Labari game da ƙirƙirar hoto ta hanyar ruwan tabarau mai bambanta (ruwan tabarau mai concave)
Domin fahimtar yadda hoton yake samuwa ta hanyar ruwan tabarau mai siffar ƙwallo, duba misalin da ke ƙasa: Matsaloli da mafita. A wannan yanayin, ana ɗauka cewa abin yana da nisa daga ruwan tabarau mai siffar ƙwallo,
sannan a zana siffar hoton ta hanyar ruwan tabarau mai siffar concave, nisan hoton daga ruwan tabarau mai siffar concave da kuma girman hoton ta hanyar ruwan tabarau mai siffar concave.
Tsawon ruwan tabarau mai lanƙwasa (ruwan tabarau masu nutsewa) shine 20 cm. Abubuwan da tsayinsu ya kai 10 cm suna gefen hagu na ruwan tabarau. A ƙayyade nisan hoton, girman hoton da tsayin hoton, idan:
a) nisan abu ya fi ƙanƙanta fiye da tsawon mai da hankali na ruwan tabarau mai lanƙwasa
b) nisan abu iri ɗaya ne da tsawon mai da hankali na ruwan tabarau mai lanƙwasa
c) nisan abu ya fi tsawon mai da hankali na ruwan tabarau mai lanƙwasa
Wanda aka sani:
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa (f) = -20 cm
Tsawon firikwensin ruwan tabarau mai siffar concave yana da alamar rashin kyau saboda firikwensin ruwan tabarau mai siffar concave yana kama da na kama-da-wane, inda hasken ba ya ratsawa ta wurin firikwensin.
Tsayin 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) Tsawon abin da aka mayar da hankali a kai shine -20 cm kuma idan nisan abu (yi) = 5 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = -1/20 – 1/5 = -1/20 – 4/20 = -5/20
di = -20/5 = -4 cm
Alamar nisan hoton, ko kuma korau, tana nufin hoton yana kama-da-wane, inda hasken bai ratsa ta cikin hoton ba.
Nisa tsakanin hoton, 4 cm, ya fi ƙasa da nisan abu, 5 cm.
Girman hoto (M)
M = -di / yi = -(-4)/5 = 4/5 = 0.8
Girman hoton da ya fi ƙasa da 1 yana nufin cewa hoton ya ragu, ko kuma girman hoton ya fi ƙasa da girman abu.
Tsayin hoton (h')
Daidaiton girman hoto:
M = h' / h
h' = M h = (0.8)(10 cm) = 8 cm
Tsayin hoton alama ce mai kyau, ma'ana hoton yana tsaye a tsaye.
b) Tsawon abin da aka mayar da hankali a kai shine -20 cm kuma idan nisan abu (yi) = 10 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = -1/20 – 1/10 = -1/20 – 2/20 = -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 shine 6.7 cm, ƙasa da nisan abu, 10 cm.
Girman hoto (M)
M = -di / yi = -(-6.7)/10 = 6.7 / 10 = 0.67
Girman hoton ya fi ƙasa da 1 yana nufin cewa hoton ya ragu, ko kuma girman hoton ya fi ƙasa da girman abu.
Tsayin hoton (h')
Daidaiton girman hoto:
M = h'/h
h' = M h = (0.67)(10 cm) = 6.7 cm
Tsayin hoton alama ce mai kyau, ma'ana hoton yana tsaye a tsaye.
c) Tsawon abin da aka mayar da hankali a kai shine -20 cm kuma nisan abu (do) = 15 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = -1/20 – 1/15 = -3/60 – 4/60 = -7/60
di = -60/7 = -8.6 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 na'urar ta nuna shine 8.7 cm, ƙasa da nisan da aka yi amfani da shi, 15 cm.
Girman hoto (M)
M = -di / yi = -(-8.6)/10 = 8.6 / 10 = 0.86
Girman hoton da ya fi ƙasa da 1 yana nufin cewa girman hoton ya fi ƙanƙanta da girman abu.
Tsayin hoton (h')
Daidaiton girman hoto:
M = h'/h
h' = M h = (0.86)(10 cm) = 8.6 cm
Tsayin hoton yana da kyau, ma'ana hoton yana tsaye.
Nisa tsakanin abu da tsawon mai da hankali na ruwan tabarau mai lanƙwasa (do = f)
Tsawon mai da hankali (f) = nisan abu (do) = 20 cm.
Nisa ta hoton (di)
1/di = 1/f – 1/do = -1/20 – 1/20 = -2/20 = -2/20
di = -20/2 = -10 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 na'urar ta nuna shine 10 cm, ƙasa da nisan da aka yi amfani da shi, 20 cm.
Girman hoto (M)
M = -di / yi = -(-10)/20 = 10/20 = 0.5
Girman hoton ya fi ƙasa da 1, ma'ana girman hoton ya fi ƙasa da girman abu.
Tsayin hoton (h')
Daidaiton girman hoton:
M = h'/h
h' = M h = (0.5)(10 cm) = 5 cm
Tsayin hoton yana da kyau, ma'ana hoton yana tsaye.
Nisa tsakanin abu da na'urar ya fi tsayin daka na ruwan tabarau mai lanƙwasa (yi > f)
A ce nisan abubuwa shine 30 cm da 40.
a) Tsawon abin da aka mayar da hankali a kai shine -20 cm kuma idan nisan abu (yi) = 30 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
di = -60/5 = -12 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 abin da ke ciki da kuma hoton da ke ciki shine 12 cm, wanda ya fi ƙasa da nisan da ke tsakanin abin da ke ciki da kuma na 30 cm.
Girman hoto (M)
M = -di / yi = -(-12)/30 = 12/30 = 0.4
Girman hoton ya fi ƙasa da 1, ma'ana girman hoton ya fi ƙasa da girman abu.
Tsayin hoton (h')
Daidaiton girman hoto:
M = h'/h
h' = M h = (0.4)(10 cm) = 4 cm
Tsayin hoton alama ce mai kyau, ma'ana hoton yana tsaye a tsaye.
b) Tsawon mai da hankali -20 cm kuma idan nisan abu (yi) = 40 cm
Nisa ta hoton (di)
1/di = 1/f – 1/do = -1/20 – 1/40 = -2/40 – 1/40 = -3/40
di = -40/3 = -13 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 abin ya shafa shine 13 cm, ƙasa da nisan da abin ya shafa shine 40 cm.
Girman hoto (M)
M = -di / yi = -(-13)/40 = 13/40 = 0.3
Girman hoton ya fi ƙasa da 1, ma'ana girman hoton ya fi ƙasa da girman abu.
Tsayin hoton (h')
Daidaiton girman hoton:
M = h'/h
h' = M h = (0.3)(10 cm) = 3 cm
An sanya alamar tsayin hoton a kan tabbatacce, ma'ana hoton a tsaye yake.
