, te nekehanga ā-wāhanga, me te matotoru o ngā kiriata angiangi.
2. Ngā Paninga Ārai-Whakaata: Ka whakamahia ngā tikanga whakararuraru hei hoahoa i ngā paninga ārai-whakaata i runga i ngā karāhe kāmera me ngā mōhiti. Ka whakaitihia e ēnei paninga te whakaata mārama mā te hanga i te whakararuraru kino.
3. Matawai: Ka whakamahia te pokanoa i roto i te matawai whakawhiti-Fourier (FTIR) hei tātari i te matawai o te mārama e whakaatahia ana, e tukuna ana rānei e tētahi tauira.
4. Whakawhitiwhiti Kōrero Whatu: I roto i te hangarau muka whatu, ka whakamahia te pokanoa hei ine me te whakahaere i te kounga o ngā tohu mārama e tukuna ana mā roto i ngā muka whatu.
5. Holography: Ko te holography he tikanga whakaahua e whakamahi ana i te pokanoa mārama hei hopu me te whakaputa anō i ngā whakaahua toru-ahu.
Tauira o te Raru Whakararuraru Mārama
Hei whakamārama i tō tātou māramatanga ki te pokanoa o te mārama, me titiro tātou ki ētahi tauira pātai:
Tauira Pātai 1: Te Whakararuraru Takirua
I te mea ka whiti te mārama he 600 nm te roangaru mā roto i ngā kōhao e rua, he 0,5 mm te tawhiti, tatauhia te koki mō te whitiki kanapa tuatahi (n=1) i runga i te mata e tawhiti ana i ngā kōhao.
Otinga:
Whakamahia te tātai pokanoa takirua mō ngā roopu kanapa:
\[ d \sin \theta = n \lambda \]
Whakakapia ngā uara e mōhiotia ana:
\[ 0,5 \times 10^{-3} \sin \theta = 1 \times 600 \times 10^{-9} \]
\[ \sin \theta = \frac{600 \times 10^{-9}}{0,5 \times 10^{-3}} \]
\[ \sin \theta = 1,2 \times 10^{-3} \]
\[ \theta \approx \arcsin(1,2 \times 10^{-3}) \approx 0,069 \text{ nekehanga} \]
Tauira Pātai 2: Te Whakararuraru Kiriata Angiangi
Ka whakatakotoria he kiriata angiangi he 1,5 te taupū whakaata me te 300 nm te matotoru ki runga i tētahi papa. Tātaihia te roanga ngaru o te mārama ka pāngia e te wawaotanga hangahanga mēnā ka tau te mārama ki te kiriata.
Otinga:
Whakamahia te tātai wawaotanga hangahanga ki ngā paparanga angiangi:
\[ 2t = (m + \frac{1}{2}) \frac{\lambda}{n} \]
Mō te wawaotanga hanganga tuatahi (m=0):
\[ 2 \times 300 \times 10^{-9} = \frac{1}{2} \frac{\lambda}{1,5} \]
\[ 600 \times 10^{-9} = \frac{\lambda}{3} \]
\[ \lambda = 1800 \times 10^{-9} \]
\[ \lambda = 600 \text{ nm} \]
Whakamutunga
He āhuatanga nui te pokanoa mārama i roto i te ahupūngao whatu, he mea nui tēnei i roto i ngā tono hangarau maha. Mā te mārama ki ngā tātai e pā ana ki te pokanoa mārama, pērā i ngā mea e whakamahia ana i roto i te whakamātautau rua-kōhatu, te pokanoa kiriata-angiangi, me te ine whakawhiti Michelson, ka taea e tātou te tātari me te whakamahi i tēnei āhuatanga mō ngā kaupapa pūtaiao me ngā kaupapa hangarau maha. Ehara i te mea ka āwhina noa tēnei āhuatanga i a tātou ki te mārama ki te āhua taketake o te mārama, engari ka whakarato hoki i ngā taputapu mō te auahatanga i roto i ngā mara maha, mai i ngā whatu tika ki ngā whakawhitiwhitinga whatu me te holography.
