1. Ko te roa arotahi o te whakaata pūkohu he 10 cm, ā, ko te tawhiti o te mea he 20 cm. Whakatauhia (a) te tawhiti o te ahua (b) te whakanui o te ahua
Mōhiotia:
Ko te roa o te arotahi (f) = -10 cm
Ko te tohu tango e tohu ana he mariko te pūwāhi arotahi o te whakaata pūkohu.
Ko te tawhiti o te mea ( d o ) = 20 cm
Rongoā:
Te hanganga o te ahua mā te whakaata kōpiko:
Te tawhiti o te ahua (d i ):
1/ d i = 1/ f – 1/ d o = -1/10 – 1/20 = -2/20 – 1/20 = -3/20
d i = -20/3 = -6.7 cm
Ko te tohu tango e tohu ana he mariko te ahua.
Te whakanui i te ahua:
m = – d i / d o = -(-6.7)/20 = 6.7/20 = 0.3
m = 0,3 te wā iti iho i te mea.
Ko te tohu tāpiri e tohu ana kei runga te ahua.
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2. Ka whakatakotoria tētahi mea 10-cm te teitei ki mua i tētahi whakaata pūkohu me te roa arotahi o te 20 cm. Tātaihia te teitei o te ahua mēnā ko te tawhiti o te mea ko (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm
Mōhiotia:
Ko te roa arotahi o te whakaata pūkohu (f) = -20 cm
Ko te tohu tango e tohu ana he mariko te pūwāhi arotahi
Ko te pūtoro o te piko ( r ) = 2 f = 2(20) = 40 cm
Te teitei o te mea (h) = 10 cm
Rongoā:
a) ko te roa arotahi (f) = -20 cm me te tawhiti o te mea (d o ) = 10 cm
Te tawhiti o te ahua (d i ) :
1/ d i = 1/ f – 1/ d o = -1/20 – 1/10 = -1/20 – 2/20 = -3/20
d i = -20/3 = -6.7
Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata te ahua.
Te whakanui i te ahua ( m ):
m = – d i / d o = -(-6.7)/10 = 6.7/10 = 0.67
Ko te tohu tāpiri e tohu ana kei te poutū te ahua.
He 0.67 te iti iho o te ahua i te mea.
Te teitei o te ahua (h i ):
m = h i / h o
teitei = teitei = (10 henimita )(0.67) = 6.7 henimita
b) te roa arotahi (f) = -20 cm me te tawhiti o te mea ( d o ) = 30 cm
Te tawhiti o te ahua ( d i ):
1/ d i = 1/ f – 1/ d o = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
d i = -60/5 = -12
Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata te ahua.
Te whakanui i te ahua ( m ):
m = – d i / d o = -(-12)/30 = 12/30 = 0.4
Ko te tohu tāpiri e tohu ana kei te poutū te ahua.
He 0,4 ngā wā te iti ake o te ahua i te mea.
Te teitei o te ahua (h i ):
m = h i / h o
teitei = teitei = (10 henimita )(0.4) = 4 henimita
c) Ko te roa arotahi (f) = -20 cm me te tawhiti o te mea ( d o ) = 40 cm
Te tawhiti o te ahua ( d i ):
1/ d i = 1/ f – 1/ d o = -1/20 – 1/40 = -2/40 – 1/40 = -3/40
d i = -40/3 = -13.3
Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata pūkohu te ahua.
Te whakanui i te ahua ( m ):
m = – d i / d o = -(-13.3)/40 = 13.3/40 = 0.3
Ko te tohu tāpiri e tohu ana kei te poutū te ahua.
He 0.3 te iti iho o te ahua i te mea.
Te teitei o te ahua ( h i ) :
m = h i / h o
h i = h o m = (10 cm)(0.3) = 3 cm
d) Ko te roa arotahi (f) = -20 cm me te tawhiti o te mea ( d o ) = 50 cm
Te tawhiti o te ahua ( d i ):
1/ d i = 1/ f – 1/ d o = -1/20 – 1/50 = -5/100 – 2/100 = -7/100
d i = -100/7 = -14.3
Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata pūkohu te ahua.
Te whakanui i te ahua ( m ):
m = – d i / d o = -(-14.3)/50 = 14.3/50 = 0.3
Ko te tohu tāpiri e tohu ana kei te poutū te ahua.
He 0.3 te iti iho o te ahua i te mea.
Te teitei o te ahua (h i ) :
m = h i / h o
teitei = teitei = (10 henimita)(0.3) = 3 henimita
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3. Kei runga i te mea kei te 20 cm te tawhiti i mua i te whakaata pūkohu . Mena he 1/5 te teitei o te ahua i te teitei o te mea, tautuhia ( a) te roa o te ahua b) te roa arotahi c) ngā āhuatanga o te ahua
Mōhiotia:
Ko te tawhiti o te mea ( d o ) = 20 cm
Te teitei o te ahua (h i ) = 1/5 h = 0.2 h
Ko te teitei o te mea (h) = h
Rongoā:
a) te tawhiti o te ahua ( d i )
Te tātai mō te whakanui i te ahua :
m = h i / h o = 0.2h / h = 0.2
Ko te tohu tāpiri e tohu ana kei te poutū te ahua.
He 0.2 te iti iho o te ahua i te mea.
Te tawhiti o te ahua ( d i ):
– d i = md o
d i = – m d o = -(0.2)(20 henimita) = -4 henimita
Ko te tohu tango e tohu ana he mariko te ahua, kei muri rānei i te whakaata pūkohu te ahua.
b) Te roa o te arotahi ( f)
Te roa o te arotahi (f):
1/f = 1/ d o + 1/ d i = 1/20 – 1/4 = 1/20 – 5/20 = -4/20
f = -20/4 = -5 henemita
Ko te tohu tango e tohu ana he mariko te pūwāhi arotahi.
c) Ngā āhuatanga o te ahua:
– Tū tika
– Iti ake
– mariko
4. Ka whakaatahia te mārama ki te whakaata pūkohu e whakarara ana ki te tuaka….
A. ki te pūwāhi arotahi o te whakaata
B. mai i te pūwāhi arotahi o te whakaata
C. mā waenganui o te piko o te whakaata
D. poutū ki te papa whakaata
otinga
Kei te pikitia i raro nei te āhua o te raruraru.
Ko te whakautu tika ko B.
5. Ka kite te kaieke pahikara i te ahua o te motopaika i muri i a ia, 1/6 o tōna rahi taketake ina 30 mita te tawhiti i waenganui i te kaieke me te motopaika. Tātaihia te pūtoro piko o te whakaata tirohanga whakamuri…
A. 7.14 mita
B. 8.57 mita
C. 12.00 mita
D. 24.00 mita
Mōhiotia:
Te whakanui i te ahua (M) = 1/6 ngā wā
Te tawhiti o te mea (d) = 30 mita
E hiahiatia ana: Te pūtoro o te piko o te whakaata tirohanga whakamuri (R)
Rongoā:
Tātaihia te tawhiti o te ahua (d')
Nā te mea kua mōhiotia te whakanui o te ahua (M) me te tawhiti o te mea (s), ka taea te mōhio ki te tawhiti o te ahua mā te whakamahi i te tātai whakanui o te ahua:
Ko te tohu kino he tohu mariko te ahua. E 5 mita te tawhiti o te ahua i muri i te whakaata pūkohu.
Tātaihia te roa arotahi (f)
Nā te mea ko te tawhiti o te mea (d) me te tawhiti o te ahua (d'), ka taea te tatau i te roa o te arotahi mā te whakamahi i te tātai o te whakaata:
Te pūtoro o te piko (R)
Ko te pūtoro o te piko o te whakaata pūkohu e rua te roa o te arotahi o te whakaata pūkohu.
R = 2 f = 2 (6 mita) = 12 mita
Ko te radius o te piko o te whakaata pūkohu he 12 mita.
Ko te whakautu tika ko C.
6. I whiriwhiria te whakaata pūkohu hei whakaata tirohanga whakamuri mō te motopaika nā te mea ko ngā āhuatanga o te ahua i puta mai i te whakaata ko…
A. tūturu, poutū, whakaititia
B. tūturu, poutū, whakanuia
C. mariko, poutū, whakaititia
D. mariko, poutū, whakanuia
Rongoā:
I runga i ngā whakaahua e rua i runga ake nei, ka taea te whakatau ko ngā āhuatanga o te ahua he mariko, he poutū, he whakaiti.
Ko te whakautu tika ko C.
7. Kei mua i te whakaata pūkohu te mea he 12 cm te tawhiti, ā, he 6 cm te whānui o tōna whānui. Ko ngā āhuatanga o te ahua ko…
A. tūturu, hurihia i te tawhiti o te 12 cm
B. tūturu, poutū i te tawhiti o te 4 cm
C. mariko, poutū i te tawhiti o te 2.4 cm
D. mariko, hurihia i te tawhiti o te 6 cm
Mōhiotia:
Te tawhiti o te mea (d) = 12 cm
Ko te whānui o te whakaata pūkohu (r) = 6 cm.
Ko te roa arotahi o te whakaata pūkohu (f) = 6 cm / 2 = -3 cm
Ko te roa arotahi o te whakaata pūkohu he tohu kino nā te mea he mariko. He mariko nā te mea kāore te mārama e whiti atu.
E hiahiatia ana: Ngā āhuatanga o te ahua
Rongoā:
Te tawhiti o te ahua (d'):
1/rā' = 1/w – 1/rā = -1/3 – 1/12 = -4/12 – 1/12 = -5/12
d' = -12/5 = -2.4 henimita
Ko te tawhiti o te ahua kua tohua ki te kino e tohu ana he mariko te ahua.
Te whakanui i te ahua (m):
m = -d' / d = -(-2.4) / 12 = 2.4 / 12 = 0.2 ngā wā
Ko te whakanui o te ahua he tohu pai ko te tikanga he poutū te ahua, ā, ko te whakanui o te ahua he 0.2 ko te tikanga he iti ake te rahi o te ahua i te rahi o te mea (kua whakaitihia).
Ko te whakautu tika ko C.
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- Ngā raruraru me ngā otinga o te whakaata kōpiko
- Ngā raruraru me ngā otinga o te whakaata pūkohu
- Ngā raruraru me ngā otinga o te arotahi wehewehe
- Ngā raruraru me ngā otinga o ngā karāhe arotahi
- Ngā taputapu whatu Ngā raruraru kanohi tangata me ngā otinga
- Ngā raruraru me ngā otinga mō ngā karaihe whakapā o ngā taputapu whatu
- Ngā mōhiti taputapu whatu
- Ngā raruraru me ngā otinga mō ngā taputapu whatu mō te karāhe whakanui
- Te karu hikohiko taputapu whatu – ngā raruraru me ngā otinga
- Ngā raruraru me ngā otinga o ngā karu tirohanga whatu
