Domin fahimtar hoton wani abu da aka samar ta hanyar ruwan tabarau mai siffar ƙwallo, bincika misali mai zuwa tambaya da tattaunawa. A cikin wannan tambayar, ana ɗauka cewa abin yana da wani nisa daga ruwan tabarau mai siffar ƙwallo, sannan an bayyana samuwar hoton abin ta hanyar ruwan tabarau mai siffar ƙwallo , nisan hoton daga ruwan tabarau mai siffar ƙwallo da kuma girman hoton ta hanyar ruwan tabarau mai siffar ƙwallo .
Tsawon ruwan tabarau mai siffar ƙwallo (ruwan tabarau masu karkata) shine 20 cm. Akwai wani abu mai tsawon cm 10 a gefen hagu na ruwan tabarau. A tantance 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 abin yayi daidai da tsawon mai da hankali na ruwan tabarau mai lanƙwasa
c) nisan abu ya fi tsawon mai da hankali na ruwan tabarau mai lanƙwasa,
Tattaunawa
An sani :
Tsawon maƙasudi (f) na ruwan tabarau mai lanƙwasa = -20 cm
Tsawon firikwensin ruwan tabarau mai siffar ƙwallo yana da kyau saboda wurin firikwensin ruwan tabarau mai siffar ƙwallo yana kama da na kama-da-wane ko kuma hasken bai wuce ta ba.
Tsawon abu (h) = 10 cm
Jawab :
Nisa tsakanin abu da na'urar ya fi ƙanƙanta fiye da tsawon mai da hankali na ruwan tabarau mai lanƙwasa (s > f)
A ce nisan abin shine 5 cm, 10 cm da 15 cm.
a) Tsawon maƙasudi -20 cm kuma idan nisan abu (s) = 5 cm
Nisa tsakanin hotuna (s)
1/s' = 1/f – 1/s = -1/20 – 1/5 = -1/20 – 4/20 = -5/20
s' = -20/5 = -4 cm
Nisa mara kyau ta hoto yana nufin hoto na kama-da-wane, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da santimita 4 ya fi ƙasa da nisan abu da santimita 5.
Ƙara girman hoto (M)
M = -s'/s = -(-4)/5 = 4/5 = 0,8
Girman hoton bai kai 1 ba, ma'ana an rage hoton ko kuma girman hoton ya fi girman abin.
Tsawon inuwar (h')
Tsarin ƙara girman inuwa:
M = h'/h
h' = M h = (0,8)(10 cm) = 8 cm
Tsayin inuwar yana da kyau, ma'ana inuwar tana tsaye.
b) Tsawon maƙasudi -20 cm kuma idan nisan abu (s) = 10 cm
Nisa tsakanin hotuna (s)
1/s' = 1/f – 1/s = -1/20 – 1/10 = -1/20 – 2/20 = -3/20
s' = -20/3 = -6,7 cm
Nisa mara kyau ta hoto yana nufin hoto na kama-da-wane, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da santimita 6,7 ya fi ƙasa da nisan abu da santimita 10.
Ƙara girman hoto (M)
M = -s'/s = -(-6,7)/10 = 6,7/10 = 0,67
Girman hoton bai kai 1 ba, ma'ana an rage hoton ko kuma girman hoton ya fi girman abin.
Tsawon inuwar (h')
Tsarin ƙara girman inuwa:
M = h'/h
h' = M h = (0,67)(10 cm) = 6,7 cm
Tsayin inuwar yana da kyau, ma'ana inuwar tana tsaye.
c) Tsawon maƙasudi -20 cm kuma idan nisan abu (s) = 15 cm
Nisa tsakanin hotuna (s)
1/s' = 1/f – 1/s = -1/20 – 1/15 = -3/60 – 4/60 = -7/60
s' = -60/7 = -8,6 cm
Nisa mara kyau ta hoto yana nufin hoto na kama-da-wane, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da santimita 8,7 ya fi ƙasa da nisan abu da santimita 15.
Ƙara girman hoto (M)
M = -s'/s = -(-8,6)/10 = 8,6/10 = 0,86
Girman hoton bai kai 1 ba, ma'ana an rage hoton ko kuma girman hoton ya fi girman abin.
Tsawon inuwar (h')
Tsarin ƙara girman inuwa:
M = h'/h
h' = M h = (0,86)(10 cm) = 8,6 cm
Tsayin inuwar yana da kyau, ma'ana inuwar tana tsaye.
Nisa tsakanin abu da tsawon mai da hankali na ruwan tabarau mai lanƙwasa (s = f)
Tsawon maƙasudi (f) = nisan abu (s) = 20 cm.
Nisa tsakanin hotuna (s)
1/s' = 1/f – 1/s = -1/20 – 1/20 = -2/20 = -2/20
s' = -20/2 = -10 cm
Nisa mara kyau ta hoto yana nufin hoto na kama-da-wane, inda hasken ba ya ratsawa ta cikin inuwa.
Nisa tsakanin hoton da santimita 10 ya fi ƙasa da nisan abu da santimita 20.
Ƙara girman hoto (M)
M = -s'/s = -(-10)/20 = 10/20 = 0,5
Girman hoton bai kai 1 ba, ma'ana an rage hoton ko kuma girman hoton ya fi girman abin.
Tsawon inuwar (h')
Tsarin ƙara girman inuwa:
M = h'/h
h' = M h = (0,5)(10 cm) = 5 cm
Tsayin inuwar yana da kyau, ma'ana inuwar tana tsaye.
Nisa tsakanin abu da na'urar ya fi tsayin daka na ruwan tabarau mai lanƙwasa (s > f)
A ce nisan da ke tsakanin abubuwan shine 30 cm da 40.
a) Tsawon maƙasudi -20 cm kuma idan nisan abu (s) = 30 cm
Nisa tsakanin hotuna (s)
1/s' = 1/f – 1/s = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
s' = -60/5 = -12 cm
Nisa mara kyau ta hoto yana nufin hoto na kama-da-wane, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da santimita 12 ya fi ƙasa da nisan abu da santimita 30.
Ƙara girman hoto (M)
M = -s'/s = -(-12)/30 = 12/30 = 0,4
Girman hoton bai kai 1 ba, ma'ana an rage hoton ko kuma girman hoton ya fi girman abin.
Tsawon inuwar (h')
Tsarin ƙara girman inuwa:
M = h'/h
h' = M h = (0,4)(10 cm) = 4 cm
Tsayin inuwar yana da kyau, ma'ana inuwar tana tsaye.
b) Tsawon maƙasudi -20 cm kuma idan nisan abu (s) = 40 cm
Nisa tsakanin hotuna (s)
1/s' = 1/f – 1/s = -1/20 – 1/40 = -2/40 – 1/40 = -3/40
s' = -40/3 = -13 cm
Nisa mara kyau ta hoto yana nufin hoto na kama-da-wane, inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da santimita 13 ya fi ƙasa da nisan abu da santimita 40.
Ƙara girman hoto (M)
M = -s'/s = -(-13)/40 = 13/40 = 0,3
Girman hoton bai kai 1 ba, ma'ana an rage hoton ko kuma girman hoton ya fi girman abin.
Tsawon inuwar (h')
Tsarin ƙara girman inuwa:
M = h'/h
h' = M h = (0,3)(10 cm) = 3 cm
Tsayin inuwar yana da kyau, ma'ana inuwar tana tsaye.
