27 Ngā tauira o te pokanoa me te whakarara o te mārama – te āputa takirua
1. E rua ngā āputa whaiti, he 0,5 mm te tawhiti, e whakamāramahia ana e te mārama, he 600 nm te roangaru. Tātaihia ngā uara koki iti rawa e toru e (1) puta ai te wawaotanga hanga (b) te wawaotanga whakangaro.
Kōrero
Ko ngā koki iti rawa e toru e puta ai te pokanoa hangahanga:
Ko ngā koki iti rawa e toru e puta ai te pokanoa hangahanga:
2. Ka whiti te mārama kotahi-tae mā roto i ngā kōhao whaiti, whakarara e rua. Ko te tawhiti i waenganui i ngā kōhao he 0,6 mm. Ko te tawhiti i waenganui i te mata me ngā kōhao he 60 cm. Ko te tauira pokanoa e puta ana i runga i te mata he rārangi kanapa me te rārangi pōuri e wehea ana e te tawhiti ōrite. Mena he 0,2 mm te tawhiti i waenganui i ngā rārangi kanapa e rua e tata ana, tātaihia te roangaru o te mārama e whakamahia ana.
Kōrero
E mōhiotia ana:
d = 0,6 mm = 0,0006 m = 6 x 10-4 m
y = 0,2 mm = 0,0002 m = 2 x 10-4 m
l = 60 henimita = 600 mm = 0,6 mita
I pātaihia: He aha te roangaru o te mārama e whakamahia ana?
Whakautu:
3. Ka whakamāramahia he kōhao takirua ki te mārama he 560 nm te roanga ngaru. Ka whakatakotoria he mata ki te 1 m mai i te āputa. Mena he 0,5 mm te tawhiti i waenganui i ngā kōhao e rua, ko te tawhiti i waenganui i ngā whitiki kanapa e rua e tata ana ko...
A. 1,00 mm
B. 1,12 mm
C. 1,40 mm
D. 1,60 mm
E. 2,00 mm
Kōrero:
E mōhiotia ana :
I pātaihia :
Te tawhiti i waenganui i ngā awhi kanapa e rua e tata ana (y)
Whakautu :
Ko te whakautu tika ko B.
4. Ko te tawhiti i waenganui i ngā rama o mua o ngā waka e rua he 110 cm. Ko te roanga ngaru toharite o te mārama e tukuna ana e ngā rama e rua he 600 nm. Mena ka kitea ngā rama e rua e te tangata ko tōna whānui o te karu he 2 mm, ko te tawhiti mōrahi i waenganui i te waka me te tangata kia āhua motuhake tonu ngā rama o ngā rama e rua ko...
A. 450 mita
B. 2500 mita
C. 3000 mita
D. 4000 mita
E. 5000 m
Kōrero:
E mōhiotia ana :
D = 2 mm = 2 x 10-3 mita
Roangaru o te mārama = 600 nm = 600 x 10-9 mita
Te tawhiti i waenganui i ngā rama waka e rua = 110 henemita = 1,1 mita
I pātaihia :
Ko te tawhiti i waenganui i te motuka me te tangata e mātaki ana i ngā rama e rua (l)?
Whakautu :
Kia kitea ai ngā rama e rua hei mea motuhake e rua, me nui ake te koki (theta) i te koki whakahirahira, e tutuki ai te whārite:
Ko te whakautu tika ko C.
5. E whakaatu ana te hoahoa i raro nei i te whakamātautau a Young. Mena ko d te tawhiti i waenganui i ngā kōhao e rua, ko L te tawhiti mai i te kōhao ki te mata, ā, ko P2 ko te tawhiti o te rārangi kanapa tuarua mai i te rārangi kanapa o waenganui, kātahi ko te roanga ngaru o te mārama i whakamahia (1 Å = 10-10 m) ko…
A. 3.000 Å
B. 4.000 Å
C. 5.000 Å
D. 5.500 Å
E. 6.000 Å
Kōrero
E mōhiotia ana :
Te tawhiti i waenganui i ngā kōhao e rua (d) = 1 mm = 1 x 10-3 mita
Te tawhiti mai i te kohao ki te mata (L) = 1 mita
Ko te tawhiti o te rārangi kanapa tuarua mai i te rārangi kanapa o waenganui (P2) = 1 mm = 1 x 10-3 mita
Raupapa (n) = 2 (ko te rama pokapū te rama tuatahi, nō reira n = 0. Ko te rama tuarua te rārangi rama tuatahi, nō reira n = 1, n = 2 rārangi rama tuarua)
I pātaihia Ko te roangaru o te mārama (λ) e whakamahia ana ko…
Whakautu :
Tātai pokanoa takirua (pokanoa hanga) :
d sin θ = n λ
hara θ ≈ tan θ = P2 / R = (1 x 10-3) / 1 = 1 x 10-3 mita
Te roanga ngaru o te māramatanga :
λ = d sin θ / n
λ = (1 x 10-3)(1 x 10-3) / 2 = (1 x 10-6) / 2
λ = 0,5 x 10-6 mita = 5 x 10-7 mita
λ = 5000 x 10-10 mita
λ = 5000 Å
Ko te whakautu tika ko C.
6. I roto i tētahi whakamātautau pokanoa rua-kōhao, ko ngā raraunga hua koia tēnei e whakaaturia ana i te ahua kei te taha. Nō reira, ko te uara roangaru i whakamahia ko… (1 m = 1010 Ā)
A. 4500 Å
B. 5000 Å
C. 6000 Å
D. 6500 Å
E. 7000 Å
Kōrero
E mōhiotia ana :
Te tawhiti i waenganui i ngā kōhao e rua (d) = 0,8 mm = 8 x 10-4 mita
Te tawhiti mai i te kohao ki te mata (L) = 1 mita
Te tawhiti o te rārangi kanapa tuawhā mai i te rārangi kanapa o waenganui (P) = 3 mm = 3 x 10-3 mita
Raupapa (n) = 4
I pātaihia Ko te roangaru o te mārama (λ) e whakamahia ana ko…
Whakautu :
Tātai pokanoa takirua (pokanoa hanga) :
d sin θ = n λ
hara θ ≈ tan θ = P / L = (3 x 10-3) / 1 = 3 x 10-3 mita
Te roanga ngaru o te māramatanga :
λ = d sin θ / n
λ = (8 x 10-4)(3 x 10-3) / 4 = (24 x 10-7) / 4
λ = 6 x 10-7 mita = 6000 x 10-10 mita
λ = 6000 Å
Ko te whakautu tika ko C.
7. Ko te ahua kei te taha he tātuhi o te ara o ngā hihi mārama i roto i te takahanga pokanoa rua S.1 tāne S2, ko ngā pūwāhi A me B he rārangi pōuri e rua e karapīpiti ana, ā, ko te roanga ngaru i whakamahia ko 6000 Å (1 Å = 10-10 m). Ko te tawhiti i waenganui i ngā kōhao e rua ko…
A. 0,015 mm
B. 0,2 mm
C. 1,5 mm
D. 1,6 mm
E. 1,8 mm
Kōrero
Ka tatauhia te tawhiti i waenganui i ngā kōhao e rua mā te whakamahi i te tātai te pokanoa hangahanga mā te whakaaro ko te tawhiti i waenganui i ngā rārangi pōuri e rua e karapīpiti ana he rite ki te tawhiti i waenganui i ngā rārangi kanapa e rua e karapīpiti ana.
E mōhiotia ana :
Te tawhiti mai i te kohao ki te mata (L) = 1 mita
Ko te roangaru i whakamahia (λ) = 6000 Å = 6000 x 10-10 mita = 6 x 10-7 mita
Ko te tawhiti i waenganui i te rārangi kanapa o waenganui ki te rārangi kanapa tuatahi (P) = 0,2 mm = 0,2 x 10-3 mita = 2 x 10-4 mita
Te raupapa rārangi kanapa tuatahi (n) = 1
I pātaihia Te tawhiti i waenganui i ngā āputa e rua (d)
Whakautu :
Tātai wawaotanga hangahanga :
d = n λ / sin θ
hara θ ≈ tan θ = P / L = (2 x 10-4) / 1 = 2 x 10-4 mita
Te tawhiti i waenganui i ngā āputa e rua :
d = n λ / hara θ = (1)(6 x 10-7) / (2 x 10-4)
d = (6 x 10-7) / (2 x 10-4) = (3 x 10-3)
d = 0,003 mita
d = 3 mm
8. Mena ka pāngia ngā ngaru mārama e rua, he 600 nm te roangaru, e hia te rerekētanga o te ara o ngā ngaru?
Kōrero: Mō te pokanoa hangahanga, ko te rerekētanga o ngā ara ngaru me nλ, ko n he tauoti. Mena ko n=0, ko te rerekētanga o ngā ara ngaru he 0 nm.
9. Ka tukuna he ngaru mārama he 500 nm te roangaru mā roto i tētahi āputa whaiti. Mena he 2 m te tawhiti i waenganui i te āputa me te mata, ā, he 5 mm te tawhiti i waenganui i te pokapū o te tauira āputa me te raupapa tuatahi, he aha te whānui o te āputa?
Kōrero: Mā te whakamahi i te whārite whakarara \( a\sin \theta = m\lambda \), ko \( a \) te whānui o te kohao, ko \( m \) te raupapa, ā, ko \( \theta \) te koki, ka kitea te whānui o te kohao: \( a = \frac{{m\lambda}}{{\sin \theta}} = \frac{{(1)(500 \times 10^{-9}\, \text{m})}}{{\sin \left( \frac{{5 \times 10^{-3}\, \text{m}}}{{2\, \text{m}}} \right)}} \approx 5 \times 10^{-4}\, \text{m} \).
10. Mena ka pāngia ngā ngaru mārama e rua, he 400 nm te roangaru, e hia te rerekētanga o te ara o ngā ngaru?
Kōrero: Mō te pokanoa whakangaro, ko te rerekētanga o ngā ara ngaru me \( (n + \frac{1}{2})\lambda \). Mena ko n=0, ko te rerekētanga o ngā ara ngaru he 200 nm.
11. He aha te mea ka tupu mēnā he nui ake te whānui o te āputa i roto i tētahi whakamātautau whakarara i te roanga ngaru o te mārama?
Kōrero: Mena he nui ake te whānui o te kōhao i te roanga ngaru o te mārama, ka kore e tino mārama te tauira whatuwhatu, ā, ka uaua ake te tirotiro.
12. I roto i te whakamātautau rua-kōhatu a Young me te roangaru o te 650 nm, ka wehea ngā kōhatu 0,1 mm e te 0,2 mm. He aha te tawhiti i waenga i ngā whitiki pouri tuatahi me te tuarua i runga i te mata e 1 m te tawhiti?
Kōrero: Ka taea te kimi i te tawhiti i waenga i ngā roopu pouri mā te whakamahi i te whārite taupatupatu \( y = \frac{{m\lambda D}}{{d}} \), ko \( m = 1 \) te raupapa tuatahi, ko \( D \) te tawhiti ki te mata, ā, ko \( d \) te tawhiti i waenga i ngā āputa. Kātahi ko te tawhiti i waenganui i ngā roopu pōuri tuatahi me te tuarua ko: \( y = \frac{{(1)(650 \times 10^{-9}\, \text{m})(1\, \text{m})}}{{0,1 \times 10^{-3}\, \text{m}}} – \frac{{(0)(650 \times 10^{-9}\, \text{m})(1\, \text{m})}}{{0,1 \times 10^{-3}\, \text{m}}} \approx 6,5\, \text{mm} \).
13. Mena ka pā te mārama he 700 nm te roangaru ki tētahi āputa takirua he 0,3 mm te tawhiti i waenganui i ngā āputa, he aha te tawhiti i waenganui i ngā whitiki kanapa tuatahi me te tuarua i runga i tētahi mata e 1,5 m te tawhiti?
**Kōrero**: Mā te whakamahi i tētahi whārite rite ki te pātai 5, ka kitea e tātou te tawhiti i waenga i ngā roopu kanapa tuatahi me te tuarua: \( y \approx 7\, \text{mm} \).
13. He aha te wawaotanga hangahanga, ā, me pēhea te puta?
Kōrero: Ka puta te whakararuraru hangahanga ina tūtaki ngā ngaru mārama e rua, ā, ko te rerekētanga o tō rāua ara he tauwehenga o te roanga ngaru (nλ). Ka hua ake tēnei i te whakanui ake i te kaha o te ngaru.
14. He aha te wawaotanga whakangaro, ā, me pēhea tōna putanga mai?
Kōrero: Ka puta te pokanoa whakangaro ina tūtaki ngā ngaru mārama e rua, ā, ko te rerekētanga o tō rāua ara he tauwehenga tauhou o te haurua o te roanga ngaru \((n + \frac{1}{2})\lambda\). Ka hua ake tēnei i te whakaiti, i te whakaiti rānei i te kaha o te ngaru.
15. I roto i te whakarara i roto i tētahi kōhao kotahi, ka aha te tauira whakarara mēnā ka whakaitihia te whānui o te kōhao?
Kōrero: Ki te whakaitihia te whānui o te kume, ka whānui ake te tauira whakawehewehe, ā, ka wehewehea ake ngā whitiki mārama me ngā whitiki pōuri.
16. Ka ahatia te tauira taupatupatu i roto i tētahi whakamātautau āputa-rua mēnā ka whakanuia te tawhiti i waenganui i ngā āputa?
Kōrero: Ki te whakanuia te tawhiti i waenga i ngā āputa, ka kikī ake te tauira pokanoa, ā, ka iti haere te tawhiti i waenga i ngā whitiki kanapa me ngā whitiki pōuri.
17. I roto i te whakamātautau rua-kōhatu a Young me te roanga ngaru o te 550 nm me te kōhatu o te 0,15 mm, he aha te tawhiti i waenga i te tuarima me te tekau o ngā whitiki kanapa i runga i te mata e 2 m te tawhiti?
Kōrero: Mā te whakamahi i tētahi whārite rite ki te raruraru 5, ka kitea e tātou te tawhiti i waenga i te tuarima me te tekau o ngā roopu kanapa: \( y \approx 36,67\, \text{mm} \).
18. He aha te pānga o te roanga ngaru ki ngā tauira whatuwhatu?
Kōrero: Ka whānui ake te tauira whakawhitiwhiti ina nui ake te roangaru, engari ka whaiti ake te tauira whakawhitiwhiti ina iti ake te roangaru.
19. Ki te pā te mārama he 450 nm te roangaru ki tētahi āputa takirua he 0,25 mm te tawhiti i waenganui i ngā āputa, he aha te tawhiti i waenganui i ngā whitiki pouri tuatahi me te tuarua i runga i te mata e 1 m te tawhiti?
Kōrero: Mā te whakamahi i tētahi whārite rite ki te pātai 5, ka kitea e tātou te tawhiti i waenga i ngā roopu pouri tuatahi me te tuarua ko: \( y \approx 1,8\, \text{mm} \).
20. Me pēhea te whakatau i te tūranga o te awhi kanapa i roto i te tauira pokanoa takirua?
Kōrero: Ka taea te whakatau i te tūranga o te whitiki kanapa i roto i te tauira pokanoa takirua mā te whakamahi i te whārite \( y = \frac{{m\lambda D}}{{d}} \), ko \( m \) te raupapa, ko \( \lambda \) te roanga ngaru, ko \( D \) te tawhiti ki te mata, ā, ko \( d \) te tawhiti i waenganui i ngā poka.
21. Me pēhea te whakatau i te tūranga o te awhi pōuri i roto i te tauira wehewehe kotahi-kōhao?
Kōrero: Ka taea te whakatau i te tūranga o te awhi pōuri i roto i te tauira wehewehenga kotahi-wāhanga mā te whakamahi i te whārite \( a\sin \theta = m\lambda \), ko \( a \) te whānui o te wāhanga, ko \( m \) te raupapa, ā, ko \( \theta \) te koki.
22. Ka ahatia te tauira pokanoa mēnā ka whakakapia te pūtake mārama ki tētahi roangaru poto ake?
Kōrero: Ki te poto ake te roanga ngaru, ka kikī ake te tauira pokanoa, ā, ka whakaitihia te tawhiti i waenga i ngā roopu kanapa me ngā roopu pōuri.
23. Me pēhea te mahi a te whakamātautau rua-kōhao hei whakaatu i te āhua ngaru o te mārama?
Kōrero: E whakaatu ana te whakamātautau rua-kōhatu i te āhua ngaru o te mārama mā te whakaputa i tētahi tauira whakararuraru kanapa me te pōuri ki runga i tētahi mata. Ka hangaia tēnei tauira mā te whakakotahitanga o ngā ngaru mai i ngā kōhatu e rua, e whakaatu ana i te āhua ngaru o te mārama.
24. Whakamāramahia te rerekētanga i waenga i te pokanoa me te whakarara.
Kōrero: Ko te whakararuraru e pā ana ki te whakakotahitanga o ngā ngaru e rua, neke atu rānei, ka hua ake he pikinga, he hekenga rānei o te kaha, ko te whakarara ia e pā ana ki te piko o ngā ngaru i a rātou e haere ana i roto i tētahi pūaha, i te taha rānei o tētahi mea.
25. I roto i te whakamātautau rua-kōhatu a Young, whakamāramahia he aha i puta ai ngā tauira pōuri me ngā tauira mārama ki te mata.
Kōrero: Ka puta ngā tauira pōuri me ngā tauira mārama nā te pokanoa hanga me te pokanoa whakangaro i waenga i ngā ngaru mai i ngā kōhao e rua. Ka puta ngā tauira mārama ina puta te pokanoa hanga (ko te rerekētanga ara he tauwehenga o te roanga ngaru), ā, ka puta ngā tauira pōuri ina puta te pokanoa whakangaro (ko te rerekētanga ara he tauwehenga tauhou o te haurua o te roanga ngaru).
25. He aha te rerekētanga o te tauira whakarara mō te āputa kotahi i tērā mō te āputa takirua?
Kōrero: Ko te tauira whakarara mō te āputa kotahi he whitiki kanapa kei waenganui me ngā whitiki pouri me ngā whitiki kanapa kei ia taha. I roto i te āputa takirua, he tauira pokanoa anō kei reira nā te taunekeneke o ngā ngaru mai i ngā āputa e rua, ka uaua ake te tauira.
Te Whakararuraru Mārama
He āhuatanga ā-tinana te whakararuraru e puta ana ina tūtaki, ka honoa ngā ngaru mārama e rua, neke atu rānei. Ka puta he tauira hou me te kaha ka nui ake, ka iti iho rānei i te kaha o ngā ngaru taketake.
Te Whakararuraru Hanga
Ka puta te pokanoa hangahanga ina he tauwehe te rerekētanga o te ara o ngā ngaru ki te roanga ngaru (nλ), ka hua ake he whakanui ake i te kaha o te ngaru. Ka puta tēnei tauira hei whitiki kanapa i runga i te mata i roto i ngā whakamātautau pēnei i te rua-kōhatu a Young.
Te Whakararuraru Whakangaro
Ka puta te pokanoa whakangaro ina he tauwehenga tauhou o te haurua o te roanga ngaru te rerekētanga o te ara o ngā ngaru . Ka hua ake tēnei i te whakaiti, i te whaiti rānei o te kaha o ngā ngaru, ka kitea hei whitiki pouri i roto i te tauira pokanoa.
Te Whakarerekētanga o te Mārama
He āhuatanga te whakarara e puta ana ina haere ngā ngaru mārama mā roto i tētahi kōhao whaiti, mā te taha rānei o tētahi mea. Mā tēnei ka piko, ka horapa hoki ngā ngaru mārama, ka puta he tauira whakarara āhua motuhake.
Te Whakarerekētanga mā roto i te Āputa Kotahi
I roto i tētahi āputa kotahi, ka puta he tauira kanapa i waenganui i te whakarara me ngā whitiki pouri me ngā whitiki mārama i ia taha. He rite whakamuri te whānui o te āputa ki te whānui o te tauira whakarara.
Te Whakarerekētanga mā roto i te Āputa Takirua
I roto i te āputa takirua, ka puta he tauira uaua ake i te whakarara. Haunga te tauira whakarara mai i ia āputa, kei reira anō hoki he tauira pokanoa i puta mai i te taunekeneke o ngā ngaru mai i ngā āputa e rua.
Ngā Whakamātautau Hira
Te Whakamātautau Takirua a Young
Ko te whakamātautau rua-kōhatu a Thomas Young tētahi huarahi hei tirotiro i te pokanoa me te whakarara. Ko ngā tauira mārama me te pōuri i runga i te mata e whakaatu ana i te āhua ngaru o te mārama, e tautoko ana i te ariā ngaru o te mārama.
Whakamutunga
Ko te pokanoa me te whakarara he āhuatanga e whakaatu ana i te āhua ngaru o te mārama. Mā te mārama ki te mahi a te pokanoa me te whakarara ka taea e tātou te mārama ake ki ngā āhuatanga me te whanonga o te mārama, he mea nui ēnei e whakamahia ana i roto i ngā mara pēnei i te tirohanga, te hangarau whakawhitiwhiti kōrero, me te rongoā.
Mā te ako i te pokanoa me te diffraction ka āwhina anō hoki i te whanaketanga o ngā hangarau pēnei i te karu hiko, ngā karu tiro, me ētahi atu taputapu whatu, e whakawhirinaki ana ki ngā tauira pokanoa me te diffraction hei whakapai ake i te taumira me te whai huatanga.
