Te Ture a Snell i roto i te Whakaata o te Mārama
He āhuatanga whatu te hurihanga o te mārama, he mea nui hei mārama ki te taunekeneke a te mārama me ngā momo pāpāho. Ko tētahi o ngā ture matua e whakamahia ana hei whakamārama i te hurihanga o te mārama ko te Ture a Snell. Ka matapakihia e tēnei tuhinga te Ture a Snell me te taipitopito, e kapi ana i tōna hītori, ngā mātāpono taketake, ngā tātai pāngarau, ngā tono, me ngā tauira.
Papamuri Hītori
I tapaina te Ture a Snell i muri i a Willebrord Snellius (1580–1626), he tohunga pāngarau me te tohunga whetū Tatimana. Ahakoa i kitea te ture e Snellius i te tau 1621, kua mōhiotia te ariā o te hurihanga o te mārama mai anō i ngā wā onamata. I whakahaerehia e ngā kaipūtaiao pērā i a Ptolemy rāua ko Ibn Sahl he rangahau tōmua mō tēnei āhuatanga, engari mā te Ture a Snell ka whakaratohia he whakatakotoranga pāngarau tika.
I kitea e Snellius ina haere te mārama mā roto i tētahi rohe i waenganui i ngā momo pāpāho e rua, pērā i te hau me te wai, te hau me te karāhe rānei, ka piko ngā hihi mārama—he āhuatanga e mōhiotia ana ko te whakaata. Ka taea te whakamārama i tēnei āhuatanga mā te ture taketake e mōhiotia nei ko te Ture a Snell.
Ngā Mātāpono Taketake o te Ture a Snell
E whakaahua ana te ture a Snell i te whanaungatanga i waenga i te koki o te taunga me te koki o te whakaata o te hihi mārama i a ia e haere ana i roto i te rohe i waenga i ngā pāpāho e rua he rerekē ngā taupū whakaata. Ka taea te whakarāpopoto i te kaupapa matua o tēnei ture penei:
\[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
\]
Kei hea:
– Ko te \( n_1 \) te taupū whakaata o te reo tuatahi.
– Ko \( \theta_1 \) te koki taunga, arā, te koki i waenganui i te hihi taunga me te rārangi noa i te rohe o te reo.
– Ko \( n_2 \) te taupū whakaata o te reo tuarua.
– Ko te koki whakaataata ko \( \theta_2 \) te koki whakaataata, koinei te koki i waenganui i te hihi whakaataata me te rārangi noa i te rohe o te reo.
Taupū Whakaata
Ko te taupū whakaata (\( n \)) o tētahi reo he pūmau e whakaahua ana i te nui o te mārama ka piko, ka whakaata rānei ina uru ki taua reo. Ko te taupū whakaata te mea i hangaia penei:
\[
n = \frac{c}{v}
\]
Ko \( c \) te tere o te mārama i roto i te korehau, ā, ko \( v \) te tere o te mārama i roto i te reo. Hei tauira, ko te taupū whakaata o te hau he tata ki te 1,0, ko te taupū whakaata o te karāhe he tata ki te 1,5.
Whakamārama ā-tinana mō te Hurihuri o te Mārama
Ka taea te whakamārama i te hurihanga o te mārama mā te whakamahi i ngā mātāpono taketake o te whatu. Ina uru te mārama ki tētahi reo he rerekē te taupū hurihanga, ka tukuna ētahi o te pūngao mārama, ā, ka whakaatahia ētahi. Ka rerekē te tere o te wāhanga kua tukuna, ka puta he huringa o te ahunga. Koia te take ka taea e te karāhe te hanga i ngā mea kei muri i a ia kia ahua piko, kia nekehia rānei.
Ka pāngia hoki te hurihanga e te roanga ngaru o te mārama. E mōhiotia ana tēnei āhuatanga ko te marara, ā, ka kitea ina haere te mārama mā i roto i tētahi porohita, ka puta he whānuitanga tae. Ka puta te marara nā te mea ka hurihanga te mārama me ngā roanga ngaru rerekē i ngā koki rerekē ina haere i roto i tētahi reo he taupū hurihanga kore-taurite.
Ngā Tauira o te Whakamahinga o te Ture a Snell
1. Muka Whatu: Ko tētahi whakamahinga mahi a te Ture a Snell kei roto i te hangarau muka whatu. Ko ngā muka whatu he taura i hangaia ki te karāhe pai, ki te kirihou rānei e whakamahi ana i ngā mātāpono o te whakaata me te whakaata ā-roto katoa hei tuku raraunga. Ko te mārama e tukuna ana mā roto i ngā muka whatu ka whakaatahia tonutia, ka whakaatahia hoki i te taura, ka taea ai te tuku raraunga i ngā tere teitei me ngā tawhiti roa.
2. Ngā Arotahi me ngā Mōhiti: Ko ngā arotahi i roto i ngā karu hiko, ngā karu tiro, ngā kāmera, me ngā mōhiti, he mea hanga katoa i runga i te Ture a Snell. Mā te whakakotahi i ngā arotahi i hangaia ki ngā rauemi me ngā taupū whakaata motuhake, ka taea e tātou te arotahi i te mārama hei whakapai ake i te tirohanga, te whakanui rānei i ngā whakaahua o ngā mea tawhiti, o ngā mea tino iti rānei.
3. Te Whakamārama me te Marara: Ka whakamahia ngā whakamārama i roto i ngā taputapu whatu hei wehewehe i te mārama i runga i tōna roangaru. Ko te marara, te wehewehe rānei i te mārama ki roto i te whānuitanga o ngā tae, ka puta mai i ngā rerekētanga o te taupū whakaata mō ngā roangaru rerekē o te mārama. Mā te ture a Snell ka āwhina ki te whakamārama me pēhea te piko me te wehe i te mārama i roto i te whakamārama.
4. Upoko Makutu: Ko ngā pānga tirohanga pēnei i ngā matakite he tauira anō hoki o te hurihanga o te mārama. I raro i ētahi āhuatanga, ka taea e ngā rerekētanga o te mātotoru o te hau (nō reira ko tōna taupū hurihanga) te mea kia piko te mārama i roto i te huarahi e whakaatu ana i ngā mea tawhiti kei runga ake i te whenua, i te wai rānei.
Ngā Pātai Tauira me ngā Whakaoti
Hei mārama ake i te whakamahinga o te Ture a Snell, me titiro tātou ki tētahi tauira raruraru māmā:
> Pātai: Ka puta mai he hihi mārama mai i te hau ki te wai i te koki o te taunga o \( 30^\circ \). Mena ko te taupū whakaata o te hau he 1 (n_1) ā, ko te taupū whakaata o te wai he 1,33 (n_2), he aha te koki whakaata i roto i te wai (θ_2)?
Otinga:
Mā te whakamahi i te tātai Ture a Snell:
\[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
\]
Mā te whakakapinga \( n_1 = 1 \), \( \theta_1 = 30^\circ \), me \( n_2 = 1,33 \):
\[
1 \sin(30^\circ) = 1,33 \sin(\theta_2)
\]
Mai i te mea ko \( \sin(30^\circ) = 0.5 \):
\[
0.5 = 1.33 \sin(\theta_2)
\]
\[
\sin(\theta_2) = \frac{0.5}{1.33} \approx 0.375
\]
Mā te tango i te arc sine o te 0.375, ka whiwhi tātou:
\[
\theta_2 \tata \sin^{-1}(0.375) \tata 22^\circ
\]
Nō reira, ko te koki whakaata he tata ki te \( 22^\circ \).
Whakamutunga
Ko te Ture a Snell tētahi mātāpono taketake i roto i ngā mahi whatu e whakamārama ana i te hurihanga o te mārama i a ia e haere ana i roto i tētahi rohe i waenganui i ngā pāpāho e rua he rerekē ngā taupū hurihanga. Mā te mārama ki tēnei ture ka taea e tātou te hoahoa i ngā momo taputapu whatu he tino whai hua i roto i te oranga o ia rā, mai i ngā mōhiti kanohi ki ngā pūnaha whakawhitiwhiti muka-whatu. E whakaatu ana hoki tēnei matapaki i te mahi nui a te Ture a Snell i roto i ngā āhuatanga whatu taiao e kitea ana e tātou i ia rā.
