2 Ngā tauira pātai mō ngā taputapu whatu kāmera
1. Ko te roa arotahi o tētahi kāmera anaro kotahi-arotahi he 10 cm. I te tīmatanga, ka whakaritea te kāmera ki te whakaahua i tētahi mea i te mutunga kore. Ki te hiahia tētahi ki te whakamahi i te kāmera ki te whakaahua i tētahi mea e 5 mita te tawhiti, tatauhia:
(a) Te tawhiti i waenganui i te kiriata me te arotahi ina whakaritea te kāmera ki te whakaahua i tētahi mea i te mutunga kore,
(b) Te tawhiti i waenganui i te kiriata me te arotahi ina whakaritea te kāmera ki te tango whakaahua i tētahi mea e 100 mita te tawhiti,
(c) Hurihia te tūnga o te arotahi mai i te tautuhinga mutunga kore ki te tautuhinga 100 mita. Kua nekehia te arotahi ki tawhiti atu i te kiriata, ki te tata atu rānei ki te kiriata?
Kōrero
E mōhiotia ana:
Roa arotahi arotahi (f) = 10 cm = 100 mm
Whakautu:
(a) Te tawhiti i waenganui i te kiriata me te arotahi ina whakaritea te kāmera ki te tango whakaahua i tētahi mea i te mutunga kore.
Te tawhiti i waenga i te arotahi me te kiriata = te tawhiti o te ahua (s')
Ko te tikanga o te tawhiti mutunga kore o te mea he mutunga kore te tawhiti o te mea (ngā mea rānei).
Ina whakaritea te kāmera ki te tango whakaahua i tētahi mea, ka whakaritea te tawhiti i waenga i te arotahi me te kiriata kia arotahi ai te hihi mārama mai i te mea e te arotahi hei hanga i tētahi ahua tika ki runga i te kiriata.
Mō te kaupapa o ngā karāhe kōpuku, kua whakamāramahia mēnā tawhiti o te mea = mutunga kore kātahi tawhiti atarangi = te roa o te arotahi (f) o te arotahi.
Te tawhiti i waenga i te arotahi me te kiriata = te tawhiti o te ahua (s') = te roa o te arotahi (f) o te arotahi = 100 mirimita.
(b) Te tawhiti i waenganui i te kiriata me te arotahi ina whakaritea te kāmera ki te tango whakaahua i tētahi mea e 5 mita te tawhiti.
Te tawhiti o te mea (s) = 5 m = 5000 mm
Roa arotahi o te karu (f) = 100 mm
Ko te tawhiti i waenganui i te kiriata me te arotahi = te tawhiti o te ahua, i tatauhia mā te whakamahi i te tātai arotahi pūkohu nā te mea he arotahi pūkohu te arotahi kāmera:
1/s' = 1/f – 1/s = 1/100 – 1/5000 = 50/5000 – 1/5000 = 49/5000
s' = 5000/49 = 102 mirimita
(c) Te huringa o te tūranga arotahi mai i te tautuhinga mutunga kore ki te tautuhinga 100 mita
Ina whakatakotoria hei whakaahua i tētahi mea i te mutunga kore, ko te tawhiti i waenganui i te arotahi me te kiriata he 100 mirimita. Ina whakatakotoria hei whakaahua i tētahi mea e 5 mita te tawhiti, ko te tawhiti i waenganui i te arotahi me te kiriata he 102 mirimita. Nō reira, ko te huringa o te tawhiti o te arotahi mai i te kiriata he 102 mm – 100 mm = 2 mm.
Kua nekehia te arotahi ki tawhiti atu i te kiriata, ki te tata atu rānei ki a ia? Ko te tikanga, kua nekehia te arotahi ki tawhiti atu i te kiriata nā te mea i te mutunga kore, ko te tawhiti i waenga i te arotahi me te kiriata = te roa arotahi o te arotahi. Mena ka nekehia te arotahi ki tata atu ki te kiriata, ko te tawhiti i waenga i te arotahi me te kiriata he iti iho i te 100 mm.
2. E rua ngā karāhe kōpikopiko, ko te roa arotahi o ia karāhe he 40 mm me te 20 mm. E whakamahia ana ngā karāhe e rua i roto i tētahi kāmera anaro hei whakaahua i tētahi mea e 10 mita te tawhiti. Whakatauhia:
(a) Te tawhiti i waenganui i te kiriata me te arotahi me te roa arotahi o te 40 mm ina whakaritea te kāmera ki te whakaahua i te mea. Tātaihia hoki te whakanui rārangi.
(b) Te tawhiti i waenganui i te kiriata me te arotahi me te roa arotahi o te 20 mm ina whakaritea te kāmera ki te whakaahua i te mea. Tātaihia hoki te whakanui rārangi.
Kōrero
E mōhiotia ana:
Ko te roa arotahi o te karu arotahi ko te 1 (f1) = 40 mm
Ko te roa arotahi o te karu arotahi ko te 2 (f2) = 20 mm
Te tawhiti o te mea (s) = 10 m = 10.000 mm
Whakautu:
(a) Te tawhiti i waenganui i te kiriata me te arotahi me te roa arotahi o te 40 mm ina whakaritea te kāmera ki te whakaahua i tētahi mea
Ko te tawhiti i waenganui i te kiriata me te arotahi = te tawhiti o te ahua (s'), i tatauhia mā te whakamahi i te tātai arotahi pūkohu nā te mea he arotahi pūkohu te arotahi kāmera:
1/s' = 1/f – 1/s = 1/40 – 1/10.000 = 250/10.000 – 1/10.000 = 249/10.000
s' = 10.000/249 = 40,2 mm
Whakanuitanga rārangi (m):
m = s'/s = 40,2/10.000 = 0,004 ngā wā
(b) Te tawhiti i waenganui i te kiriata me te arotahi me te roa arotahi o te 20 mm ina whakaritea te kāmera ki te whakaahua i tētahi mea
Ko te tawhiti i waenganui i te kiriata me te arotahi = te tawhiti o te ahua (s'), i tatauhia mā te whakamahi i te tātai arotahi pūkohu nā te mea he arotahi pūkohu te arotahi kāmera:
1/s' = 1/f – 1/s = 1/20 – 1/10.000 = 500/10.000 – 1/10.000 = 499/10.000
s' = 10.000/499 = 20,0 mm
Whakanuitanga rārangi (m):
m = 20,0/10.000 = 0,002 ngā wā
Whakatauritea te whakanui rārangi i tēnei tataunga ki te mea o mua. I runga i ēnei whakanui rārangi e rua, ka taea te whakatau ko te whakanui rārangi ka piki ake me te roa o te arotahi o te karu. Nō reira, i te wā e whiriwhiri ana i tētahi karu kāmera, me whakaaro anō hoki koe ki tōna roa arotahi. Mō ngā mea tawhiti, me whakamahi he karu he roa ake te roa arotahi hei whakanui i te ahua i hangaia e te karu, ā, i tuhia ki te kiriata.
Ki te whakaahuahia e tātou tētahi mea tawhiti mā te whakamahi i tētahi kāmera me te karāhe whakanui, ka whakanuia e tātou te ahua i hangaia mā te whakawhiti karāhe me te whakamahi i tētahi karāhe he roa ake te arotahi. Ka taea e tātou te whakawhiti karāhe nā te mea he maha ngā karāhe o te karāhe whakanui e titoa ana me ngā roa arotahi rerekē.
Mēnā kei te tango whakaahua koe i ngā mea tawhiti mā te whakamahi i tētahi kāmera arotahi kotahi, he pai ake te whakamahi i tētahi arotahi he roa te arotahi. He papatahi te āhua o tēnei arotahi.
