He tuhinga mō te Whārite o karaihe whakanui karaihe whakanuia
E ai ki te kaupapa o te karāhe whakanui (loupe), he iti te āhua o te mea ina tirohia mai i tawhiti, ā, he ātaahua te āhua ina tirohia mai i te tawhiti tata. Ko te rerekētanga o te rahi o te mea e kitea ana e te kanohi nā te rerekētanga o te koki i waenganui i te kanohi me te mea. Ina tawhiti rawa te mea i te kanohi, ka iti ake te koki i waenganui i te kanohi me te mea, ā, ka iti ake te ahua i hangaia ki te retina o te kanohi. I tetahi atu taha, ina tata te mea ki te kanohi, ka nui ake te koki i waenganui i te kanohi me te mea, ā, ka nui ake te ahua i hangaia ki te retina o te kanohi. Ko te tata atu ki te kanohi, ko te teitei ake o te koki i waenganui i te kanohi me te mea, ā, ka nui haere te ahua e hangaia ana ki te retina. Kia mōhio koe, ko te pūwāhi tata o te kanohi tangata he 25 cm, ā, kāore e taea te iti iho i te 25 cm te tawhiti i waenganui i te kanohi me te mea. Ka taea te whakatau ko te koki i waenganui i te kanohi noa o te tangata me te mea te mea nui rawa atu ina 25 cm te tawhiti i waenganui i te kanohi me te mea.
Mena kāore e taea te kite mārama i tētahi mea i muri i te whakatata atu ki te 25 cm mai i te kanohi noa, ka hiahiatia he taputapu whatu hei āwhina i te kanohi kia kite i te mea. Ko te mahi a te loupe, te whakanui rānei, he whakanui noa iho, hei whakanui ake i te koki i waenganui i te kanohi me te mea. Ko te kaha o te loupe ki te whakanui i te ahua ka whakaatuhia e te whakanui koki (M). Ko te loupe he whakanui koki 2x te nui, he pai ake i te loupe he whakanui koki 1x te nui. He rerekē te whakanui koki (M) i te whakanui raina (m).
Te whakanui koki o te loupe
Ko te whakanui koki o te loupe (M) ko te ōwehenga o te koki i waenganui i te kanohi me te ahua o te mea (θ') ina kitea te mea mā roto i te koropiko, ki te koki i waenganui i te kanohi me te mea (θ) ina kitea tika te mea mai i te pūwāhi tata o te kanohi noa. Mā te pāngarau:
M = θ' / θ
Te whārite o te whakanui koki o te loupe
Ka whakamāramahia te whārite whānui o te whakanui koki i roto i te arotake e whai ake nei. Hei whakamāmā ake i tō māramatanga, tirohia te ahua i raro nei.
I te ahua 1, ka kitea tika mai ngā mea mai i te pūwāhi tata o te kanohi noa.
N = te pūwāhi tata o te kanohi noa
θ = Te koki i waenganui i ngā kanohi me ngā pito e rua o ngā mea
h = ho = teitei o te mea
I te Pikitia 2, ka kitea ngā mea mā roto i tētahi loupe
s = do = te tawhiti i waenga i ngā mea me ngā karāhe arotahi
θ' = te koki i waenganui i te loupe me ngā pito e rua o te mea
h = ho = teitei o te mea
Mena he iti te koki, ko te pānihi θ ≈ θ
θ = h o / N
θ' = h o / do
Ko te whārite whānui o te whakanui koki (M) o te loupe:
M = te whakanui koki, N = te pūwāhi tata o te kanohi noa, do = te tawhiti o te mea. Koinei te whārite whānui mō te whakanui koki o te loupe. Ka kiia he whārite whānui nā te mea kāore te tawhiti i waenga i ngā mea me te loupe (do) i te uara motuhake, engari ka taea te whai uara.
Ko te whārite o te whakanui koki ina arotahi te kanohi ki tētahi pūwāhi tawhiti
A, mehemea, i te wā e tiro ana i ngā mea mā te whakamahi i te loupe, ka arotahi ngā kanohi o te kaimātakitaki ki te pūwāhi tawhiti? Mena he iti rawa te tawhiti o ngā kanohi, kāti he mutunga kore te tawhiti o te ahua. Kia mutunga kore te ahua, me rite te tawhiti i waenga i te mea me te porowhita ki te roa arotahi o te loupe (whakatairitehia te whakamārama mō te loupe (karāhe whakanui)). Tirohia te ahua i raro nei.
I te ahua 3, ka kitea tika mai ngā mea mai i te pūwāhi tata o te kanohi noa.
N = te pūwāhi tata o te kanohi noa
θ = te koki i waenganui i ngā kanohi me ngā pito e rua o ngā mea
h = te teitei o te mea
I te Pikitia 4, ka kitea ngā mea mā roto i tētahi loupe, ā, ko te wāhi e iti rawa ai te wāhi e nohoia ai ngā kanohi o te kaimātakitaki (e arotahi ana te kanohi ki te pūwāhi tawhiti).
s = do = te tawhiti i waenga i ngā mea me te arotahi = f = te roa arotahi o te loupe
θ' = te koki i waenganui i te koropiko me ngā pito e rua o te mea
h = te teitei o te mea
Mena he iti te koki, ko te pānihi θ ≈ θ
Ko te whārite o te whakanui koki o te loupe (M) ina iti rawa te taunga o te kanohi (te arotahi o te kanohi ki te pūwāhi tawhiti):
M = whakanui koki, N = tata ki te pūwāhi o te kanohi noa, f = te roa arotahi o te loupe.
E whakaatu ana tēnei whārite ko te whakanui koki (M) o te loupe he rite whakamuri ki te roa arotahi (f). Ko te teitei ake o te roa arotahi, ko te iti ake o te whakanui koki. I tetahi atu taha, ko te iti ake o te roa arotahi, ko te teitei ake o te whakanui koki. He karāhe pūkohu te loupe, nō reira me whakamahi he karāhe pūkohu he iti te roa arotahi, he karāhe pūkohu rānei he iti te radius o te piko kia nui ai te whakanui o te loupe.
Ko te whārite o te whakanui koki ina arotahi te kanohi ki te pūwāhi tata
A, mehemea, ina kite koe i ngā mea e whakamahi ana i te loupe, ka arotahi ngā kanohi o te kaimātakitaki ki te pūwāhi tata (ko te wāhi noho te mōrahi)? Mena he wāhi noho te kanohi mōrahi, ko te tawhiti o te ahua i hangaia e te loupe he rite ki te pūwāhi tata o te kanohi noa. He mariko ngā ahua, nō reira he kino te tawhiti o te ahua (in).
Ina rite te tawhiti o te ahua (di) ki te pūwāhi tata (N), ko te tawhiti o te mea (do):
Mena he iti te koki, ko te pānihi θ ≈ θ
Ko te whārite o te whakanui koki o te loupe ina arotahi te kanohi ki te pūwāhi tata (ko te urunga te mōrahi):
M = te whakanui koki, N = te pūwāhi e tata ana ki te kanohi noa, f = te roa arotahi o te loupe.
Whakatauritea te whārite o te whakanui koki ina iti rawa te wāhi noho (arotahi te kanohi ki te pūwāhi tawhiti) ki te whārite o te whakanui koki ina mōrahi te wāhi noho (arotahi te kanohi ki te pūwāhi tata).
I runga i ēnei whārite e rua, ka taea te whakatau he nui ake te whakanui koki ina teitei te taunga (te arotahi o te kanohi ki te pūwāhi tata).
