Misalai 2 na tambayoyi game da tabarau biyu masu convex-concave
1. Gilashin ruwan tabarau mai siffar convex yana da tsawon mai siffar convex na 30 cm kuma gilashin ruwan tabarau mai siffar convex yana da tsawon mai siffar convex na 20 cm wanda aka sanya kusa da juna inda nisan da ke tsakanin gilashin biyu shine 150 cm. Idan abin ya kasance 40 cm a gaban gilashin tabarau mai siffar convex, a tantance nisan hoton da girman hoton da gilashin ya samar. ruwan tabarau mai lanƙwasa dan ruwan tabarau mai lanƙwasa tafe!
Tattaunawa
An san cewa:
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa (f)1) = +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.
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa (f)2) = -20 cm
Tsawon firikwensin ruwan tabarau mai siffar ƙwallo yana da kyau saboda hasken ba ya ratsawa ta wurin firikwensin ruwan tabarau mai siffar ƙwallo.
Nisa tsakanin ruwan tabarau biyu (l) = 150 cm
Nisa tsakanin abin da ke cikin ruwan tabarau mai lanƙwasa (s) da ruwan tabarau mai lanƙwasa (s)1= 40 cm
Nisa tsakanin abu yana da kyau domin hasken yana ratsa ta cikin abu.
Amsa:
a) Nisa tsakanin inuwa
Nisa da hoton da ruwan tabarau mai lanƙwasa ya samar (nisan hoton farko):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/30 – 1/40 = 4/120 – 3/120 = 1/120
s1' = 120/1 = 120 cm
Hoton farko yana da nisan santimita 120 daga ruwan tabarau mai lanƙwasa.
Nisa na hoton farko yana da kyau, ma'ana hoton farko gaskiya ne domin hasken haske ne ke ratsa hoton.
Nisa da hoton da aka yi da ruwan tabarau mai lanƙwasa (nisan hoton ƙarshe):
Ana ɗaukar hoton da aka yi da ruwan tabarau mai lanƙwasa a matsayin abu ta hanyar ruwan tabarau mai lanƙwasa. Nisa na hoton/abu na farko daga ruwan tabarau mai lanƙwasa (s)2) = nisan da ke tsakanin ruwan tabarau biyu (l) - nisan hoton farko daga ruwan tabarau mai lanƙwasa (s1') = 150 cm – 120 cm = 30 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= -1/20 – (1/30) = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
s2' = -60/5 = -12 cm
Hoton ƙarshe yana da nisan santimita 12 daga ruwan tabarau mai lanƙwasa.
Nisa ta ƙarshe ta hoton ba ta da kyau, ma'ana hoton ƙarshe na ƙarya ne ko na ƙarya saboda hasken bai ratsa ta hoton ba.
b) Girman hoton
Girman hoton ta hanyar ruwan tabarau mai lanƙwasa:
m1 = -s1'/s1 = -120 cm/40 cm = -3 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 siffar concave:
m2 = -s2'/s2 = -(-12 cm)/30 cm = 12/30 = sau 0,4
Gilashin ruwan tabarau na biyu yana ƙara girman abin (hoton gilashin ido mai siffar ido) da sau 0,4.
Jimillar girman hoton shine:
m = (m1)(m2) = (-3)(0,4) = -1,2 sau
Girman hoton ƙarshe ya fi girman abu sau 1,2 girma ko kuma tsayin hoton ƙarshe ya fi tsayin abu sau 1,2 girma. Jimlar girman hoto mara kyau yana nufin an juya hoton.
2. Nisa tsakanin ruwan tabarau mai lanƙwasa da ruwan tabarau mai lanƙwasa shine 120 cm. Ruwan tabarau mai lanƙwasa yana da tsawon mai lanƙwasa na 50 cm, ruwan tabarau mai lanƙwasa kuma yana da tsawon mai lanƙwasa na 100 cm. Abu yana da 100 cm a gaban ruwan tabarau mai lanƙwasa. Kayyade nisan hoton da girmansa da ruwan tabarau biyu suka samar!
Tattaunawa
An sani :
Nisa tsakanin ruwan tabarau biyu (l) = 120 cm
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa (f)1= 50 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.
Tsawon mai da hankali na ruwan tabarau mai lanƙwasa (f)2) = -100 cm
Tsawon firikwensin ruwan tabarau mai siffar ƙwallo yana da kyau saboda hasken ba ya ratsawa ta wurin firikwensin ruwan tabarau mai siffar ƙwallo.
Nisa tsakanin abin da ke cikin ruwan tabarau mai lanƙwasa (s) da ruwan tabarau mai lanƙwasa (s)1= 100 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 ya samar (nisan hoton farko):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/50 – 1/100 = 2/100 – 1/100 = 1/100
s1' = 100/1 = 100 cm
Hoton farko yana da santimita 100 a gefen dama na ruwan tabarau mai lanƙwasa.
Nisa na hoton farko yana da kyau, ma'ana hoton farko gaskiya ne domin hasken haske ne ke ratsa hoton.
Nisa da hoton da aka yi da ruwan tabarau mai lanƙwasa (nisan hoton ƙarshe):
Ana ɗaukar hoton da aka yi da ruwan tabarau mai lanƙwasa a matsayin abu ta hanyar ruwan tabarau mai lanƙwasa. Nisa na hoton/abu na farko daga ruwan tabarau mai lanƙwasa (s)2) = nisan da ke tsakanin ruwan tabarau biyu – nisan hoton farko daga ruwan tabarau mai lanƙwasa = 120 cm – 100 cm = 20 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= -1/100 – 1/20 = -1/100 – 5/100 = -6/100
s2' = -100/6 = -16,7 cm
Hoton ƙarshe yana da nisan santimita 16,7 daga ruwan tabarau mai lanƙwasa.
Nisa ta ƙarshe ta hoton ba ta da kyau, ma'ana hoton ƙarshe na ƙarya ne ko na ƙarya saboda hasken bai ratsa ta hoton ba (hoton ƙarshe yana hagu na ruwan tabarau mai lanƙwasa).
b) Girman hoton
Girman hoton ta hanyar ruwan tabarau mai lanƙwasa:
m1 = -s1'/s1 = -100 cm/100 cm = -1 sau
Gilashin ruwan tabarau mai lanƙwasa yana sa girman hoton ya zama iri ɗaya da girman abu.
Girman hoton da alama mara kyau yana nufin hoton ya juya.
Girman hoton ta hanyar ruwan tabarau mai siffar concave:
m2 = -s2'/s2 = -(-16,7 cm)/20 cm = 16,7/20 = sau 0,8
Gilashin ruwan tabarau mai siffar ƙwallo yana rage girman abu (abu = hoton gilashin tabarau mai siffar ƙwallo) da sau 0,8.
Jimillar girman hoton shine:
m = (m1)(m2) = (-1)(0,8) = -0,8 sau
Girman hoton ƙarshe ya fi ƙasa da girman abu sau 0,8 ko kuma tsayin hoton ƙarshe ya fi ƙasa da tsayin abu sau 0,8. Jimillar girman hoto mara kyau yana nufin an juya hoton.
Tambayoyi game da ruwan tabarau biyu masu siffar Concave-convex
1. An sanya ruwan tabarau mai siffar convex mai tsawon 10 cm da ruwan tabarau mai siffar concave mai tsawon 40 cm kusa da juna inda nisan da ke tsakanin ruwan tabarau biyu ya kai 100 cm. Idan nisan abin da ke gaban ruwan tabarau mai siffar convex ya kai 20 cm, a tantance nisan hoton da girman hoton da ruwan tabarau mai siffar convex da concave suka samar!
Maɓallin amsawa:
(a) nisan hoto na ƙarshe = s2' = -26,7 cm.
(b) jimlar girman hoton = m = sau 0,33
