Tauira o ngā Pātai Whakamahinga Ngaru Mārama
He āhuatanga taiao ngā ngaru mārama, he maha ngā whakamahinga i roto i te oranga o ia rā me te pūtaiao. Mai i ngā tirohanga ki ngā hangarau whakawhitiwhiti kōrero hou, he mea nui te mārama ki ngā ngaru mārama i roto i te whanaketanga o te hangarau me te pūtaiao. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira whakamahinga o ngā ngaru mārama, me te whakamārama i ngā ariā taketake e pā ana ki tēnei kaupapa.
Pendahuluan
He momo pūngao e kitea ana e te kanohi tangata te mārama. Hei ngaru hikohiko, he āhuatanga tō te mārama pērā i te roangaru, te auau, me te tere. Kei roto i te awhe 400–700 nanometer (nm) te roangaru o te mārama e kitea ana. Mā te ako i ēnei āhuatanga, ka taea e tātou te mārama ki ngā tono maha e pā ana ki ngā ngaru mārama, pērā i te hangarau whatu, te whetū, me ētahi atu.
Ariā Taketake o ngā Ngaru Mārama
I mua i te hoatutanga o ngā tauira, he mea pai kia akohia ētahi ariā taketake e pā ana ki ngā ngaru mārama:
1. Tere o te Mārama: I roto i te korehau, ka haere te mārama i te tere pumau o te 299.792.458 mita ia hekona (ka whakaawhiwhia rānei ki te 3 x 10^8 m/s).
2. Roangaru me te Auautanga: Ko te whanaungatanga i waenga i te roangaru (λ) me te auautanga (f) o te mārama e whakaatuhia ana e te whārite:
\[
c = \lambda \cdot f
\]
ko \( c \) te tere o te mārama. Mai i tēnei whārite, ka taea e tātou te whakatau i tētahi mēnā e mōhio ana tātou ki tētahi atu.
3. Te Hurihuri o te Mārama: Ina haere te mārama mā roto i tētahi mata rohe i waenganui i ngā pāpāho rerekē e rua, ka rerekē tōna tere, ā, ka puta te hurihuri. Ko te ture a Snell te pūtake o tēnei āhuatanga:
\[
n_1 \cdot \sin(\theta_1) = n_2 \cdot \sin(\theta_2)
\]
ko \( n_1 \) me \( n_2 \) ngā taupū whakaata o te reo tuatahi me te reo tuarua, ā, ko \( \theta_1 \) me \( \theta_2 \) ngā koki taunga me te koki whakaata.
4. Te Whakararuraru: Ina tūtaki ngā ngaru mārama e rua, neke atu rānei, ka taea e rāua te whakakaha, te whakangāwari rānei tetahi i tetahi. Ka kiia tēnei he whakararuraru.
5. Te Whakapolarisasi: Ko te tukanga e huri ai ngā ngaru mārama ki te wiri i te papa kotahi anake.
Ngā Pātai Tauira me te Kōrero
I tēnei wāhanga, ka tūhuratia ētahi tauira rapanga e pā ana ki ngā whakamahinga o ngā ngaru mārama.
Pātai 1: Te Whakararuraru Mārama
E rua ngā āputa whaiti, he 0,5 mm te tawhiti, e whakamāramahia ana e te mārama, he roangaru 600 nm te roa. Ko te mata e whakaaturia ana te tauira pokanoa, e 2 mita te tawhiti mai i ngā āputa takirua. Tātaihia te tawhiti i waenganui i te whitiki kanapa tuatahi me tōna pokapū.
Kōrero:
Ka taea te tatau i te tauira pokanoa i hangaia e te āputa takirua mā te whakamahi i te tātai:
\[
y = \dfrac{m \cdot \lambda \cdot L}{d}
\]
Mō te awhi kanapa tuatahi, \( m = 1 \):
\[
y = \dfrac{1 \cdot 600 \times 10^{-9} \cdot 2}{0.5 \times 10^{-3}}
\]
\[
y = \dfrac{1200 \times 10^{-9}}{0.5 \times 10^{-3}}
\]
\[
y = 2.4 \times 10^{-3} \text{ mita} \]
\]
Nō reira, ko te tawhiti i waenganui i te awhi kanapa tuatahi me te pokapū he 2.4 mm.
Pātai 2: Te Hurihanga o te Mārama
Ka puta mai i te hau tētahi hihi mārama me te roangaru o te 550 nm ki te wai i te koki taunga o te 30°. Tātaihia te koki whakaata i roto i te wai. Ko te taupū whakaata o te wai he 1,33.
Kōrero:
Whakamahia te ture a Snell hei whakaoti i tēnei raruraru:
\[
1.0 \cdot \sin(30^\circ) = 1.33 \cdot \sin(\theta_2)
\]
\[
0.5 = 1.33 \cdot \sin(\theta_2)
\]
\[
\sin(\theta_2) = \dfrac{0.5}{1.33} \approx 0.375
\]
\[
\theta_2 = \sin^{-1}(0.375) \approx 22^\circ
\]
Nō reira, ko te koki whakaata i roto i te wai he tata ki te 22°.
Pātai 3: Te Whakapūmautanga o ngā Wai
Ka tukuna he mārama kore-porowhita ki roto i tētahi wai he 1,5 te taupū whakaata. Tātaihia te koki e tino porowhita ana te mārama (te koki a Brewster).
Kōrero:
Ka puta te koki Brewster (\( \theta_B \)) ina:
\[
\tan(\theta_B) = n
\]
\[
\tan(\theta_B) = 1.5
\]
\[
\theta_B = \tan^{-1}(1.5) \tata ki te 56.3^\circ
\]
Nō reira, ko te koki Brewster mō te wai he tata ki te 56.3°.
Whakamutunga
Mā te mārama ki ngā ariā taketake o te mārama me ōna ngaru ka taea e tātou te whakaoti rapanga maha e pā ana ki te mārama i roto i ngā horopaki mahi. E ai ki te kōrero, he mea nui ngā ariā pēnei i te pokanoa, te whakaata, me te whakapolarisasi i roto i ngā tono hangarau hou, tae atu ki ngā tirohanga me ngā whakawhitiwhiti kōrero. He mea nui te ako me te mārama hohonu ki ngā ngaru mārama, ehara i te mea mō ngā kaipūtaiao anake, engari mō te hunga katoa e hiahia ana ki te hangarau me te ahupūngao matua. Mā te whakamahi i tēnei mōhiotanga, ka taea e tātou te aro atu ki ngā wero o te whanaketanga hangarau ā muri ake nei.
