Hei mārama ki te ahua o tētahi mea i hangaia e te karāhe pūkohu, tirohia te tauira pātai me te kōrero e whai ake nei. I roto i tēnei pātai, e whakaarohia ana kei tētahi tawhiti te mea mai i te karāhe pūkohu, kātahi ka whakaahuahia te hanganga o te ahua. whakaahua o tētahi mea mā te arotahi pūkohu, te tawhiti o te ahua mai i te karu arotahi me te whakanui o te ahua mā karāhe kōpiko
Ko te roa o te arotahi o tētahi karāhe kōpikopiko (karāhe whakapūmau) he 20 cm. Kei te taha maui o te karāhe tētahi mea he 10 cm te teitei. Tātaihia te tawhiti o te ahua, te whakanui o te ahua, me te teitei o te ahua mēnā:
a) he iti ake te tawhiti o te mea mai i te karāhe kōpikopiko i te roanga arotahi o te karāhe kōpikopiko (s < f),
b) he rite te tawhiti o te mea mai i te karāhe kōpiko ki te roa arotahi o te karāhe kōpiko (s = f),
c) he nui ake te tawhiti o te mea mai i te karāhe kōpikopiko i te roanga arotahi o te karāhe kōpikopiko (s > f).
Kōrero
E mōhiotia ana :
Te roa o te arotahi (f) o te karu arotahi kōpiko = 20 cm
He pai te roa arotahi o te karu arotahi pūkohu nā te mea he tūturu te pūwāhi arotahi o te karu arotahi pūkohu, he hihi mārama rānei e tukuna ana mā roto.
Teitei o te mea (h) = 10 cm
Whakautu :
He iti ake te tawhiti o te mea i te roa arotahi o te karāhe kōpiko (s > f)
Me kī ko te tawhiti o te mea he 5 henimita, he 10 henimita, he 15 henimita hoki.
a) Mēnā ko te tawhiti (s) o te mea = 5 cm
Te tawhiti o te ahua (s')
1/s' = 1/f – 1/s = 1/20 – 1/5 = 1/20 – 4/20 = -3/20
s' = -20/3 = -6,7 henemita
Ko te tawhiti āhua kino he āhua mariko, arā, kāore te hihi mārama e tika ana mā roto i te āhua.
He nui ake te tawhiti o te ahua he 6,7 cm i te tawhiti o te mea he 5 cm.
Whakanuia o te ahua (M)
M = -s'/s = -(-6,7)/5 = 6,7/5 = 1,3
He nui ake te whakanui o te ahua i te 1, arā, kua whakanuia te ahua, kua nui ake rānei te rahi o te ahua i te rahi o te mea.
Teitei o te atarangi (h')
Tātai whakanui atarangi:
M = h'/h
h' = M h = (1,3)(10 henimita) = 13 henimita
He pai te teitei o te atarangi, arā, he poutū te atarangi.
b) Mēnā ko te tawhiti o te mea (s) = 10 cm
Te tawhiti o te ahua (s')
1/s' = 1/f – 1/s = 1/20 – 1/10 = 1/20 – 2/20 = -1/20
s' = -20/1 = -20 henemita
Ko te tawhiti āhua kino he āhua mariko, arā, kāore te hihi mārama e tika ana mā roto i te āhua.
He nui ake te tawhiti o te ahua he 20 cm i te tawhiti o te mea he 10 cm.
Whakanuia o te ahua (M)
M = -s'/s = -(-20)/10 = 20/10 = 2
He nui ake te whakanui o te ahua i te 1, arā, kua whakanuia te ahua, kua nui ake rānei te rahi o te ahua i te rahi o te mea.
Teitei o te atarangi (h')
Tātai whakanui atarangi:
M = h'/h
h' = M h = (2)(10 henimita) = 20 henimita
He pai te teitei o te atarangi, arā, he poutū te atarangi.
c) Mēnā ko te tawhiti o te mea (s) = 15 cm
Te tawhiti o te ahua (s')
1/s' = 1/f – 1/s = 1/20 – 1/15 = 3/60 – 4/60 = -1/60
s' = -60/1 = -60 henemita
Ko te tawhiti āhua kino he āhua mariko, arā, kāore te hihi mārama e tika ana mā roto i te āhua.
He nui ake te tawhiti o te ahua he 60 cm i te tawhiti o te mea he 15 cm.
Whakanuia o te ahua (M)
M = -s'/s = -(-60)/15 = 60/15 = 4
He nui ake te whakanui o te ahua i te 1, arā, kua whakanuia te ahua, kua nui ake rānei te rahi o te ahua i te rahi o te mea.
Teitei o te atarangi (h')
Tātai whakanui atarangi:
M = h'/h
h' = M h = (4)(10 henimita) = 40 henimita
He pai te teitei o te atarangi, arā, he poutū te atarangi.
He rite te tawhiti o te mea ki te roa arotahi o te karāhe kōpikopiko (s = f)
Kei tawhiti mutunga kore te atarangi.
He nui ake te tawhiti o te mea i te roa arotahi o te karāhe kōpiko (s > f)
Me kī ko te tawhiti o te mea he 30 henimita, he 40 henimita, he 50 henimita hoki.
a) Mēnā ko te tawhiti (s) o te mea = 30 cm
Te tawhiti o te ahua (s')
1/s' = 1/f – 1/s = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s' = 60/1 = 60 henimita
Ko te tawhiti pai o te ahua he ahua tūturu, arā, ko te hihi o te mārama e tika ana mā roto i te ahua.
He nui ake te tawhiti o te ahua he 60 cm i te tawhiti o te mea he 30 cm.
Whakanuia o te ahua (M)
M = -s'/s = -60/30 = -2
He nui ake te whakanui o te ahua i te 1, arā, kua whakanuia te ahua, kua nui ake rānei te rahi o te ahua i te rahi o te mea.
Teitei o te atarangi (h')
Tātai whakanui atarangi:
M = h'/h
h' = M h = (-2)(10 henimita) = -20 henimita
He tōraro te teitei o te atarangi, arā, kua hurihia te atarangi.
b) Mēnā ko te tawhiti o te mea (s) = 40 cm
Te tawhiti o te ahua (s')
1/s' = 1/f – 1/s = 1/20 – 1/40 = 2/40 – 1/40 = 1/40
s' = 40/1 = 40 henimita
Ko te tawhiti pai o te ahua he ahua tūturu, arā, ko te hihi o te mārama e tika ana mā roto i te ahua.
He rite te tawhiti o te atarangi he 40 cm ki te tawhiti o te mea he 40 cm.
Whakanuia o te ahua (M)
M = -s'/s = -40/40 = -1
Ko te whakanui o te ahua he ōrite ki te 1, arā, he rite te rahi o te ahua ki te rahi o te mea.
Teitei o te atarangi (h')
Tātai whakanui atarangi:
M = h'/h
h' = M h = (-1)(10 henimita) = -10 henimita
He tōraro te teitei o te atarangi, arā, kua hurihia te atarangi.
b) Mēnā ko te tawhiti o te mea (s) = 50 cm
Te tawhiti o te ahua (s')
1/s' = 1/f – 1/s = 1/20 – 1/50 = 5/100 – 2/100 = 3/100
s' = 100/3 = 33,3 henimita
Ko te tawhiti pai o te ahua he ahua tūturu, arā, ko te hihi o te mārama e tika ana mā roto i te ahua.
He iti iho te tawhiti o te ahua he 33,3 cm i te tawhiti o te mea he 50 cm.
Whakanuia o te ahua (M)
M = -s'/s = -33,3/40 = -0,8
He iti iho i te 1 te whakanui o te ahua, arā, he iti iho te rahi o te ahua i te rahi o te mea.
Teitei o te atarangi (h')
Tātai whakanui atarangi:
M = h'/h
h' = M h = (-0,8)(10 henimita) = -8 henimita
He tōraro te teitei o te atarangi, arā, kua hurihia te atarangi.
