3 Ngā tauira o ngā pātai mō ngā mōhiti whatu
1. Me kī, he mōhiti kanohi kei tō hoa, he -2 ngā karāhe o ōna karaihe. Ngā karaihe mōhiti ko te tikanga e 2 henemita mai i te kanohi.
(a) He mōhiti ā tō hoa karāhe kōpiko ranei karāhe kōpiko ?
(b) He aha te roa o te arotahi o te karu arotahi?
(c) Ngā kanohi o tō hoa te tirohanga tata ranei tirohanga tawhiti Mena he kanohi tata koe, ko tēhea te tawhiti tino tawhiti ka taea e ō kanohi te kite? Mena he kanohi tata koe, ko tēhea te tawhiti tino tata ka kitea e te kanohi?
Kōrero
E mōhiotia ana :
Mana arotahi (P) = -2 diopters
Whakautu :
(a) He karāhe kōpiko, he karāhe kōpiko rānei?
He kino te mana o te arotahi, nō reira ko te arotahi e whakamahia ana he arotahi kino, arā, he arotahi kōpiko, arā, he arotahi wehewehe.
(b) He aha te roa o te arotahi o te karu arotahi?
P = 1/f
-2 = 1/w
f = 1/-2 = -0,5 mita = -50 henemita
Ko te roa arotahi o tētahi karāhe kōpiko he 50 henemita.
(c) He kanohi tata, he kanohi tawhiti rānei tō hoa?
Mena he karaihe kōpiko te karaihe e whakamahia ana, ka pērā ngā kanohi o tō hoa te tirohanga tata. Mena he kanohi tata tōna, ko tēhea te tawhiti rawa atu ka taea e ngā kanohi o tō hoa te kite?
Ko te pito tawhiti o te kanohi noa he mutunga kore, ko tō hoa ia he tirohanga tawhiti, nō reira ko te tawhiti rawa atu e kitea ana e te kanohi o tō hoa he iti iho i te mutunga kore. Kia taea ai e te kanohi o tō hoa te kite i ngā mea i te tawhiti mutunga kore pērā i te kanohi noa, me hanga e te karāhe mōhiti he ahua o te mea i te tawhiti x cm i mua i te karāhe. Kei mua te ahua i te karāhe mōhiti, nō reira he poutū, he mariko te ahua (whakatairitehia te whakamārama i roto i te kaupapa whakaahua karaihe kōpiko). Nā te mea he mariko te ahua, he kino te tawhiti (s') o te ahua. Waihoki, he kino te roa arotahi o te arotahi nā te mea he karāhe kōpiko.
-1/s' = 1/f – 1/s
-1/s' = -1/50 – 1/~ = -1/50 – 0
-1/s' = -1/50
s' = 50 henemita
Ko te tawhiti o te ahua i mua i te karu o te mōhiti he 50 cm. Ko ngā mōhiti he 2 cm i mua i te kanohi, nō reira ko te tawhiti o te ahua i mua i te kanohi he 50 cm + 2 cm = 52 cm. Ko te 52 cm te tawhiti tawhiti rawa atu ka kitea e te kanohi tata i roto i te raruraru i runga ake nei. Ko te tawhiti tawhiti rawa atu ka kitea e te kanohi noa ko te mutunga kore.
2. Me kī kei te mau tō hoa wahine i ngā mōhiti he 4 ngā karāhe arotahi diopter. Ko ngā karāhe arotahi e 2 cm te tawhiti ki mua i ōna kanohi.
(a) He karaihe kōpiko, he karaihe pūkohu rānei ngā karaihe o ngā mōhiti a tō hoa wahine?
(b) He aha te roa o te arotahi o te karu arotahi?
(c) He kanohi tata, he kanohi tawhiti rānei tō hoa wahine? Mena he kanohi tata koe, ko tēhea te tawhiti tino tawhiti ka taea e ō kanohi te kite? Mena he kanohi tata koe, ko tēhea te tawhiti tino tata ka taea e te kanohi te kite?
Kōrero
E mōhiotia ana :
Mana arotahi (P) = 4 diopters
Whakautu :
(a) He karāhe kōpiko, he karāhe kōpiko rānei?
He pai te mana o te arotahi, nō reira ko te arotahi e whakamahia ana he arotahi pai, arā, he arotahi kōpuku, arā, he arotahi hūpeke.
(b) He aha te roa o te arotahi o te karu arotahi?
P = 1/f
4 = 1/w
f = 1/4 = 0,25 mita = 25 cm
Ko te roa arotahi o tētahi karāhe arotahi kōpuku he 25 henemita.
(c) He kanohi tata, he kanohi tawhiti rānei tō hoa?
Mena he karaihe pūkohu te karaihe e whakamahia ana, ka pērā ngā kanohi o tō hoa wahine tirohanga tawhiti. Ki te mea he kanohi tata koe, ko tēhea te tawhiti tata rawa atu ka taea e te kanohi te kite?
Ko te pūwāhi tata o te kanohi noa he 25 cm. Kia taea ai e ngā kanohi o tō hoa wahine te kite i tētahi mea e 25 cm te tawhiti, pērā i te kanohi noa, me hanga e te karāhe mōhiti he ahua i te tawhiti o te x cm i mua i te karāhe. Ko te karāhe mōhiti he 2 cm i mua i te kanohi, nō reira ko te tawhiti o te mea i mua i te karāhe he 25 cm – 2 cm = 23 cm. Kei mua te ahua i te karāhe mōhiti, nō reira he poutū, he mariko te ahua (whakatairitehia te whakamārama i roto i te kaupapa whakaahua karaihe kōpiko)He mariko te ahua, nō reira he tohu kino tō te tawhiti (s') o te ahua.
-1/s' = 1/f – 1/s
-1/s' = 1/25 – 1/23 = 23/575 – 25/575 = -2/575
-s' = 575/-2 = -287,5 henimita = -2,875 mita
s' = 287,5 henimita = 2,875 mita
Ko te tawhiti o te ahua i mua i te karu o te karu he 287,5 cm. Ko te tawhiti o te ahua i mua i te kanohi he 287,5 cm + 2 cm = 289,5 cm. Ko te 289,5 cm te tawhiti tata rawa atu ka kitea e te kanohi kite tata i roto i te raruraru i runga ake nei. Ko te tawhiti tata rawa atu ka kitea e te kanohi noa ko te 25 cm.
3. Ka taea e te tangata te pānui mārama i te tawhiti o te 50 cm. Hei taea te pānui mārama i te tawhiti o te 30 cm, ko te kaha arotahi e hiahiatia ana ko…
A. 1/3 diopter
B. 2/3 diopters
C. 3/4 diopters
D. 4/3 diopters
Kōrero
Ka pāngia te tangata e te tirohanga tata, ko ngā karāhe e whakamahia ana hei whakatika i te tirohanga tata ko ngā karāhe pūkohu, ngā karāhe taupū rānei, ngā karāhe pai rānei.
Kia kitea ai tētahi mea i te tawhiti o te 30 cm i mua i te kanohi, me hanga e te karu arotahi he ahua i te tawhiti o te 50 cm i mua i te kanohi. Kei mua i te karu arotahi te ahua, nō reira he poutū, he mariko te ahua.
E mōhiotia ana:
Te tawhiti o te mea (s) = 30 cm
Te tawhiti o te ahua (s') = -50 cm (kino nā te mea he mariko)
Pātai: Mana arotahi (P)
Whakautu:
Te roa o te arotahi (f) o te arotahi:
1/h = 1/h + 1/h'
1/f = 1/30 + 1/-50
1/f = 5/150 – 3/150
1/f = 2/150
f = 150/2 = 75 cm = 0,75 mita = 75/100 mita
Ko te roa arotahi pai ko te arotahi e whakamahia ana he arotahi kōpuku.
Mana arotahi:
P = 1/f
P = 1 : 75/100 = 1 x 100/75
P = 100/75 (wehea ki te 25)
P = 4/3 diopters
Ko te whakautu tika ko D.
Ngā Pātai mō ngā Mōhiti Tirotiro
1. Ka whakamahia e tetahi mōhiti he -2,5 ngā diopters tōna mana. Mēnā kei te 2 cm te tawhiti o te karu tirohanga mai i te kanohi, tautuhia:
(a) He karaihe pūkohu, he karaihe kōpiko rānei ngā karaihe e whakamahia ana e ngā mōhiti?
(b) He aha te roa o te arotahi o te karāhe mōhiti?
(c) He tirohanga tata, he tirohanga tawhiti rānei ngā kanohi o te tangata? Mena he tirohanga tata koe, ko tēhea te tawhiti tino tawhiti ka taea e ō kanohi te kite? Mena he tirohanga tata koe, ko tēhea te tawhiti tino tata ka taea e te kanohi te kite?
Kī Whakautu:
a = karāhe wehewehe = karāhe kino = karāhe….
b = 40 henemita
c = Wenerei Roa. Ko te tawhiti tawhiti rawa = 42 cm
2. Me kī kei te whakamahi tō hoa tāne o mua i mōhiti me te mana o te 4,5 diopters 🙂 . Mena kei te 2 cm te tawhiti o te karu tirohanga mai i te kanohi, tautuhia:
(a) I whakamahia e ngā mōhiti o tō hoa tāne o mua he karaihe piko, he karaihe pūkohu rānei?
(b) He aha te roa o te arotahi o te karāhe mōhiti?
(c) He kanohi tata, he kanohi tawhiti rānei tō hoa tāne o mua? Mēnā he kanohi tawhiti, ko tēhea te tawhiti tino tawhiti ka kitea e te kanohi? Mēnā he kanohi tawhiti, ko tēhea te tawhiti tino tata ka kitea e te kanohi?
Kī Whakautu:
a = karāhe hūnuku = karāhe pai = karāhe….
b = 22,2 henemita
c = Te tirohanga tata. Te tawhiti tata rawa = 13,3 cm
