Te Roa Arotahi me te Pūtoro o te Piko o te Arotahi
I roto i te ao whatu, he taputapu te karāhe arotahi hei huri i te mārama me te hanga whakaahua. He rerekē ngā āhua me ngā rahi o ngā karāhe arotahi, engari i te nuinga o te wā, ka taea te wehewehe kia rua ngā momo matua: ngā karāhe arotahi pūkohu me ngā karāhe arotahi piko. He mea nui te mārama ki te mahi a ngā karāhe arotahi i roto i te whānuitanga o ngā tono, mai i ngā mōhiti tirohanga ki ngā karu tiro me ngā karu hiko. Ko tētahi āhuatanga matua o te mārama ki ngā karāhe arotahi ko tō rātou roa arotahi me te pūtoro piko. Ka matapakihia e tēnei tuhinga ngā tātai nui e pā ana ki te roa arotahi me te pūtoro piko, me ō rātou tono i roto i te oranga o ia rā.
Te Mārama ki te Roa Arotahi me te Pūtoro o te Piko
Ko te roa arotahi ko te tawhiti i waenga i te pokapū whatu o te arotahi me te pūwāhi arotahi, arā, te pūwāhi e tūtaki ai ngā hihi e whakarara ana ki te tuaka matua o te arotahi i muri i te whitinga i roto i te arotahi. Ko te roa arotahi te tohu o te reta **f**.
Ko te Pūtoro o te Piko ko te pūtoro o tētahi porowhita pohewa e rite ana tōna mata ki te mata o te arotahi. E rua ngā mata piko o ia arotahi, nō reira e rua ngā pūtoro piko e whai wāhi ana, e tohuhia ana e R1 me R2 mō ngā mata tuatahi me te tuarua.
Tātai Roa Arotahi Arotahi Angiangi
Ko te tātai matua e hono ana i te roa arotahi ki te pūtoro o te piko i roto i te arotahi angiangi ka hoatuhia e te Whārite Arotahi Angiangi, e te Tātai rānei a te Kaihanga Arotahi:
\[ \frac{1}{f} = (n – 1) \left( \frac{1}{R1} – \frac{1}{R2} \right) \]
Kei hea:
– ko f te roa arotahi o te arotahi
– ko n te taupū whakaata o te rauemi arotahi
– Ko R1 te pūtoro o te piko o te mata tuatahi o te arotahi
– Ko R2 te pūtoro piko o ngā mata o ngā karāhe e rua
Ngā Arotahi Pūpū me ngā Arotahi Kōpiko
Mō te karu arotahi kōpikopiko, he kōpikopiko te mata o te karu arotahi ki waho, nō reira he pai a R1, ā, he kino a R2. I tetahi atu taha, mō te karu arotahi kōpikopiko, he kōpikopiko te mata o te karu arotahi ki roto, nō reira he kino a R1, ā, he pai a R2. He mea nui tēnei hei whakatau i te tohu o te pūtoro piko ina whakamahia te tātai i runga ake nei.
Te Whakaputa i te Tātai Roa Arotahi
I ahu mai te whārite arotahi angiangi i ngā mātāpono taketake o ngā whatu āhuahanga me te ture whakaata a Snell. He maha ngā taahiraa e whai wāhi ana ki tōna whakaputanga:
1. Te whakamahi i te Ture a Snell:
E ai ki te ture a Snell, ko \( n1 \sin(\theta1) = n2 \sin(\theta2) \), ko \( n1 \) me \( n2 \) ngā taupū whakaata o ngā momo pāpāho e rua, ā, ko \( \theta1 \) me \( \theta2 \) ngā koki o te taunga me te whakaata.
2. Tātaritanga Hihi i te Mata Tuatahi:
Mō te mata tuatahi o te arotahi me te pūtoro o te piko R1, ka whakamahia e mātou te ture a Snell hei tatau i te whakaata o te mārama e pā ana ki taua mata.
3. Tātaritanga Hihi i te Mata Tuarua:
I muri i te haerenga o te hihi i te mata tuatahi, ka hurihia anō e te mata tuarua me te radius piko o R2.
4. Te Whakakotahi i te Whakaata o ngā Mata e Rua:
Mā te whakakotahi i ngā pānga whakaata o ngā mata e rua, me te whakamahi i te whakatata koki iti (ko te sin(θ) ≈ θ), ka taea e tātou te hanga i tētahi whārite e hono ana i te roa arotahi ki ngā rādius o te piko o ngā mata arotahi e rua.
Ngā Whakamahinga Whai Hua
He mea nui te roa o te arotahi me te pūtoro o te piko o te arotahi i roto i ngā momo mahi:
1. Ngā Mōhiti:
Ka whakamahia e ngā mōhiti kanohi ngā karāhe piko, piko rānei hei whakatika i te tirohanga. Ka whakamahia ngā karāhe piko mō te hyperopia (tiro tata), ko ngā karāhe piko ia ka whakamahia mō te myopia (tiro tawhiti). Me whakarite te roa o te arotahi o te karāhe kia rite ki ngā hiahia whakatika tirohanga a te tangata.
2. Kāmera:
He mea hanga ngā karāhe arotahi kāmera me ngā roa arotahi motuhake hei whakatau i te koki tirohanga me te whakanui. Ka kapi te karāhe arotahi poto (koki whānui) i te whānuitanga tirohanga whānui, ko te karāhe arotahi roa (whakaahua tawhiti) ia ka nui ake te whakanui.
3. Karuārai me te Karuārai:
Ka whakamahia e ngā karuārai he karāhe poto te roa o te arotahi hei whakanui i ngā mea ririki, ko ngā karuārai ia ka whakamahia he karāhe roa te roa o te arotahi hei tiro i ngā mea tawhiti pērā i ngā whetū me ngā aorangi.
4. Pūwhakaata:
Ka whakamahia e ngā pūwhakaata ngā karāhe hei arotahi i ngā whakaahua ki te mata. Me whakarite te roa o te arotahi o te karāhe pūwhakaata kia mārama, kia koi hoki ngā whakaahua.
Tauira raruraru
Hei whakamārama i te whakamahinga o te tātai roa arotahi, me titiro tātou ki te tauira e whai ake nei:
Pātai:
He karu arotahi kōpikopiko me te taupū whakaata o te 1,5, ko te radius o te piko o te 10 cm i runga i tōna mata tuatahi me te -15 cm i runga i tōna mata tuarua. Tātaihia te roa arotahi o te karu arotahi.
Otinga:
Mā te whakamahi i te tauira arotahi angiangi:
\[ \frac{1}{f} = (n – 1) \left( \frac{1}{R1} – \frac{1}{R2} \right) \]
E mōhiotia ana:
– n = 1,5
– R1 = 10 henemita
– R2 = -15 henimita
Whakakapia ēnei uara ki roto i te tātai:
\[ \frac{1}{f} = (1,5 – 1) \left( \frac{1}{10} – \frac{1}{-15} \right) \]
\[ \frac{1}{f} = 0,5 \left( \frac{1}{10} + \frac{1}{15} \right) \]
\[ \frac{1}{f} = 0,5 \left( \frac{15 + 10}{150} \right) \]
\[ \frac{1}{f} = 0,5 \times \frac{25}{150} \]
\[ \frac{1}{f} = 0,5 \times \frac{1}{6} \]
\[ \frac{1}{f} = \frac{1}{12} \]
Nō reira, ko te roa arotahi f he 12 cm.
Whakamutunga
He mea nui ngā ariā o te roa arotahi me te pūtoro o te piko hei mārama ki te mahi a ngā karāhe arotahi. Mā te tātai karāhe arotahi angiangi ka taea te tatau i te roa arotahi i runga i te pūtoro o te piko me te taupū whakaata o te rauemi karāhe arotahi. Ehara i te mea he mea nui te mārama ki tēnei tātai i roto i te ahupūngao anake, engari he tono mahi anō hoki i roto i ngā hangarau whatu rerekē e whakamahia ana e tātou i ia rā. Mai i ngā mōhiti kanohi ki ngā kāmera, ngā karu hiko, me ngā karu tiro, ka āwhina ēnei mātāpono whatu i a tātou ki te kite i te ao me te mārama me te taipitopito ake.
