Hei mārama ki te ahua o tētahi mea i hangaia e te whakaata kōpiko, tirohia te tauira pātai me te kōrero e whai ake nei. I roto i tēnei pātai, e whakaarohia ana kei tētahi tawhiti te mea i te whakaata kōpiko, kātahi ka whakaahuahia te hanganga o te ahua o te mea e te whakaata kōpiko , te tawhiti o te ahua mai i te whakaata kōpiko me te whakanui i te ahua i hangaia e te whakaata kōpiko .
Mehemea he 20 cm te roa o te arotahi o tētahi whakaata kōpiko. Whakaahuahia te hanganga o te ahua, kātahi ka whakatau i te tawhiti o te ahua me te whakanui o te ahua mēnā:
a) he iti ake te tawhiti o te mea i te tawhiti o te pūwāhi arotahi (s < f)
b) kei te pūwāhi arotahi o te whakaata te mea (s = f)
c) kei waenganui i te pūwāhi arotahi me te pokapū piko o te whakaata te mea (f < s < R)
d) kei waenganui o te piko o te whakaata te mea (s = R)
e) he nui ake te tawhiti o te mea i te pūtoro o te piko o te whakaata (s > R)
Kōrero
E mōhiotia ana :
Ko te roa arotahi o te whakaata kōpiko (f) = 20 cm
He pai te roa arotahi o te whakaata kōpiko nā te mea ka tika te hihi mārama mā te pūwāhi arotahi o te whakaata kōpiko.
Te pūtoro o te piko (R) = 2 f = 2 (20) = 40 cm
Whakautu :
He iti ake te tawhiti o te mea i te roa arotahi o te whakaata kōpiko (s < f)
Me kī ko te tawhiti o te mea mai i te whakaata he 5 henimita, he 10 henimita, he 15 henimita hoki.
1) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 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
He tōraro te tawhiti (s') o te ahua, arā, he mariko te ahua, kei muri rānei i te whakaata kōpiko te ahua, kei reira te hihi mārama e kore e tika mā roto i te ahua.
He nui ake te tawhiti (s') o te ahua 6,7 cm i te tawhiti (s') o te mea 5 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -(-6,7)/5 = 6,7/5 = 1,3 ngā wā
Ko te whakanui rārangi o te ahua (M) he nui ake i te 1, ko te tikanga he nui ake te rahi o te ahua i te rahi o te mea.
He pai te whakanui rārangi o te ahua (M), arā, he poutū te ahua.
2) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 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
He tōraro te tawhiti (s') o te ahua, arā, he mariko te ahua, kei muri rānei i te whakaata kōpiko te ahua, kei reira te hihi mārama e kore e tika mā roto i te ahua.
He nui ake te tawhiti (s') o te ahua 20 cm i te tawhiti (s') o te mea 10 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -(-20)/10 = 20/10 = 2 ngā wā
Ko te whakanui rārangi o te ahua (M) he nui ake i te 1, ko te tikanga he nui ake te rahi o te ahua i te rahi o te mea.
He pai te whakanui rārangi o te ahua (M), arā, he poutū te ahua.
3) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 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
He tōraro te tawhiti (s') o te ahua, arā, he mariko te ahua, kei muri rānei i te whakaata kōpiko te ahua, kei reira te hihi mārama e kore e tika mā roto i te ahua.
He nui ake te tawhiti (s') o te ahua 60 cm i te tawhiti (s') o te mea 15 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -(-60)/15 = 60/15 = 4 ngā wā
Ko te whakanui rārangi o te ahua (M) he nui ake i te 1, ko te tikanga he nui ake te rahi o te ahua i te rahi o te mea.
He pai te whakanui rārangi o te ahua (M), arā, he poutū te ahua.
Kei te pūwāhi arotahi o te whakaata kōpiko te mea (s = f)
Kei te pūwāhi arotahi o te whakaata kōpiko te mea, nō reira ko te tawhiti o te mea (s) = te roa arotahi (f) = 20 cm
Te tawhiti o te whakaahua (s'):
1/s' = 1/f – 1/s = 1/20 – 1/20 = 0
s' = 0
Whakanuia o te ahua (M):
M = s'/s = 0
Mena he rite te tawhiti o te mea (s) ki te roa arotahi o te whakaata (f), kāore he ahua i hangaia e te whakaata.
Kei waenganui i te pūwāhi arotahi me te pokapū piko o te whakaata kōpiko te mea (f < s < R)
Me kī ko te tawhiti o te mea mai i te whakaata he 25 henimita, he 30 henimita, he 35 henimita hoki.
1) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 25 cm
Te tawhiti o te ahua (s') :
1/s' = 1/f – 1/s = 1/20 – 1/25 = 5/100 – 4/100 = 1/100
s' = 100/1 = 100 henimita
He pai te tawhiti (s') o te ahua, arā, he tūturu te ahua, kei mua rānei i te whakaata kōpiko te ahua, te wāhi e whiti ai te hihi mārama mā roto i te ahua.
He nui ake te tawhiti (s') o te ahua 100 cm i te tawhiti (s') o te mea 25 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -(100)/25 = -4 ngā wā
Ko te whakanui rārangi o te ahua (M) he nui ake i te 1, ko te tikanga he nui ake te rahi o te ahua i te rahi o te mea.
He kino te whakanui rārangi o te ahua (M), arā, kua hurihia te ahua.
2) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 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
He pai te tawhiti (s') o te ahua, arā, he tūturu te ahua, kei mua rānei i te whakaata kōpiko te ahua, te wāhi e whiti ai te hihi mārama mā roto i te ahua.
He nui ake te tawhiti (s') o te ahua 60 cm i te tawhiti (s') o te mea 30 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -60/30 = -2 ngā wā
Ko te whakanui rārangi o te ahua (M) he nui ake i te 1, ko te tikanga he nui ake te rahi o te ahua i te rahi o te mea.
He kino te whakanui rārangi o te ahua (M), arā, kua hurihia te ahua.
3) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 35 cm
Te tawhiti o te ahua (s') :
1/s' = 1/f – 1/s = 1/20 – 1/35 = 7/140 – 4/140 = 3/140
s' = 140/3 = 46,7 henimita
He pai te tawhiti (s') o te ahua, arā, he tūturu te ahua, kei mua rānei i te whakaata kōpiko te ahua, te wāhi e whiti ai te hihi mārama mā roto i te ahua.
He nui ake te tawhiti (s') o te ahua 46,7 cm i te tawhiti (s') o te mea 35 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -46,7/35 = -1,3 ngā wā
Ko te whakanui rārangi o te ahua (M) he nui ake i te 1, ko te tikanga he nui ake te rahi o te ahua i te rahi o te mea.
He kino te whakanui rārangi o te ahua (M), arā, kua hurihia te ahua.
Kei te pūwāhi piko o te whakaata kōpiko te mea (s = R)
Kei te pūwāhi piko o te whakaata kōpiko te mea, nō reira ko te tawhiti mai i te mea (s) = te pūtoro piko o te whakaata (R) = 40 cm
Te tawhiti o te whakaahua (s'):
1/s' = 1/f – 1/s = 1/20 – 1/40 = 2/40 – 1/40 = 1/40
s' = 40/1 = 40 henimita
He pai te tawhiti (s') o te ahua, arā, he tūturu te ahua, kei mua rānei i te whakaata kōpiko te ahua, te wāhi e whiti ai te hihi mārama mā roto i te ahua.
Ko te tawhiti o te atarangi (s') 40 cm he rite ki te tawhiti o te mea (s') 40 cm
Whakanuia o te ahua (M):
M = -s'/s = -40/40 = -1
Ko te whakanui rārangi o te ahua (M) he ōrite ki te 1, ko te tikanga he rite te rahi o te ahua ki te rahi o te mea.
He kino te whakanui rārangi o te ahua (M), arā, kua hurihia te ahua.
He nui ake te tawhiti o te mea i te pūtoro piko o te whakaata kōpiko (s > R)
Me kī ko te tawhiti o te mea mai i te whakaata he 45 henimita, he 50 henimita, he 60 henimita hoki.
1) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 45 cm
Te tawhiti o te ahua (s') :
1/s' = 1/f – 1/s = 1/20 – 1/45 = 9/180 – 4/180 = 5/180
s' = 180/5 = 36 henimita
He pai te tawhiti (s') o te ahua, arā, he tūturu te ahua, kei mua rānei i te whakaata kōpiko te ahua, te wāhi e whiti ai te hihi mārama mā roto i te ahua.
He iti iho te tawhiti (s') o te ahua 36 cm i te tawhiti (s') o te mea 45 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -(36)/45 = -0,8 ngā wā
He iti iho i te 1 te whakanui rārangi o te ahua (M), arā, he iti iho te rahi o te ahua i te rahi o te mea.
He kino te whakanui rārangi o te ahua (M), arā, kua hurihia te ahua.
2) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 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
He pai te tawhiti (s') o te ahua, arā, he tūturu te ahua, kei mua rānei i te whakaata kōpiko te ahua, te wāhi e whiti ai te hihi mārama mā roto i te ahua.
He iti iho te tawhiti (s') o te ahua 33 cm i te tawhiti (s') o te mea 50 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -33/50 = -0,7 ngā wā
He iti iho i te 1 te whakanui rārangi o te ahua (M), arā, he iti iho te rahi o te ahua i te rahi o te mea.
He kino te whakanui rārangi o te ahua (M), arā, kua hurihia te ahua.
3) Te tawhiti arotahi (f) = 20 cm, ā, ki te mea ko te tawhiti (s) o te mea he 60 cm
Te tawhiti o te ahua (s') :
1/s' = 1/f – 1/s = 1/20 – 1/60 = 3/60 – 1/60 = 2/60
s' = 60/2 = 30 henimita
He pai te tawhiti (s') o te ahua, arā, he tūturu te ahua, kei mua rānei i te whakaata kōpiko te ahua, te wāhi e whiti ai te hihi mārama mā roto i te ahua.
He iti iho te tawhiti (s') o te ahua 30 cm i te tawhiti (s') o te mea 60 cm
Whakanuitanga rārangi o te ahua (M) :
M = -s'/s = -30/60 = -0,5 ngā wā
He iti iho i te 1 te whakanui rārangi o te ahua (M), arā, he iti iho te rahi o te ahua i te rahi o te mea.
He kino te whakanui rārangi o te ahua (M), arā, kua hurihia te ahua.
