Labari game da Tsarin Hoto ta hanyar ruwan tabarau mai haɗuwa (convex)
Domin fahimtar yadda hoton yake samuwa ta hanyar ruwan tabarau mai siffar convex, koyi misalan matsaloli da mafita a ƙasa. A wannan yanayin, ana ɗauka cewa abin yana da nisa daga ruwan tabarau mai siffar convex.
sannan a zana siffar hoton ta hanyar ruwan tabarau mai siffar convex, nisan hoton daga ruwan tabarau mai siffar convex da kuma girman hoton ta hanyar ruwan tabarau mai siffar convex.
Gilashin ruwan tabarau mai lanƙwasa yana da tsawon mai da hankali na santimita 20. Abubuwan da tsayinsu ya kai santimita 10 suna gefen hagu na gilashin. A ƙayyade nisan hoton, girman hoton da tsayin hoton, idan:
a) nisan abu daga ruwan tabarau mai lanƙwasa ya fi ƙanƙanta fiye da tsawon mai da hankali na ruwan tabarau mai lanƙwasa (do < f),
b) nisan abu daga ruwan tabarau mai lanƙwasa iri ɗaya ne da tsawon mai da hankali na ruwan tabarau mai lanƙwasa (do = f),
c) nisan abu daga ruwan tabarau mai lanƙwasa ya fi tsayin daka na ruwan tabarau mai lanƙwasa (yi > f).
Wanda aka sani:
Tsawon mai da hankali (f) na ruwan tabarau mai lanƙwasa = 20 cm
Tsawon firikwensin ruwan tabarau mai siffar convex an sanya shi a matsayin alama mai kyau saboda firikwensin ruwan tabarau mai siffar convex gaskiya ne, inda haske ke ratsawa ta cikin firikwensin.
Tsawon abu (h) = 10 cm
Magani:
Nisa tsakanin abu da na'urar ya fi ƙanƙanta fiye da tsawon mai da hankali na ruwan tabarau mai lanƙwasa (yi > f)
A ce nisan abu shine 5 cm, 10 cm da 15 cm.
a) Idan nisan abu (yi) = 5 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = 1/20 – 1/5 = 1/20 – 4/20 = -3/20
di = -20/3 = -6.7 cm
Nisa tsakanin hoton da hoton ba shi da kyau, ma'ana hoton yana kama da na kama-da-wane, inda hasken bai ratsa ta cikin hoton ba.
Nisa tsakanin hoton da hoton ya kai santimita 6.7, ya fi nisan da aka yi da abu santimita 5.
Girman hoto (M)
M = -di / yi = -(-6.7) / 5 = 6.7 / 5 = 1.3
Girman hoton ya wuce 1 yana nufin cewa girman hoton ya fi girman abu girma.
Tsawon hoton (hi)
Daidaiton girman hoto:
M = sannu / sannu
hi = M ho = (1.3) (10 cm) = 13 cm
Tsawon hoton, wanda aka sanya hannu a kan tabbatacce, yana nufin hoton yana tsaye.
b) Idan nisan abu (yi) = 10 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = 1/20 – 1/10 = 1/20 – 2/20 = -1/20
di = -20/1 = -20 cm
Nisa ta hoton ba ta da kyau, ma'ana hoton yana kama da na kama-da-wane, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da santimita 20 ya fi nisan da ke tsakanin abu da santimita 10 girma.
Girman hoto (M)
M = -di / yi = -(-20)/10 = 20/10 = 2
Girman hoton ya wuce 1 yana nufin cewa girman hoton ya fi girman abu girma.
Tsawon hoton (hi)
Daidaiton girman hoto:
M = sannu / sannu
gajimare = M h = (2)(10 cm) = 20 cm
Tsayin hoton yana da kyau ma'ana hoton yana tsaye.
c) Idan nisan abu (yi) = 15 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = 1/20 – 1/15 = 3/60 – 4/60 = -1/60
di = -60/1 = -60 cm
Nisa ta hoton ba ta da kyau, ma'ana hoton yana kama da na kama-da-wane, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da santimita 60 ya fi nisan da ke tsakanin abu da santimita 15 girma.
Girman hoto (M)
M = -di / yi = -(-60)/15 = 60/15 = 4
Girman hoton ya wuce 1 yana nufin cewa girman hoton ya fi girman abu girma.
Tsawon hoton (hi)
Daidaiton girman hoto:
M = gajimare / gajimare
gajimare = M h = (4)(10 cm) = 40 cm
Tsawon hoton yana da kyau ma'ana hoton yana tsaye.
Nisa tsakanin abu da ruwan tabarau mai lanƙwasa (do = f) daidai yake da tsawon mai da hankali (do = f)
Hoton yana da nisa mara iyaka.
Nisa tsakanin abu da na'urar ya fi tsayin daka na ruwan tabarau mai lanƙwasa (yi > f)
A ce nisan abu shine 30 cm, 40 cm da 50 cm.
a ) Idan nisan abu (yi) = 30 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
di = 60/1 = 60 cm
Nisa tsakanin hoton da hoton yana da kyau, ma'ana hoton gaskiya ne, inda hasken haske ke ratsawa ta cikin hoton.
Nisa tsakanin hoton da santimita 60 ya fi nisan da ke tsakanin abu da santimita 30 girma.
Girman hoto (M)
M = -di / yi = -60/30 = -2
Girman hoton ya wuce 1, ma'ana girman hoton ya fi girman abu girma.
Tsawon hoton (hi)
Daidaiton girman hoto:
M = gajimare / gajimare
gajimare = M h = (-2)(10 cm) = -20 cm
Tsayin hoton yana nuna cewa hoton ya juya.
b) Idan nisan abu (yi) = 40 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = 1/20 – 1/40 = 2/40 – 1/40 = 1/40
di = 40/1 = 40 cm
Nisa tsakanin hoton da hoton yana da kyau, ma'ana hoton gaskiya ne, inda hasken haske ke ratsawa ta cikin hoton.
Nisa tsakanin hoton da santimita 40, daidai yake da nisan da santimita 40 tsakanin abu.
Girman hoto (M)
M = -di / yi = -40/40 = -1
Girman hoto shine 1 yana nufin girman hoton yayi daidai da girman abu.
Tsawon hoton (hi)
Daidaiton girman hoto:
M = sannu / sannu
gajimare = M h = (-1)(10 cm) = -10 cm
Tsawon hoton yana da korau ma'ana hoton ya juye.
b) Idan nisan abu (yi) = 50 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = 1/20 – 1/50 = 5/100 – 2/100 = 3/100
di = 100/3 = 33.3 cm
Nisa tsakanin hoton da hoton yana da kyau, ma'ana hoton gaskiya ne, inda hasken haske ke ratsawa ta cikin hoton.
Nisa tsakanin hoton da santimita 33.3 ya fi ƙasa da nisan abu da santimita 50.
Girman hoto (M)
M = -di / yi = -33.3/40 = -0.8
Girman hoton ya fi ƙasa da 1, ma'ana girman hoton ya fi ƙasa da girman abu.
Tsawon hoton (hi)
Daidaiton girman hoto:
M = gajimare / gajimare
gajimare = M h = (-0.8)(10 cm) = -8 cm
Tsawon hoton yana da korau, ma'ana hoton an juya shi.
