Misalai 2 na tambayoyin ruwan tabarau masu siffar convex
1. An sanya ruwan tabarau guda biyu masu lanƙwasa, kowannensu yana da tsawon mai da hankali na 20 cm da 30 cm, kusa da juna, inda nisan da ke tsakanin ruwan tabarau masu lanƙwasa biyu ya zama 70 cm. Abu yana da nisan 30 cm a gaban ruwan tabarau na farko. A ƙayyade nisan hoton da girmansa da aka yi ta ruwan tabarau guda biyu. ruwan tabarau mai lanƙwasa tafe!
Tattaunawa
An san cewa:
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa na farko (f)1) = +20 cm
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa na biyu (f)2) = +30 cm
Tsawon haske na ruwan tabarau mai siffar convex yana da kyau saboda hasken yana ratsawa ta cikin wurin da ruwan tabarau mai siffar convex yake.
Nisa tsakanin ruwan tabarau biyu masu lanƙwasa (l) = 50 cm
Nisa tsakanin abin da ke cikin ruwan tabarau mai lanƙwasa na farko (s)1= 30 cm
Nisa tsakanin abu da abu yana da kyau domin hasken yana fitowa ta cikin abu.
Amsa:
a) Nisa tsakanin inuwa
Nisa da hoton da ruwan tabarau mai lanƙwasa na farko ya samar (nisan hoton farko):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s1' = 60/1 = 60 cm
Hoton farko yana da nisan santimita 60 daga ruwan tabarau mai lanƙwasa 1.
Nisa tsakanin hoton farko da na farko yana da kyau, ma'ana hoton farko na gaske ne, ma'ana yana wanzuwa da gaske saboda hasken yana ratsa hoton.
Nisa da hoton da aka samu ta hanyar ruwan tabarau mai lanƙwasa na biyu (nisan hoton ƙarshe):
Ana ɗaukar hoton da aka samar da ruwan tabarau mai siffar convex na farko a matsayin abu ta hanyar ruwan tabarau mai siffar convex na biyu. Nisa na hoton/abu na farko daga ruwan tabarau mai siffar convex na biyu (s)2) = nisan da ke tsakanin ruwan tabarau biyu masu lanƙwasa – nisan hoton farko daga ruwan tabarau mai lanƙwasa na farko = 70 cm – 60 cm = 10 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= 1/30 – 1/10 = 1/30 – 3/30 = -2/30
s2' = -30/2 = -15 cm
Hoton ƙarshe yana da nisan santimita 15 daga ruwan tabarau na biyu mai lanƙwasa.
Nisa ta ƙarshe ta hoton ba ta da kyau, ma'ana hoton ƙarshe na ƙarya ne ko na ƙarya domin ba a wuce hoton ta hanyar hasken ba (hoton ƙarshe yana hagu na ruwan tabarau na biyu mai lanƙwasa).
b) Girman hoton
Girman hoton ta hanyar ruwan tabarau mai lanƙwasa na farko:
m1 = -s1'/s1 = -60 cm/30 cm = -2 sau
Gilashin ruwan tabarau mai lanƙwasa yana sa girman hoton ya fi girman abin sau biyu.
Girman hoton da alama mara kyau yana nufin hoton ya juya.
Girman hoton ta hanyar ruwan tabarau mai lanƙwasa na biyu:
m2 = -s2'/s2 = -(-15 cm)/10 cm = 15/10 = sau 1,5
Gilashin ruwan tabarau na biyu yana ƙara girman abin (hoton gilashin tabarau na farko) da maki 1,5.
Jimillar girman hoton shine:
m = (m1)(m2) = (-2)(1,5) = -3 sau
Girman hoton ƙarshe ya fi girman abu sau 3 girma ko kuma tsayin hoton ƙarshe ya fi tsayin abu sau 3 girma. Jimlar girman hoto mara kyau ne ma'ana hoton ya juya. (hoton ƙarshe ya juya don haka hoton ƙarshe dole ne ya kasance a hagu na ruwan tabarau na biyu mai lanƙwasa).
2. Nisa tsakanin ruwan tabarau masu lanƙwasa guda biyu shine 100 cm. Ruwan tabarau masu lanƙwasa guda biyu kowannensu yana da tsayin daka na 20 cm da 80 cm. Abu yana da 30 cm a gaban ruwan tabarau na farko. Kayyade nisan hoton da girmansa da ruwan tabarau masu lanƙwasa guda biyu suka samar!
Tattaunawa
An sani :
Nisa tsakanin ruwan tabarau biyu (l) = 100 cm
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa na farko (f)1= 20 cm
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa na biyu (f)2= 80 cm
Tsawon haske na ruwan tabarau mai siffar convex yana da kyau saboda hasken yana ratsawa ta cikin wurin da ruwan tabarau mai siffar convex yake.
Nisa tsakanin abin da ke cikin ruwan tabarau mai lanƙwasa na farko (s)1= 30 cm
Nisa tsakanin abu da abu yana da kyau domin hasken yana fitowa ta cikin abu.
Jawab :
a) Nisa tsakanin inuwa
Nisa da hoton da ruwan tabarau mai lanƙwasa na farko ya samar (nisan hoton farko):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s1' = 60/1 = 60 cm
Hoton farko yana da nisan santimita 60 daga ruwan tabarau mai lanƙwasa 1.
Nisa tsakanin hoton farko da na farko yana da kyau, ma'ana hoton farko na gaske ne, ma'ana yana wanzuwa da gaske saboda hasken yana ratsa hoton.
Nisa da hoton da aka samu ta hanyar ruwan tabarau mai lanƙwasa na biyu (nisan hoton ƙarshe):
Ana ɗaukar hoton da aka samar da ruwan tabarau mai siffar convex na farko a matsayin abu ta hanyar ruwan tabarau mai siffar convex na biyu. Nisa na hoton/abu na farko daga ruwan tabarau mai siffar convex na biyu (s)2) = nisan da ke tsakanin ruwan tabarau biyu masu lanƙwasa – nisan hoton farko daga ruwan tabarau mai lanƙwasa na farko = 100 cm – 60 cm = 40 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= 1/80 – 1/40 = 1/80 – 2/80 = -1/80
s2' = -80/1 = -80 cm
Hoton ƙarshe yana da nisan santimita 80 daga ruwan tabarau na biyu mai lanƙwasa.
Nisa ta ƙarshe ta hoton ba ta da kyau, ma'ana hoton ƙarshe na ƙarya ne ko na ƙarya domin ba a wuce hoton ta hanyar hasken ba (hoton ƙarshe yana hagu na ruwan tabarau na biyu mai lanƙwasa).
b) Girman hoton
Girman hoton ta hanyar ruwan tabarau mai lanƙwasa na farko:
m1 = -s1'/s1 = -60 cm/30 cm = -2 sau
Gilashin ruwan tabarau mai lanƙwasa yana sa girman hoton ya fi girman abin sau biyu.
Girman hoton da alama mara kyau yana nufin hoton ya juya.
Girman hoton ta hanyar ruwan tabarau mai lanƙwasa na biyu:
m2 = -s2'/s2 = -(-80 cm)/40 cm = 80/40 = sau 2
Gilashin ruwan tabarau na biyu yana ƙara girman abin (hoton gilashin tabarau na farko) da maki 2.
Jimillar girman hoton shine:
m = (m1)(m2) = (-2)(2) = -4 sau
Girman hoton ƙarshe ya fi girman abu sau 4 girma ko kuma tsayin hoton ƙarshe ya fi tsayin abu sau 4. Jimlar girman hoto mara kyau ne ma'ana hoton ya juya (hoton ƙarshe an juya shi don haka hoton ƙarshe dole ne ya kasance a hagu na ruwan tabarau na biyu mai lanƙwasa).
Tambayoyi game da ruwan tabarau mai siffar Concave convex biyu
1. Gilashin tabarau guda biyu masu siffar ƙwallo kowannensu yana da tsawon 40 cm da 20 cm an sanya su kusa da juna inda nisan da ke tsakanin gilashin tabarau guda biyu masu siffar ƙwallo ya kai 100 cm. A ƙayyade nisan hoton da kuma girman hoton da aka yi ta hanyar gilashin tabarau guda biyu masu siffar ƙwallo a kan wani abu da yake da nisan 120 cm a gaban gilashin tabarau na farko masu siffar ƙwallo!
Maɓallin amsawa:
(a) nisan hoto na ƙarshe = s2' = 40
(b) jimlar girman hoton = m = 0,5
2. Abu yana da nisan santimita 10 a hagu na ruwan tabarau mai siffar ƙwallo mai tsawon santimita 20. A gefen dama na ruwan tabarau mai siffar ƙwallo akwai ruwan tabarau mai siffar ƙwallo mai tsawon santimita 50. Idan nisan da ke tsakanin ruwan tabarau biyu ya kai santimita 120, a tantance nisan hoton da girman hoton da ruwan tabarau masu siffar ƙwallo biyu suka samar!
Maɓallin amsawa:
(a) nisan hoto na ƙarshe = s2' = 133 cm
(b) jimlar girman hoton = m = -1,7 sau. Ma'ana mara kyau yana nufin hoton ya juya.
