ahupūngao

1. He aha te whakaterenga nā te kaha ā-papatipu i te mata o te Marama? Ko te papatipu o te Marama = 7.35 x 1022 ^kg , ko te pūtoro o te Marama he 1.7 x ¹⁰⁶ m, ko te pūmau whānui he 6.67 x 10 ^-11 N ^m² / ^kg²

otinga

Ko te tātai o te ture tuarua o te nekehanga a Newton :

Ko te tātai o te ture a Newton mō te kaha ā-ao :

G = pūmau whānui, M = papatipu o Papatūānuku, m = papatipu o te mea, r = te tawhiti i waenganui i te pokapū o Papatūānuku me te mea. Mena kei te mata o Papatūānuku te mea, r = te radius o Papatūānuku

Whakakapia a F ki te whārite 1 ki a F ki te whārite 2:

He aha te whakaterenga nā te kaha ā-papa i te mata o te Marama?

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2. Ko te whakaterenga nā te kaha ā-papa i te mata o Papatūānuku ko g. I R (ko R te mata o Papatūānuku), ko te whakaterenga nā te kaha ā-papa ko…

otinga

R = te pūtoro o te Ao. I te R i runga ake i te mata o te Ao = i te 2R i runga ake i te pokapū o te Ao.

I te R i runga ake i te mata o te Ao, ko te whakaterenga nā te kaha ā-papa = ¼ karamu. Mena ko te g = 9.8 m/s² ^, i te R i runga ake i te mata o te Ao, ko te whakaterenga nā te kaha ā-papa = 2.45 m/ ^s².

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1. Ngā raruraru me ngā otinga o te ture a Newton mō te kaha ā-ao
2. Ngā kaha ā-papa, ngā raruraru taumaha, me ngā otinga
3. Te whakaterenga nā ngā raruraru ā-papa me ngā otinga
4. Ngā raruraru me ngā otinga o te amiorangi tukutahi-whenua
5. Ngā raruraru me ngā otinga o te ture a Kepler ngā raruraru me ngā otinga

Pānuitia atu

5 Te kaha ā-papatipu Taumaha – Ngā Raru me ngā Otinga

1. He aha te kaha o te kaha ā-papa e pā ana ki tētahi mea i te mata o te Ao? Ko te papatipu o te Ao = 5.98 x 1024 ^kg , ko te papatipu o te mea = 1000 kg, ko te pūtoro o te Ao he 6.38 x 106 ^m.

Mōhiotia:

Papatipu o te Ao (m _E ) = 5.98 x ¹⁰²⁴ kg

Papatipu o te mea (m _o ) = 1000 kg

Ko te radius o te Ao (r _E ) = 6.38 x ¹⁰⁶ m

Pūmau whānui (G) = 6.67 x 10 ^-11 N ^m² / ^kg²

Te whakaterenga nā te kaha ā-papa (g) = 9.8 m/s ²

E hiahiatia ana: Te Mana o te Āhuatanga

Rongoā:

w = taumaha, F = kaha, G = pūmau ao, m _E = papatipu o Papatūānuku , m _o = papatipu o te mea , r = te tawhiti i waenganui i te pokapū o Papatūānuku me te mea.

Kei te mata o Papatūānuku te mea, nō reira ko r = te radius o Papatūānuku

Te taumaha o te mea ( te ture nekehanga tuarua a Newton ):

w = mg

w = (1000 kg)(9.8 m/ ^s² )

w = 9800 N

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2. He aha te kaha o te kaha ā-papa e pā ana ki tētahi mea i te 10,000 mita i runga ake i te mata o te Ao? Ko te papatipu o te Ao = 5.98 x 1024 ^kg , ko te papatipu o te mea = 1000 kg, ko te pūtoro o te Ao he 6.38 x 106 ^m.

Rongoā:

3. Ko te taumaha o tētahi waka mokowhiti ko w. Mena ko D te whānui o Papatūānuku, tātaihia te taumaha o te waka mokowhiti ina kei te 2D te teitei o te waka mokowhiti i runga ake i te mata o Papatūānuku.

Mōhiotia:

D = te whānui o te Ao,

R = te pūtoro o te Ao

1 D = 2 R, 2 D = 4 R

E hiahiatia ana: te taumaha o te waka mokowhiti i te 2D i runga ake i te mata o te Ao?

Rongoā:

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4. Ko te ōwehenga o ngā papatipu o te aorangi A me te aorangi B he 2 : 3, ko te ōwehenga ia o te pūtoro o te aorangi A me te aorangi B he 1 : 2. Mena ko te taumaha o tētahi mea i runga i te aorangi A he w, he aha te taumaha o te mea i runga i te aorangi B?

Mōhiotia:

Papatipu o te aorangi A (m _A ) = 2

Papatipu o te aorangi B (m _B ) = 3

Te whānui o te aorangi A (r _A ) = 1

Te whānui o te aorangi B (r _B ) = 2

Papatipu o te mea = m

Taumaha o te mea i runga i te aorangi A = w

E hiahiatia ana: Te taumaha o te mea i runga i te aorangi B

Rongoā:

Ko te whārite o te kaha o te taumaha mai i te ture ā-papatipu a Newton:

w = taumaha, G = pūmau ā-papa, M = papatipu o te aorangi, m = papatipu o te mea, r = te tawhiti i waenga i te mea me te aorangi. Mena kei runga te mea i te mata o te aorangi, ko te r = te radius o te aorangi.

Te taumaha o te mea i runga i te aorangi A:

Te taumaha o te mea i runga i te aorangi B:

He rite te papatipu o te mea, nō reira me whakakapi te m ki te w/2G.

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5. Ka whakarewaina poutū mai i te mata o Papatūānuku tētahi rōkete, ko tōna taumaha he w. Ko D te whānui o Papatūānuku. Ina eke te rōkete ki te teitei o te 0.5 D i runga ake i te mata o Papatūānuku, he aha te taumaha o te rōkete?

Mōhiotia:

Taumaha o te rōkete = w

Ko te radius o Papatūānuku = te tawhiti mai i te pokapū o Papatūānuku = R

Te whānui o te whenua = D = 2R

E hiahiatia ana: Taumaha o te rōkete i te teitei o te rōkete i te 0.5 D i runga ake i te mata o te Ao.

Rongoā:

0.5 D = 0.5 (2R) = R

Ko te tawhiti o te rōkete mai i te pokapū o Papatūānuku = te radius o Papatūānuku + te radius o te rōkete mai i te mata o Papatūānuku = R + R = 2R

Ko te taumaha te kaha o te papatipu e pā ana ki tētahi mea. He rite whakamuri te kaha o te papatipu (F) ki te tapawhā o te tawhiti mai i te pokapū o te whenua (R) kia rite whakamuri ai te taumaha ki te tapawhā o te tawhiti.

1. Ngā raruraru me ngā otinga o te ture a Newton mō te kaha ā-ao
2. Ngā kaha ā-papa, ngā raruraru taumaha, me ngā otinga
3. Te whakaterenga nā ngā raruraru ā-papa me ngā otinga
4. Ngā raruraru me ngā otinga o te amiorangi tukutahi-whenua
5. Ngā raruraru me ngā otinga o te ture a Kepler ngā raruraru me ngā otinga

Pānuitia atu

1. Ko te roa arotahi o te karu arotahi he 400 cm, ā, ko te roa arotahi o te karu kanohi he 20 cm. Mēnā kei te wātea te kanohi , tautuhia:

a) Te whakanui whānui o te karu tiro (M)

b) te tawhiti o te ahua mai i te arotahi arotahi ( d _ob '),

c) te tawhiti o te ahua mai i te karu kanohi ( d _{o c} )

d) te tawhiti i waenganui i ngā karāhe

Mōhiotia:

Ko te roa arotahi o te arotahi arotahi (f _ob ) = 400 cm

Ko te roa arotahi o te karu arotahi ( f _{o c} ) = 20 cm

Ka whakangā te kanohi kia tae te ahua tūturu i hangaia e te karu arotahi ki te pūwāhi arotahi o te karu arotahi me te pūwāhi arotahi tuatahi o te karu kanohi.

Rongoā:

a) Te whakanui whānui (M)

M = f _ob / f _{o c}

M = 400 henimita / 20 henimita = 20 X

He mariko, he huripokitia te ahua.

b) Te tawhiti o te ahua mai i te arotahi arotahi ( d _ob ')

Ki te wātea te kanohi, ko te tawhiti o te ahua mai i te arotahi arotahi ( d _ob ') = te roa arotahi o te arotahi arotahi ( f _ob ) = 400 cm = 4 m.

c) Te tawhiti o te ahua tūturu mai i te karu kanohi ( d _{o c} )

Ki te wātea te kanohi, ko te tawhiti i waenganui i te ahua tūturu me te arotahi kanohi (s _{o c} ) = te roa arotahi o te arotahi kanohi (f _oc ) = 20 cm = 0.2 m.

d) Te tawhiti i waenganui i ngā karāhe

Ko te tawhiti i waenga i ngā karāhe = te roa o te karu tiro (l) = te roa arotahi o te karāhe whāinga (f _ob ) + te roa arotahi o te karāhe kanohi (f _oc ) = 400 cm + 20 cm = 420 cm.

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2. Ko te tawhiti i waenganui i te karu arotahi me te karu kanohi he 20 cm . Ko te whakanui whānui o te karu tiro ina okioki te kanohi he 40X. Tātaihia te roa arotahi o te karu kanohi (f _{o c} ) me te roa arotahi o te karu arotahi (f _ob )

Mōhiotia:

te roa o te karu tiro (l) = 20 cm

te whakanui whānui o te karu tiro (M) = 40

Rongoā:

Ki te wātea te kanohi, ko te roa arotahi o te karu arotahi (f _oc ) + te roa arotahi o te karu arotahi (f _ob ) = te roa o te karu tiro (l)

f _{o c} + f _ob = l

f _ob = l – f _{o c}

f _ob = 20 – f _{o c} —–> whārite 1

Te whakanui whānui o te karu tiro (M):

M = f _ob / f _{o c}

f _ob = M f _{o c}

f _ob = 40 f _{o c} —–> whārite 2

Te roa o te arotahi o te karu kanohi :

Whakakapia te f _ob i te whārite 1 ki te f _ob i te whārite 2:

f _ob = 20 – f _{o c}

40 f _{o c} = 20 – f _{o c}

40 f _{o c} + f _{o c} = 20

41 f _{o c} = 20

f _{o c} = 20 cm / 41

f _{o c} = 0.5 cm

Ko te roa arotahi o te karu arotahi = 0.5 cm.

Te roa o te arotahi o te karu arotahi :

f _ob = 20 – f _oc

f _ob = 20 – 0.5

f _ob = 19.5 cm

[wpdm_package id='876′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. Ko te roa arotahi o te karu arotahi he 2 cm, ā, ko te roa arotahi o te karu kanohi he 5 cm. Ko te tawhiti i waenganui i te karu arotahi me te karu kanohi he 30 cm. Tātaihia te whakanui whānui me te tawhiti o te mea mai i te karu arotahi ina wātea te kanohi.

Mōhiotia:

Ko te roa arotahi o te arotahi arotahi (f _ob ) = 2 cm

Ko te roa arotahi o te karu arotahi (f _oc ) = 5 cm

Te tawhiti i waenga i ngā karāhe (l) = 30 cm

Pūwāhi tata (N) = 25 cm

Rongoā:

(a) te whakanui whānui

Ko te tātai o te whakanui whānui:

M = m _ob M _oc

M = te whakanui whānui, m _ob = te whakanui o te karu arotahi, M _oc = te whakanui koki kanohi

Te whakanui ake i te karu arotahi ina wātea te kanohi (m _ob ):

Te tawhiti o te ahua mai i te arotahi arotahi (d _ob '):

d _ob ' = l – f _oc = 30 cm – 5 cm = 25 cm

Te tawhiti o te mea mai i te arotahi arotahi (d _ob ):

He karaihe hūpeke te karāhe arotahi, nō reira kei te roa arotahi te tohu tāpiri.

He tohu tāpiri kei te tawhiti o te ahua nā te mea he tūturu te ahua, nā te mea rānei e tika ana ngā hihi mā roto i te ahua.

Te whakanui i te karu arotahi :

Te whakanui koki o te kanohi ina wātea te kanohi (M _ok ):

M _oc = N / f _oc = 25 cm / 5 cm = 5X

Te whakanui whānui:

M = m _ob M _oc = (12.5)(5) = 62.5X

(b) Te tawhiti o te mea mai i te arotahi arotahi (d _ob )

Ko te tawhiti o te mea mai i te karu arotahi he 2 cm.

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2. Kei roto i tētahi karuārai he karuārai arotahi 5X me te karuārai kanohi 20X. Ko te tawhiti i waenganui i ngā karuārai he 15 cm. (a) Whakatauhia te whakanui whānui mēnā he marino te kanohi (b) whakatauhia te roa o te arotahi o te karuārai kanohi (c) te roa o te arotahi o te karuārai arotahi

Mōhiotia:

Ko te whakanui o te karāhe arotahi (m _ob ) = 5X

Te whakanui i te karu o te kanohi ( _Moc ) = 20X

Pūwāhi tata (N) = 25 cm

Ko te tawhiti i waenganui i ngā karāhe (l) = 15 cm

Rongoā:

(a) Te whakanui whānui (M)

M = m _ob M _oc

M = (5)(20) = 100X

(b) Te roa o te arotahi o te karu kanohi (f _oc )

Ko te tātai mō te whakanui koki o te karu kanohi (M _oc ) ina whakangā te kanohi:

M _oc = N / f _oc

Te roa o te arotahi o te karu arotahi:

f _oc = N / M _oc = 25 cm / 20 = 1.25 cm

(c) te roa o te arotahi o te arotahi arotahi (f _ob )

Ko te tātai mō te whakanui i te karu arotahi ina wātea te kanohi:

Te tawhiti o te ahua tūturu mai i te karu arotahi (d _ob '):

d _ob ' = l – f _oc = 15 cm – 1.25 cm = 13.75 cm

Te tawhiti o te mea mai i te arotahi arotahi (d _ob ):

Te roa o te arotahi o te karu arotahi (f _ob ):

Ko te roa arotahi o te karāhe arotahi = 2.29 cm

3. Ko te roa o te arotahi o te karu arotahi he 0.9 cm, ā, ko te roa o te arotahi o te karu kanohi he 2.5 cm. Ka whakamahia te karu hiko e te kanohi noa kāore he wāhi noho, ā, ko te whakanui whānui he 90 ngā wā. Tātaihia te tawhiti i waenganui i te mea me te karu arotahi. N = 25 cm.

Mōhiotia:

Ko te roa arotahi o te arotahi arotahi (f _ob ) = 0.9 cm

Ko te roa arotahi o te karu arotahi (f _ok ) = 2,5 cm

Ko te whakanui whānui (M) = 90 ngā wā

Ko te pūwāhi tata o te kanohi noa (N) = 25 cm

He iti rawa te wāhi e noho ai te kanohi.

E hiahiatia ana: Te tawhiti i waenganui i te mea me te karu arotahi (s _ob )

Rongoā:

Ko te whārite o te whakanui koki katoa ina iti rawa te taunga:

Tātaihia te tawhiti o te mea i te taha o te karāhe arotahi (s _ob ) mā te whakamahi i te whārite o te whanaungatanga i waenga i te roa arotahi o te karāhe arotahi (f _ob ), te tawhiti i waenga i te mea me te karāhe arotahi (s _ob ) me te tawhiti i waenga i te ahua me te karāhe arotahi (s _ob '):

4. Ko te roa arotahi o te karu arotahi he 1.8 cm, ā, ko te roa arotahi o te karu kanohi he 6 cm. Ka whakamahia te karu hiko e te kanohi noa, kāore he wāhi noho, ko te tawhiti i waenganui i te karu arotahi me te karu kanohi he 24 cm. Tātaihia te tawhiti o te mea mai i te karu arotahi.

Mōhiotia:

Ko te roa arotahi o te arotahi arotahi (f _ob ) = 1.8 cm

Ko te roa arotahi o te karu arotahi (f _ok ) = 6 cm

Ko te tawhiti i waenganui i te karāhe arotahi me te karāhe kanohi = te roa o te karuārai (l) = 24 cm

He iti rawa te wāhi noho.

E hiahiatia ana: Te tawhiti i waenga i te mea me te karu arotahi (s _ob )

Rongoā:

Ina iti rawa te taunga, ko te tawhiti i waenga i te ahua whakamutunga me te karu arotahi he mutunga kore, e whakaaturia ana i te ahua i raro nei.

Ko te tawhiti i waenganui i te karāhe arotahi me te karāhe kanohi (l) = te roa arotahi o te karāhe kanohi (f _ok ) + te tawhiti i waenganui i te ahua me te karāhe arotahi (s _ob ').

s _ob ' = l – f _ok = 24 cm – 6 cm = 18 cm

Tātaihia te tawhiti i waenganui i te mea me te karāhe arotahi (s _ob ) mā te whakamahi i te whārite o te whanaungatanga i waenganui i te roa arotahi o te karāhe arotahi (f _ob ), te tawhiti i waenganui i te mea me te karāhe arotahi (s _ob ) me te tawhiti i waenganui i te ahua me te karāhe arotahi (s _ob '):

E 2 henemita te tawhiti i waenganui i te mea me te karu arotahi.

[wpdm_package id='874′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. Ka whakatakotoria tētahi mea 2 mm te teitei ki te 10 cm mai i tētahi karāhe whakanui . Tata ki te pūwāhi N = 25 cm. Tātaihia te whakanui koki me te teitei o te ahua.

Mōhiotia:

Teitei o te mea (h _o ) = 2 mm

Pūwāhi tata (N) = 25 cm

Te tawhiti o te mea (d _o ) = 10 cm

E hiahiatia ana: Te whakanui koki (M) me te teitei o te ahua (h _i )

Rongoā:

M = N / s

M = 25 henimita / 10 henimita

M = 2.5

Ko te teitei o te ahua = 2.5 x 2 mm = 5 mm.

2. Ka whakamahia he karāhe arotahi 25 cm te roa hei karāhe whakanui. Whakatauhia (a) te whakanui koki ina arotahi te kanohi ki tōna pūwāhi tata N = 25 cm (b) te whakanui koki ina okioki te kanohi.

Mōhiotia:

Pūwāhi tata (N) = 25 cm

Ko te roa arotahi o te karāhe whakanui (f) = 25 cm

Ko te tohu tāpiri e tohu ana he karāhe arotahi hūnuku te karāhe arotahi.

Rongoā:

(a) te whakanui koki ina arotahi te kanohi ki tōna pūwāhi tata N = 25 cm

M = (N/f) + 1

M = (25 henimita / 25 henimita) + 1

M = 1 + 1

M = 2 X

Mena he 1 henemita te teitei o te mea, ko te teitei o te ahua he 2 x 1 henemita = 2 henemita.

(b) te whakanui koki ina whakangāwari te kanohi

M = N / f

M = (25 henimita / 25 henimita)

M = 1 X

Mena he 1 henemita te teitei o te mea, ko te teitei o te ahua he 1 x 1 henemita = 1 henemita.

3. Ka whakatakotoria tētahi mea 1 cm te teitei ki mua i tētahi karāhe arotahi 10 cm te roa. Tātaihia (a) te teitei o te ahua ina arotahi te kanohi ki tōna pūwāhi tata N = 25 cm (b) Te teitei o te ahua ina whakangā te kanohi.

Mōhiotia:

Ko te teitei o te mea (h _o ) = 1 cm

Ko te roa o te arotahi (f) = 10 cm

Pūwāhi tata (N) = 25 cm

Rongoā:

(a) Ko te teitei o te ahua ina arotahi te kanohi ki tōna pūwāhi tata N = 25 cm

M = (N/f) + 1

M = (25 henimita / 10 henimita) + 1

M = 2.5 + 1

M = 3.5 X

Mena he 1 henemita te teitei o te mea, ko te teitei o te ahua he 3.5 x 1 henemita = 3.5 henemita.

(b) Te teitei o te ahua ina whakangā te kanohi.

M = N/f

M = 25 henimita / 10 henimita

M = 2.5 X

Mena he 1 henemita te teitei o te mea, ko te teitei o te ahua he 2.5 x 1 henemita = 2.5 henemita.

4. Ko te whakanui koki ina wātea te kanohi = 5X. Mena ko te pūwāhi tata = 25 cm, he aha te roa arotahi o te karāhe whakanui?

Mōhiotia:

Teitei o te mea (h _o ) = 2 mm

Whakanui koki (M) = 5X

Pūwāhi tata (N) = 25 cm

E hiahiatia ana: Te roa arotahi

Rongoā:

Ko te tātai o te whakanui koki ina whakangā te kanohi:

M = N/f

5 = 25 henimita / wh

f = 25 henimita / 5

f = 5 henemita

Ko te roa arotahi o te karāhe whakanui = 5 cm.

5. Ka kitea tētahi mea e tētahi tangata mā te whakamahi i tētahi karāhe whakanui, ā, ko te roa arotahi he 15 cm. Mena ko te pūwāhi tata o ngā kanohi o te tangata = 30 cm, tātaihia te whakanui whānui o te karāhe whakanui.

Mōhiotia:

Ko te pūwāhi tata o te kanohi noa (N) = 30 cm

Ko te roa o te arotahi o te karāhe whakanui (f) = 15 cm (tohu tāpiri nā te mea kei te hūnuku te karāhe)

E hiahiatia ana: te whakanui mōrahi

Rongoā:

Ka puta te whakanui mōrahi ina tino teitei te wāhi noho o te kanohi. Ka puta te whakanui koki o te karāhe whakanui ina tino teitei te wāhi noho o te kanohi:

M = (N/f) + 1

M = (30 henimita / 15 henimita) + 1

M = 2 + 1

M = 3 ngā wā

6. He karāhe whakanui he 20 diopters te kaha whatu, ā, e whakamahia ana e te tangata he kanohi noa, he 25 cm te whānui. Mēnā he iti rawa te wāhi e uru ai, tātaihia te whakanui iti rawa.

Mōhiotia:

Te pūwāhi tata o te kanohi noa (N) = 25 cm

Te mana o te karāhe whakanui (P) = 20 diopters

E hiahiatia ana: Te whakanui iti rawa

Rongoā:

Te roa o te arotahi o te karāhe whakanui:

P = 1/f

20 = 1/w

wh = 1/20

f = 0.05 mita

f = 5 henemita

Ko te whakanui koki ina iti rawa te taunga:

M = N / f

M = (25 henimita / 5 henimita)

M = 5 ngā wā

[wpdm_package id='872′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. Ko te kaha o te karu tirohanga he -2 Diopters. Ko te tawhiti i waenganui i te kanohi me te karu tirohanga he 2 cm.

(a) He karāhe whatuwhatu, he karāhe wehewehe rānei tō te mōhiti?

(b) He aha te roa o te arotahi o te karu arotahi?

(c) He kanohi tiro tata, he kanohi tiro tawhiti rānei? Mēnā he kanohi tiro tawhiti, he aha te pūwāhi tawhiti?

Mōhiotia:

Mana arotahi (P) = -2 Diopters

Rongoā:

(a) Karāhe arotahi whakawhāiti, karāhe arotahi wehewehe rānei

Ko te tohu tango o te kaha o te karāhe arotahi e tohu ana he karāhe arotahi wehewehe te karāhe arotahi.

(b) Te roa o te arotahi

P = 1/f

-2 = 1/w

f = 1/-2 = -0.5 m = -50 cm

Ko te roa arotahi o te arotahi wehewehe he 50 cm.

(c) Kanohi tiro tata, kanohi tiro tawhiti rānei?

-1/ d _i = 1/ f – 1/ d _o

-1/ d _i = -1/50 – 1/~ = -1/50 – 0

-1/ d _i = -1/50

d _i = 50 cm

Ko te tawhiti o te ahua he 50 cm + 2 cm = 52 cm . Ko te 52 cm te pūwāhi tawhiti o te kanohi tiro tawhiti. Mō te kanohi noa, ko te pūwāhi tawhiti ko te mutunga kore.

[irp]

2. Ko te kaha o te karu tirohanga he 4 diopters. Ko te tawhiti i waenganui i te kanohi me te karu tirohanga he 2 cm.

(a) He karāhe whāiti, he karāhe wehewehe rānei tō te karāhe?

(b) He aha te roa o te arotahi o te karu arotahi?

(c) He kanohi kite tata , he kanohi kite tawhiti rānei ? Mēnā he kanohi kite tata, he aha te pūwāhi tata?

Mōhiotia:

mana arotahi (P) = 4 Diopters

Rongoā:

(a) Karāhe arotahi whakawhāiti, karāhe arotahi wehewehe rānei

Ko te tohu tāpiri o te kaha o te arotahi e tohu ana he arotahi hūnuku te arotahi whakapā.

(b) Te roa o te arotahi

P = 1/f

4 = 1/w

f = 1/4 = 0.25 m = 25 cm

Ko te roa arotahi o te karāhe arotahi e 25 henemita.

(c) Kanohi tiro tata, kanohi tiro tawhiti rānei?

-1/ d _i = 1/ f – 1/ d _o

-1/ d _i = 1/25 – 1/23 = 23/575 – 25/575 = -2/575

– d _i = 575/-2 = -287.5 cm = -2.875 mita

d _i = 287.5 henimita = 2.875 mita s

Ko te tawhiti o te ahua ko 287.5 henimita + 2 henimita = 289.5 henimita . Ko te 289.5 henimita te pūwāhi tata o te kanohi e kitea tata ana . Mō te kanohi noa, ko te pūwāhi tata ko 25 henimita.

3. Ko te pūwāhi tata o te kanohi he 16 henimita, ko te pūwāhi tawhiti he 80 henimita. Mēnā ka whakamahia e ia ngā mōhiti, ka kitea māramatia e ia ngā mea tawhiti. Mā te whakamahi i te mōhiti, ko te tawhiti o te mea tata rawa ka kitea māramatia ko….

A. 13 1/3 henimita

B. 20 henemita

C. 36 henimita

D. 48 1/3 henimita

Mōhiotia:

Ko te pito tawhiti o te tangata he 80 henemita, nō reira, e kiia ana kei te pāngia te tangata e te tirohanga tata. Ko te tirohanga tata i puta mai i te karu kanohi he piko ake i tōna āhua i te kanohi noa, nō reira ka whakaitihia te roa o te arotahi o te karu kanohi. Nā tēnei ka kore te hihi o te mārama mai i te pito tawhiti (mutunga mutunga kore) e arotahi ki te retina engari ka arotahi ki mua o te retina.

E hiahiatia ana: Te tawhiti o te mea tata rawa atu ka kitea mārama mā te whakamahi i ngā mōhiti

Rongoā:

Ko te pito tawhiti o te tangata he 80 cm. Me whakaputa e te karāhe o te mōhiti he ahua i te tawhiti o te 80 cm ki mua i a ia. Kei mua i ngā kanohi me te karāhe o ngā mōhiti te ahua kia mariko, kia poutū hoki te ahua. Nō reira, ko te tawhiti o te ahua (d') = -80 cm. Mena he mōhiti te tangata, ka taea e ia te kite mārama i ngā mea tino tawhiti. Nō reira, ko te tawhiti o te mea (d) = te pito tawhiti o te kanohi noa = mutunga kore = ~.

Te roa o te arotahi o te karu arotahi:

1/f = 1/d + 1/d'

1/f = 1/~ + (- 1/80)

1/f = 0 – 1/80

1/f = – 1/80

wh = – 80 / 1

wh = – 80 henemita

Ko te tikanga o te roa arotahi kua tohua ki te kino ko te arotahi o te mōhiti e whakamahia ana he arotahi kōpiko, he arotahi wehewehe rānei.

Mena kei te whakamahi te tangata i te karāhe mōhiti kotahi, e hia te tata o te mea tata rawa atu ka kitea mārama? Te roa o te arotahi o te karāhe (f) = -80 cm. Me whakaputa e te karāhe he ahua i te tawhiti o te 16 cm i mua i te kanohi me te karāhe, kia mariko ai te ahua, ā, kia tohu kino. Nō reira, ko te tawhiti o te ahua (d') = -16 cm.

1 / d = 1 / f – 1 / d' = -1/80 – (-1/16) = -1/80 + 1/16 = -1/80 + 5/80 = 4/80

d = 80/4 = 20 henemita.

Ko te mea tata rawa atu ka kitea mārama ko te 20 cm.

Ko te whakautu tika ko B.

4. I runga i te ahua, ka taea te whakatau ko…

Rongoā:

Kanohi tiro tawhiti	Kanohi tiro tawhiti + karāhe arotahi

Karāhe hūpeke = karāhe kōpuku = karāhe pai

Ko te whakautu tika ko B.

5. Ko te pūwāhi tata o te tangata e pāngia ana e te hypermetropy he 2 m. Hei kite i te tangata kanohi noa, me whakamahi te tangata i ngā karu…

A. -1.5 Diopters

B. -2.5 Diopters

C. +3.5 Diopters

D. +4.5 Diopters

Mōhiotia:

Ko te pūwāhi tata o te hunga e pangia ana e te hypermetry (tirotiro tawhiti) = 2 mita

Ko te pūwāhi tata o te kanohi noa = 25 cm = 0.25 mita

E hiahiatia ana: Te mana o ngā mōhiti arotahi

Rongoā:

Me whakaputa e te karu arotahi he ahua i te tawhiti o te 2 mita i mua i te kanohi kia mariko ai te ahua, ā, kia tohu kino ai. Nō reira, ko te tawhiti o te ahua (d') = – 2 mita.

Hei tiro pērā i te tangata kanohi noa, ko te tawhiti o te mea (d) = te pūwāhi tata o te kanohi noa = 25 cm = 0.25 mita.

Te roa o te arotahi o te karāhe o te mōhiti:

1/f = 1/d + 1/d'

1/f = 1/0.25 + (-1/2) = 1/0.25 – 1/2 = 8/2 – 1/2 = 7/2

wh = 2/7

Ko te roa arotahi kua tohua ki te tohu pai ko te arotahi o te karāhe e whakamahia ana he arotahi pai, he arotahi kōpuku rānei, he arotahi hūnuku rānei.

Te mana o te arotahi:

P = 1 / f = 1: 2/7 = 1 x 7/2 = 7/2 = +3.5 Ngā Diopters

Ko te whakautu tika ko C.

[wpdm_package id='870′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. Ko te mana o te karāhe whakapā he -5 Diopt.

(a) He karāhe whakapūmau , he karāhe wehewehe rānei te karāhe whakapā?

(b) He aha te roa o te arotahi o te karāhe whakapā?

(c) He kanohi kite tata , he kanohi kite tawhiti rānei ? Mēnā he kanohi kite tata, he aha te pūwāhi tata?

Mōhiotia:

Mana o te karu (P) = -5 D

Rongoā:

(a) He karāhe arotahi, he karāhe arotahi rānei?

Ko te tohu tango o te kaha o te arotahi e tohu ana ko te arotahi whakapā te arotahi wehewehe.

(b) Te roa o te arotahi?

P = 1/f

-5 = 1/w

f = 1/-5 = -0.2 m = -20 cm

Ko te roa arotahi o te karāhe arotahi wehewehe he 20 henemita.

(c) Kanohi tiro tata, kanohi tiro tawhiti rānei?

-1/ d _i = 1/ f – 1/ d _o

-1/ d _i = -1/20 – 1/~ = -1/20 – 0

-1/ d _i = -1/20

d _i = 20 cm

Ko te tawhiti o te ahua he 20 henimita. Ko te 20 henimita te pūwāhi tawhiti o te kanohi tiro tawhiti. Mō te kanohi noa, ko te pūwāhi tawhiti ko te mutunga kore.

[irp]

2. Ko te kaha o te karāhe whakapā he 1.5 Diopters.

(a) He karāhe whakapūmau, he karāhe wehewehe rānei te karāhe whakapā?

(b) He aha te roa o te arotahi o te karāhe whakapā?

(c) He kanohi kite tata, he kanohi kite tawhiti rānei? Mēnā he kanohi kite tawhiti, he aha te pūwāhi tawhiti?

Mōhiotia:

Mana arotahi (P) = 1.5 Diopters

Rongoā:

(a) te arotahi whakapūmau, te arotahi wehewehe rānei

Ko te tohu tāpiri o te kaha o te arotahi e tohu ana he arotahi hūnuku te arotahi whakapā.

(b) Te roa o te arotahi

P = 1/f

1.5 = 1/w

f = 1/ 1.5 = 0.67 mita = 67 henimita

Ko te roa arotahi o te karāhe arotahi ko 67 henemita.

(c) Kanohi tiro tata, kanohi tiro tawhiti rānei

-1/ d _i = 1/ f – 1/ d _o

-1/ d _i = 1/67 – 1/25 = 25/1675 – 67/1675 = -42/1675

– d _i = -1675/42 = -40 henimita = -0.40 mita

d _i = 40 cm

Ko te tawhiti o te ahua he 40 henimita. Ko te 20 henimita te tawhiti e tata ana ki te pito o te kanohi tiro tawhiti. Mō te kanohi noa, ko te pito tata he 25 henimita.

[wpdm_package id='868′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. He mutunga kore te pūwāhi tawhiti o te kanohi noa. Ko te roa arotahi o te karu arotahi he 2.5 cm. Tātaihia (a) te tawhiti o te ahua (b) te kaha o te karu arotahi.

Mōhiotia:

Ko te roa o te arotahi o te karu arotahi (f) = te tawhiti i waenga i te cornea me te retina = +2.5 cm ( Ko te tohu tāpiri e tohu ana i te karu arotahi e hūnuku ana ).

Ko te tawhiti o te mea ( d _o ) = te mutunga kore

E hiahiatia ana : te tawhiti o te ahua ( d _i )

Rongoā:

(a) te tawhiti o te ahua

1/f = 1/ d _o + 1/ d _i

f = te roa arotahi , d ₌ te tawhiti o te mea , d = te tawhiti _o te ahua

1/ d _i = 1/ f – 1/ d _o = 1 / 2.5 – 1 / ~ = 1 / 2.5 – 0

1/ d _i = 1 / 2.5

d _i = 2.5 cm = 0.025 mita

Mena he mutunga kore te tawhiti o te mea, ko te tawhiti o te ahua (d _i ) = te roa arotahi (f)

(b) te mana o te arotahi

P = 1/f = 1/ 0.025 m = 40 I roto i ngā kōwhiringa

[irp]

2. Ko te pūwāhi tata o te kanohi noa he 25 cm. He rite te tawhiti o te ahua ki te tawhiti i waenga i te cornea me te retina = 2.5 cm. Whakatauhia (a) te roa arotahi (b) te kaha o te arotahi

Mōhiotia:

Ko te tawhiti o te mea ( d _o ) = 25 cm

Ko te tawhiti o te ahua ( d _i ) = 2.5 cm

Rongoā:

(a) te roa o te arotahi (f)

1/f = 1/ d _o + 1/ d _i

1/w = 1/25 + 1/2,5 = 1/25 + 10/25 = 11/25

f = 2.27 henimita = 0.0227 mita

Ko te tohu tāpiri e tohu ana i te karu arotahi e hūnuku ana.

(b) te mana o te arotahi (P)

P = 1/f = 1/ 0.0227 = 44 I roto i ngā kōwhiringa

3. Ko tētahi o ngā taputapu whatu ko ngā kanohi tangata . Tāutuhia ngā āhuatanga o te ahua i hangaia e ngā kanohi tangata…

A. Tūturu, poutū

B. Tūturu, hurihia

C. Mariko, poutū

D. Mariko, hurihia

otinga

Ko te pūwāhi tata o te kanohi noa he 25 cm. Ko te pūwāhi tata ko te pūwāhi e tata ana ki te kanohi e arotahi tika ana te mea ki te retina i te wā e taunga katoa ana. He iti iho i te 25 cm te whānui o te kanohi tangata, nō reira he iti iho hoki te roa arotahi o te karu arotahi o te kanohi i te 25 cm. Nō reira, me nui ake te tawhiti o te mea (d) i te roa arotahi o te karu arotahi o te kanohi (f).

He karāhe pūkohu te karāhe kanohi. Nō reira, he rite tonu ngā āhuatanga o te ahua i hangaia e te karāhe kanohi ki te ahua i hangaia e te karāhe pūkohu. Ko ngā āhuatanga o te ahua i hangaia e te karāhe kanohi ina nui ake te tawhiti (s) o te mea i te roa arotahi (f):

tūturu, hurihia, iti iho

Me arotahi te ahua ki te retina nā te mea ka hurihia e te retina ngā ngaru mārama hei tohu hiko ka tukuna ki te roro. Ahakoa ka hurihia te ahua, ka hurihia e te roro tangata kia poutū kia poutū ai ngā mea e kitea ana e te kanohi.

Ina kite koe i tētahi rākau mai i tawhiti, ka āhua iti iho te rākau i tōna rahi tuturu. He rite tēnei ki ngā āhuatanga o te ahua kua whakaitihia.

Ko te whakautu tika ko A.

4. Ka taea e te kanohi te kite i tētahi mea ina arotahi te ahua ki te retina, kei reira ngā āhuatanga o te ahua…

A. Mariko, poutū, nui ake

B. Mariko, hurihia, iti iho

C. Tūturu, hurihia, iti iho

D. Tūturu, poutū, iti iho

otinga
– He karāhe pūkohu te karāhe o te kanohi, nō reira, he rite ngā āhuatanga o te ahua i hangaia e te karāhe kanohi ki ngā āhuatanga o te ahua i hangaia e te karāhe pūkohu.

– Ko te pūwāhi tata o te kanohi noa, arā, ko te tawhiti tata rawa e kitea tonutia ana e ngā kanohi, he 25 cm. He iti rawa ngā karu o te kanohi, ā, he iti iho i te 25 cm te pūtoro piko me te roa arotahi o te karu arotahi. Nō reira, ka taea te whakatau he nui ake te tawhiti o te mea i te roa arotahi.

– Ki te nui ake te tawhiti o te mea i te roa arotahi, ko ngā āhuatanga o te ahua i hangaia e te kanohi tangata i te retina he tūturu, he huripokitia, he iti ake. Ahakoa he huripokitia te ahua, ka hurihia e te roro kia poutū i a tātou e kite ana.

Ko te whakautu tika ko C.

[wpdm_package id='866′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. Kei te 5 cm te tawhiti o tētahi mea, he 5 cm te teitei, mai i tētahi karāhe arotahi 15 cm te roa . Tātaihia te tawhiti o te ahua , te whakanui o te ahua, te teitei o te ahua me ngā āhuatanga o te ahua.

Mōhiotia:

Ko te roa o te arotahi (f) = 15 cm

Ko te tohu tāpiri e tohu ana he tūturu te pūwāhi arotahi, he tika rānei te whiti o ngā hihi mā roto i te pūwāhi.

Ko te teitei o te mea (h _o ) = 5 cm

Ko te tawhiti o te mea ( d _o ) = 5 cm

E hiahiatia ana : te tawhiti o te ahua , te whakanui o te ahua , te teitei o te ahua me ngā āhuatanga o te ahua

Rongoā:

Te hanganga o te ahua mā te arotahi whakapūmau :

Te tawhiti o te ahua ( d _i ):

1/ d _i = 1/ f – 1/ d _o = 1/15 – 1/5 = 1/15 – 3/15 = -2/15

d _i = -15/2 = -7.5 cm

Ko te tohu tango e tohu ana he mariko te ahua, kāore rānei ngā hihi e tika ana mā roto i te ahua.

Te whakanui i te ahua ( m ):

m = – d _i / d _o = -(-7.5)/5 = 7.5/5 = 1.5

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

Te teitei o te ahua (h _i ):

m = h _i / h _o

h _i = m h _o = (1.5)5 = 10/3 = 7.5 cm

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

Ngā āhuatanga o te ahua

– mariko

– poutū

– He nui ake te ahua i te mea

– He nui ake te tawhiti o te ahua i te tawhiti o te mea

[irp]

2. Kei te 30 cm te tawhiti o tētahi mea, 10 cm te teitei , mai i tētahi karāhe arotahi 15 cm te roa . Tātaihia te tawhiti o te ahua, te whakanui o te ahua, te teitei o te ahua me ngā āhuatanga o te ahua.

Mōhiotia:

Ko te roa o te arotahi (f) = 15 cm

Ko te tohu tāpiri e tohu ana he tūturu te pūwāhi arotahi, he tika rānei te whiti o ngā hihi mā roto i te pūwāhi.

Te teitei o te mea (h) = 10 cm

Ko te tawhiti o te mea (s) = 30 cm

E hiahiatia ana: Te tawhiti o te ahua, te whakanui o te ahua, te teitei o te ahua me ngā āhuatanga o te ahua

Rongoā:

Te hanganga o te ahua e te karu arotahi:

Te tawhiti o te ahua ( d _i ):

1/ d _i = 1/ f – 1/ d _o = 1/15 – 1/30 = 2/30 – 1/30 = 1/30

d _i = 30/1 = 30 cm

Ko te tohu tāpiri e tohu ana he tūturu te ahua, he tika rānei ngā hihi e tika ana mā roto i te ahua.

Te whakanui i te ahua ( m ):

m = – d _i / d _o = -(30)/30 = -30/30 = -1

Ko te tohu tango e tohu ana kua hurihia te ahua.

Te teitei o te ahua (h _i ):

m = h _i / h _o

h _i = m h _o = (-1)10 = -10 cm

Ko te tohu tango e tohu ana kua hurihia te ahua.

Ngā āhuatanga o te ahua

– tūturu, ka whiti rānei ngā hihi mā roto i te ahua

– hurihia

– He rite te teitei o te ahua ki te teitei o te mea.

– He rite te tawhiti o te ahua ki te tawhiti o te mea.

[irp]

3. Kei te 30 cm te tawhiti o tētahi mea, 10 cm te teitei , mai i tētahi karāhe arotahi 20 cm te roa . Tātaihia te tawhiti o te ahua, te whakanui o te ahua, te teitei o te ahua me ngā āhuatanga o te ahua.

Mōhiotia:

Te roa arotahi f) = 20 cm

Ko te tohu tāpiri e tohu ana he tūturu te pūwāhi arotahi, he tika rānei te whiti o ngā hihi mā roto i te pūwāhi.

Te teitei o te mea (h) = 10 cm

Ko te tawhiti o te mea ( d _o ) = 30 cm

E hiahiatia ana: Te tawhiti o te ahua , te whakanui o te ahua , te teitei o te ahua me ngā āhuatanga o te ahua

Rongoā:

Te tawhiti o te ahua ( d _i ):

1/ d _i = 1/ f – 1/ d _o = 1/20 – 1/30 = 3/60 – 2/60 = 1/60

d _i = 60/1 = 60 cm

Ko te tohu tāpiri e tohu ana he tūturu te ahua, he tika rānei ngā hihi e tika ana mā roto i te ahua.

Te whakanui i te ahua ( m ):

m = – d _i / d _o = -(60)/30 = -2

Ko te tohu tango e tohu ana kua hurihia te ahua.

E rua ngā wā e nui ake ai te ahua i te mea.

Te teitei o te ahua (h _i ):

m = h _i / h _o

h i = m h _o = (-2)10 = -20 cm

Ko te tohu tango e tohu ana kua hurihia te ahua.

Ngā āhuatanga o te ahua

– tūturu

– hurihia

– he nui ake te teitei o te ahua i te teitei o te mea

– he nui ake te tawhiti o te ahua i te tawhiti o te mea

[irp]

4. I runga i te ahua i raro nei, tautuhia te roa o te arotahi o te karu arotahi!

Mōhiotia:

Te tawhiti o te mea ( d _o ) = 20 cm

Te tawhiti o te ahua ( d _i ) = 30 cm

E hiahiatia ana : Te roa arotahi (f)

Rongoā:

1/ d _o + 1/ d _i = 1/ f

d _o = tawhiti o te mea ( tohu tāpiri nā te mea ka puta ngā hihi mā roto i te mea )

d _i = te tawhiti o te ahua ( tohu tāpiri nā te mea ka puta ngā hihi i roto i te ahua )

f = te roa o te arotahi ( tohu tāpiri nā te mea ka puta ngā hihi mā roto i te pūwāhi arotahi, he pūwāhi tūturu rānei te pūwāhi arotahi )

Te roa o te arotahi:

1/w = 1/20 + 1/30 = 3/60 + 2/60 = 5/60

f = 60/5 = 12 henemita

5. Ko te tawhiti o te mea he 30 cm, ā, ko te roa arotahi he 20 cm. Tātaihia te whakanui o te ahua.

Mōhiotia:

Ko te roa o te arotahi o te karāhe arotahi (f) = 20 cm

Ko te tohu tāpiri e tohu ana he tūturu te pūwāhi arotahi, he whiti rānei ngā hihi mā roto i te ahua.

Te tawhiti o te mea ( d _o ) = 30 cm

E hiahiatia ana: Te whakanui i te ahua (M)

Rongoā:

Te tawhiti o te ahua:

1/ d _i = 1/ f – 1/ do = 1/20 – 1/30 = 3/60 – 2/60 = 1/60

d _i = 60/1 = 60 cm

Te whakanui i te ahua:

M = d _i / d _o = 60 cm / 30 cm = 60/30 = 2 ngā wā

[wpdm_package id='864′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu

1. Kei te 15 cm te tawhiti o tētahi mea, 5 cm te teitei, mai i tētahi karāhe arotahi e 30 cm te roa . Tātaihia te tawhiti o te ahua , te whakanui o te ahua, te teitei o te ahua, me ngā āhuatanga o te ahua.

Mōhiotia:

Ko te roa o te arotahi (f) = -30 cm

Ko te tohu tango e tohu ana he mariko te pūwāhi arotahi, kāore rānei ngā hihi e tika ana mā roto i te pūwāhi.

Ko te teitei o te mea (h _o ) = 5 cm

Ko te tawhiti o te mea (d _o ) = 15 cm

E hiahiatia ana: Te tawhiti o te ahua (d _i ), te whakanui o te ahua (m), te teitei o te ahua (h _i ) me ngā āhuatanga o te ahua.

Rongoā:

Te hanganga o te ahua mā te arotahi wehewehe:

Te tawhiti o te ahua (d _i ):

1/d _i = 1/f – 1/d _o = -1/30 – 1/15 = -1/30 – 2/30 = -3/30

d _i = -30/3 = -10 cm

Ko te tohu tango e tohu ana he mariko te ahua, kāore rānei ngā hihi e tika ana mā roto i te ahua.

Te whakanui i te ahua (m):

m = – d _i / d _o = -(-10)/15 = 10/15 = 2/3

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

He 2/3 te iti iho o te ahua i te mea.

Te teitei o te ahua (h _i ):

m = h _i / h _o

h _i = mh _o = (2/3)5 = 10/3 = 3.3 cm

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

Ngā āhuatanga o te ahua:

Ngā āhuatanga o te ahua i hangaia e te whakaata wehewehe:

– mariko

– poutū

– he iti ake te ahua i te mea

– he iti ake te tawhiti o te ahua i te tawhiti o te mea

[irp]

2. Kei te 60 cm te tawhiti o tētahi mea, 10 cm te teitei, mai i tētahi karāhe arotahi e wehe ana i te tawhiti arotahi 30 cm. Tātaihia te tawhiti o te ahua, te whakanui o te ahua, te teitei o te ahua, me ngā āhuatanga o te ahua.

Mōhiotia:

Ko te roa o te arotahi (f) = -30 cm

Ko te tohu tango e tohu ana he mariko te pūwāhi arotahi, kāore rānei ngā hihi e tika ana mā roto i te pūwāhi.

Te teitei o te mea (h) = 10 cm

Ko te tawhiti o te mea (d _o ) = 60 cm

E hiahiatia ana: Te tawhiti o te ahua (d _i ), te whakanui o te ahua (m), te teitei o te ahua (h _i ) me ngā āhuatanga o te ahua

Rongoā:

Te hanganga o te ahua mā te arotahi wehewehe:

Te tawhiti o te ahua (d _i ):

1/d _i = 1/f – 1/d _o = -1/30 – 1/60 = -2/60 – 1/60 = -3/60

d _i = -60/3 = -20 cm

Ko te tohu tango e tohu ana he mariko te ahua, kāore rānei ngā hihi e tika ana mā roto i te ahua.

Te whakanui i te ahua (m):

m = -d _i /d _o = -(-20)/60 = 20/60 = 1/3

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

He 1/3 te iti iho o te ahua i te mea.

Teitei o te ahua (h _i ):

m = h _i / h _o

h _i = mh _o = (1/3)10 = 10/3 = 3.3 cm

Ko te tohu tāpiri e tohu ana kei te poutū te ahua.

Ngā āhuatanga o te ahua

– mariko nā te mea kāore ngā hihi e tika ana mā roto i te ahua

– poutū

– he iti ake te ahua i te mea

– he iti ake te tawhiti o te ahua i te tawhiti o te mea

[wpdm_package id='862′]

1. Ngā raruraru me ngā otinga o te whakaata kōpiko
2. Ngā raruraru me ngā otinga o te whakaata pūkohu
3. Ngā raruraru me ngā otinga o te arotahi wehewehe
4. Ngā raruraru me ngā otinga o ngā karāhe arotahi
5. Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
6. Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
7. Ngā mōhiti taputapu whatu
8. Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
9. Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
10. Ngā raruraru me ngā otinga o ngā karu tirohanga whatu

Pānuitia atu