Labari game da ƙirƙirar hoto ta madubin convex
Domin fahimtar samuwar hoto ta madubin da ke kewaye da shi, koyi misalan matsaloli da mafita a ƙasa. A wannan yanayin, ana ɗauka cewa abu yana nesa da madubin da ke kewaye da shi,
sannan a zana siffar hoton ta hanyar madubin da ke da siffar lanƙwasa, nisan hoton daga madubin da ke da siffar lanƙwasa da kuma girman hoton ta hanyar madubin da ke da siffar lanƙwasa.
A ce madubi mai lanƙwasa yana da radius na 30 cm. Zana siffar hoton sannan a tantance nisan hoton da girman hoton, idan:
a) Nisa tsakanin abu da abin ya fi ƙanƙanta fiye da tsawon mai da hankali (do < f)
b) Nisa tsakanin abu da tsawon mai da hankali (do = f)
c) Nisa tsakanin abu da abin ya fi tsayin da aka mayar da hankali a kai kuma ya fi ƙanƙanta fiye da radius na lanƙwasa madubi (f < do)
d) Nisa tsakanin abu da radius na lanƙwasa madubin (do = R)
e) Nisa tsakanin abu ya fi radius na lanƙwasa madubin (yi > R)
An sani:
Radius na lanƙwasa na madubin mai lanƙwasa (R) = 30 cm
Tsawon madubin mai lanƙwasa (f) = R / 2 = 30/2 = -15 cm
Wurin da aka fi mayar da hankali a kai yana bayan madubin da ke da santsi, inda hasken ba ya ratsa wurin da aka fi mayar da hankali a kai. Saboda haka, ana ba wa madubin da ke da santsi alama mara kyau.
Magani:
Nisa tsakanin abu da abin ya fi ƙanƙanta fiye da tsawon madubin da ke da lanƙwasa (do < f)
A ce nisan da ke tsakanin abu da madubin shine 5 cm da 10 cm.
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Tsawon mai da hankali (f) = -15 cm kuma idan nisan abu (d o ) = 5 cm
Nisa ta hoton ( di ) :
1/di = 1/f - 1/s = -1/15 - 1/5 = -1/15 - 3/15 = -4/20
di = -20/4 = -5 cm
Nisa ta hoton (di) tana da alamar mara kyau ma'ana hoton yana kama da na kama-da-wane, ko kuma hoton yana bayan madubi, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton (d) 5 cm daidai yake da nisan abu (d) 5 cm
Girman hoto mai layi (M) :
M = -di / yi = -(-5)/5 = 5/5 = 1 lokaci
Girman hoto mai layi (M) 1 yana nufin girman hoton yayi daidai da girman abin.
Girman hoto mai layi (M) yana da alama mai kyau, ma'ana hoton yana tsaye.
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Tsawon mai da hankali (f) = -15 cm kuma idan nisan abu (yi) = 10 cm
Nisa ta hoton ( di ) :
1/di = 1/f – 1/do = -1/15 – 1/10 = -2/30 – 3/30 = -5/30
di = -30/5 = -6 cm
Nisa ta hoton (di) tana da alamar mara kyau ma'ana hoton yana kama da na kama-da-wane, ko kuma hoton yana bayan madubin da ke da lanƙwasa, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton (di) 6 cm ya fi ƙasa da nisan abu (do) 10 cm.
Girman hoto mai layi (M) :
M = -di / yi = -(-6)/10 = 6/10 = sau 0.6
Girman hoto (M) a layi ya fi 1 ƙasa da girmansa, ma'ana girman hoton ya fi girman abin ƙanƙanta.
Girman hoton layi (M) yana da alama mai kyau ma'ana cewa hoton yana tsaye.
Nisa tsakanin abu da tsawon madubin da ke da kusurwa (do = f) iri ɗaya ne da tsawon mai da hankali (do = f)
Tsawon mai da hankali (f) = nisan abu (do) = 15 cm.
Nisa ta hoton (di ) :
1/di = 1/f – 1/do = -1/15 – 1/15 = -2/15
di = -15/2 = -7.5 cm
Nisa ta hoton (di) tana da alamar mara kyau ma'ana hoton yana kama da na kama-da-wane, ko kuma hoton yana bayan madubin da ke da lanƙwasa, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton (di) 7.5 cm ya fi ƙasa da nisan abu (do) 15 cm
Girman hoto mai layi (M) :
M = -di / yi = -(-7,5)/15 = 7.5 / 15 = sau 0.5
Girman hoto (M) a layi ya fi 1 ƙasa da girmansa, ma'ana girman hoton ya fi girman abin ƙanƙanta.
Girman hoto mai layi (M) yana da alama mai kyau, ma'ana hoton yana tsaye.
Nisa tsakanin abu da na'urar ta fi tsayin daka kuma ta fi ƙanƙanta fiye da radius na lanƙwasa na madubin da ke lanƙwasa (f < do < R)
A ce nisan da ke tsakanin abu da madubin shine 20 cm da 25 cm.
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Tsawon mai da hankali (f) = -15 cm kuma idan nisan abu (yi) = 20 cm
Nisa ta hoton ( di ) :
1/di = 1/f – 1/do = -1/15 – 1/20 = -4/60 – 3/60 = -7/60
di = -60/7 = -8.6 cm
Nisa ta hoton (di) tana da alamar mara kyau ma'ana hoton yana kama da na kama-da-wane, ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton (di) 8.6 cm ya fi ƙasa da nisan abu (do) 20 cm
Girman hoto mai layi (M) :
M = -di / yi = -(-8.6)/20 = 8.6 / 20 = sau 0.4
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da alama mai kyau ma'ana cewa hoton yana tsaye.
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Tsawon mai da hankali (f) = -15 cm kuma idan nisan abu (yi) = 25 cm
Nisa ta hoton ( di ) :
1/di = 1/f – 1/do = -1/15 – 1/25 = -25/375 – 15/375 = -35/375
di = -375/35 = -10.7 cm
Nisa ta hoton (di) tana da alamar mara kyau ma'ana hoton yana kama da na kama-da-wane, ko kuma hoton yana bayan madubin da ke da lanƙwasa, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton (di) 10.7 cm, ƙasa da nisan abu (do) 25 cm
Girman hoto mai layi (M) :
M = -di / do = -(-10.7) / 25 = 10.7 / 25 = sau 0.4
Girman hoto (M) a layi ya fi 1 ƙasa da girmansa, ma'ana girman hoton ya fi girman abin ƙanƙanta.
Girman hoton layi (M) yana da alama mai kyau ma'ana cewa hoton yana tsaye.
Nisa tsakanin abu da radius na lanƙwasa na madubin mai lanƙwasa (do = R)
Radius na lanƙwasa madubi (R) = nisan abu (yi) = 30 cm.
Nisa ta hoton ( di ) :
1/di = 1/f – 1/do = -1/15 – 1/30 = -2/30 – 1/30 = -3/30
di = -30/3 = -10 cm
Nisa ta hoton (di) tana da alamar mara kyau ma'ana hoton yana kama da na kama-da-wane, ko kuma hoton yana bayan madubin da ke da lanƙwasa, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton (di) 10 cm, ƙasa da nisan abu (do) 30 cm
Girman hoto mai layi (M) :
M = -di / yi = -(-10)/30 = 1/3
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da alama mai kyau ma'ana cewa hoton yana tsaye.
Nisa tsakanin abu da na'urar ya fi radius na lanƙwasa na madubin da ke lanƙwasa (yi > R)
A ce nisan da ke tsakanin abu da madubin shine 40 cm da 50 cm.
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Tsawon mai da hankali (f) = -15 cm kuma idan nisan abu (yi) = 40 cm
Nisa ta hoton ( di ) :
1/di = 1/f – 1/do = -1/15 – 1/40 = -8/120 – 3/120 = -11/120
di = -120/11 = -10.9 cm
Nisa ta hoton (di) tana da alamar mara kyau ma'ana hoton yana kama da na kama-da-wane, ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton (di) 10.9 cm, ƙasa da nisan abu (do) 40 cm
Girman hoto mai layi ( M) :
M = -di / do = -(-10.9) / 40 = 10.9 / 40 = sau 0.3
Girman hoto (M) a layi ya fi 1 ƙasa da girmansa, ma'ana girman hoton ya fi girman abin ƙanƙanta.
Girman hoton layi (M) yana da alama mai kyau ma'ana cewa hoton yana tsaye.
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Tsawon mai da hankali, f) = -15 cm da nisan abu (do) = 50 cm
Nisa ta hoton ( di ) :
1/di = 1/f – 1/di = -1/15 – 1/50 = -10/150 – 3/150 = -13/150
di = -150/13 = -11.5 cm
Nisa ta hoton (di) tana da alamar mara kyau ma'ana hoton yana kama da na kama-da-wane, ko kuma hoton yana bayan madubi mai lanƙwasa, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton (a) 11.5 cm, ƙasa da nisan abu (a) 50 cm
Girman hoto mai layi (M) :
M = -di / do = -(-11.5) / 50 = 11.5 / 50 = sau 0.2
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoto mai layi (M) yana da alama mai kyau, ma'ana hoton yana tsaye.
