Tauira o te Raru Whakarerekētanga Mārama
Ko te whakarara mārama he āhuatanga e puta ana ina haere ngā ngaru mārama mā roto i tētahi kōhao whaiti, i tētahi arai rānei, ka marara ki waho. Mā tēnei āhuatanga ka kitea he āhuatanga ngaru tō te mārama, ā, he ariā nui tēnei i roto i te ahupūngao. I roto i tēnei tuhinga, ka matapakihia e tātou ngā tauira noa o ngā raruraru whakarara mārama, me ngā kōrero me ngā whakamārama.
Pendahuluan
I te rautau 17, i whakaahuahia tuatahitia te diffraction e te kaipūtaiao Itari a Francesco Maria Grimaldi. Ka puta te diffraction ina huri te ahunga horapa o ngā ngaru mārama i a rātou e haere ana i roto i tētahi whakatuwheratanga, i tētahi arai rānei. Ka hua ake tēnei i te tauira pokanoa e āhua ana i te diffraction. I te nuinga o te wā, ka kitea nuitia te diffraction ina rite te roanga ngaru o te mārama ki te rahi o te whakatuwheratanga, o te arai rānei e haere ana.
Ka taea te whakamārama i te āhuatanga o te diffraction mā te whakamahi i ngā tauira ā-tinana e rua: te Tauira Ngaru me te Tauira Whatu Āhua. Hei tatau me te matapae i ngā tauira diffraction mārama, ko te whārite diffraction i whakawhanakehia e Augustin-Jean Fresnel rāua ko Joseph von Fraunhofer te mea e whakamahia whānuitia ana.
Ariā Taketake o te Whakarerekētanga
I mua i te matapaki i ngā tauira rapanga, he mea nui kia mārama ki ētahi ariā matua o te wehewehe mārama:
1. Ngā Āputa Takitahi me ngā Āputa Takirua: Ka kitea te tauira whakarara māmā rawa atu ina haere te mārama mā roto i tētahi āputa kotahi, āputa takirua rānei. Ko te tauira ka puta he raupapa o ngā whitiki mārama me ngā whitiki pōuri i runga i te mata tirotiro.
2. Ngā Rārangi Whakararuraru: Ko ngā rārangi kanapa me ngā rārangi pōuri i runga i te mata he hua o te whakararuraru i waenga i ngā ngaru mārama kua whakapikohia. Ka kiia ngā rārangi kanapa he rārangi whakararuraru hanga, ko ngā rārangi pōuri ia he hua o te whakararuraru whakangaro.
3. Roangaru: He nui te pānga o te roangaru o te mārama e whakamahia ana ki te tauira whakarara ka puta. Mā te mārama he roa ake te roangaru ka puta he tauira whakarara whānui.
4. Koki Whakarara: Ka taea te whakatau i te koki e whakararahia ai te mārama mā te whakamahi i ngā mātāpono o te ine whārite me te roanga ngaru o te mārama e whakamahia ana.
Tauira o te Raru Whakarerekētanga Mārama
Me matapaki tātou i ētahi tauira o ngā raruraru e pāngia pinepinetia ana i roto i te rangahau i te whatu mārama.
Tauira Pātai 1: Te Whakawehewehenga Kotahi
Pātai: Ka whiti tētahi hihi taiaho me te roanga ngaru o te 600 nm mā roto i tētahi āputa kotahi me te whānui o te 0,2 mm. Tātaihia te koki whakarara θ mō te raupapa tuatahi (m=1).
Kōrero: Mō te matapōkere kotahi, ka taea e tātou te whakamahi i te whārite matapōkere e whai ake nei:
\[ a \sin \theta = m\lambda \]
Kei hea:
– Ko te whānui o te āputa ko \( a \),
– Ko te koki whakarara ko \( \theta \),
– Ko te roanga ngaru o te māramatanga ko \( \lambda \),
– Ko te raupapa whakarara te \( m \).
I hoatu:
– \( \lambda = 600 \) nm = \( 600 \times 10^{-9} \) m,
– \( a = 0.2 \) mm = \( 0.2 \times 10^{-3} \) m,
– \( m = 1 \).
Whakakapia ngā uara ki roto i te whārite,
\[ 0.2 \times 10^{-3} \sin \theta = 1 \times 600 \times 10^{-9} \]
Te whakaoti rapanga mō \( \sin \theta \),
\[ \sin \theta = \frac{600 \times 10^{-9}}{0.2 \times 10^{-3}} \]
Te tatau i te \( \sin \theta \),
\[ \sin \theta = 0.003 \]
Mā te whakamahi i tētahi tātaitai hei tiki i te koki \( \theta \),
\( \theta \tata ki te 0.172 \) nekehanga.
Nō reira, ko te koki whakawhitiwhiti mō te raupapa tuatahi he tata ki te 0.172 nekehanga.
Tauira Pātai 2: Te Whakawehewehenga Takirua
Pātai: Ka whiti te mārama he 500 nm te roangaru mā roto i tētahi āputa takirua, he 0,1 mm te tawhiti i waenganui i ngā āputa. Tātaihia te tūranga o te rārangi kanapa tuarua i runga i te mata, e 2 mita te tawhiti mai i te āputa.
Kōrero: Mā te whakamahi i te whārite whakawehewehe rua:
\[ d \sin \theta = m\lambda \]
Kei hea:
– Ko te \( d \) te tawhiti i waenganui i ngā āputa e rua,
– Ko te roanga ngaru o te māramatanga ko \( \lambda \),
– Ko te raupapa whakarara te \( m \).
Hei kimi i te tūranga i runga i te mata (\( y \)) o \( \theta \), ka whakamahia e mātou:
\[ y = L \tan \theta \]
Mō ngā mea iti, ko \( \theta \), ko \( \tan \theta \approx \sin \theta \), me \( L \) te tawhiti o te mata mai i te kohao.
I hoatu:
– \( \lambda = 500 \times 10^{-9} \) m,
– \( d = 0.1 \times 10^{-3} \) m,
– \( R = 2 \) mita,
– \( m = 2 \).
Whakakapia ngā uara ki roto i te whārite,
\[ 0.1 \times 10^{-3} \sin \theta = 2 \times 500 \times 10^{-9} \]
Te whakaoti rapanga mō \( \sin \theta \),
\[ \sin \theta = \frac{1000 \times 10^{-9}}{0.1 \times 10^{-3}} \]
Te tatau i te \( \sin \theta \),
\[ \sin \theta = 0.01 \]
Whakaarohia \( \sin \theta = \tan \theta \) mō ngā tawhiti tino roa, ā, tāpirihia ki te whārite o te tūnga,
m, 20 mm rānei.
Nō reira, ko te tūnga o te rārangi kanapa tuarua i runga i te mata he 20 mm mai i waenganui o te mata.
Te Katinga
Ko te wehewehenga o te mārama he kaupapa e whakaatu ana i te whanonga o te mārama hei ngaru. He mea nui tēnei āhuatanga ki ngā momo mara pūtaiao, inā koa ko te tirohanga me te tirotiro ira. Ko te mārama ki te wehewehenga ehara i te mea i ahu mai i te ariā anake engari mā te whakaoti rapanga mahi maha hei āwhina i te hohonu ake o te mārama ki ngā āhuatanga ngaru o te mārama.
I te whanaketanga o te hangarau mō te tirotiro me te mārama ki ngā āhuatanga o te mārama, kei te whakamahia tonutia te āhuatanga o te diffraction i roto i ngā momo kitenga me ngā tono hangarau hou, mai i ngā karu tiro tae atu ki ngā taputapu ine tino tika. Nō reira, ehara i te mea he mea ako noa te ako i te diffraction engari he pānga mahi anō hoki mō te oranga o ia rā me te whanaketanga hangarau.
