2 Tusaalooyin su'aalo ah oo ku saabsan muraayadaha laba-laaban ee isku-dhafan
1. Muraayad qaloocan waxay leedahay dherer focal ah oo ah 30 cm, muraayad qaloocanna waxay leedahay dherer focal ah oo ah 20 cm oo isku dhow halka masaafada u dhaxaysa labada muraayadood ay tahay 150 cm. Haddii shaygu uu yahay 40 cm oo ku yaal hore muraayad qaloocan, go'aami masaafada sawirka iyo weynaynta sawirka ay sameeyeen labada muraayadood. muraayad qaloocan dan muraayad qaloocan dib!
Dood
Waa la ogyahay in:
Dhererka diiradda ee muraayadda qaloocan (f)1) = +30 cm
Dhererka diiradda ee muraayadda qaloocan waa mid togan sababtoo ah iftiinka iftiinku wuxuu dhex maraa barta diiradda ee muraayadda qaloocan.
Dhererka diiradda ee muraayadda qaloocan (f)2) = -20 cm
Dhererka diiradda ee muraayadda qaloocan waa taban sababtoo ah iftiinka iftiinku ma dhex maro barta diiradda ee muraayadda qaloocan.
Masaafada u dhaxaysa labada muraayadood (l) = 150 cm
Masaafada shayga laga bilaabo muraayadda qaloocan (s)1) = 40cm
Masaafada shayga waa mid togan sababtoo ah iftiinka iftiinku wuxuu dhex maraa shayga.
Jawaab:
a) Masaafada hooska
Masaafada sawirka ee ay samaysay muraayadda qaloocan (masaafada sawirka koowaad):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/30 – 1/40 = 4/120 – 3/120 = 1/120
s1' = 120/1 = 120 cm
Sawirka ugu horreeya wuxuu 120 cm u jiraa muraayadda qaloocan.
Masaafada sawirka koowaad waa mid togan, taasoo la macno ah in sawirka koowaad uu yahay mid dhab ah sababtoo ah sawirka waxaa dhex mara iftiin.
Masaafada sawirka ee uu sameeyay muraayad qaloocan (masaafada sawirka kama dambaysta ah):
Sawirka ay samaysay muraayadda qaloocan waxaa loo arkaa shay iyadoo la adeegsanayo muraayad qaloocan. Masaafada sawirka/shayga ugu horreeya uu u jiro muraayadda qaloocan (s)2) = masaafada u dhaxaysa labada muraayadood (l) - masaafada sawirka koowaad laga bilaabo muraayadda qaloocan (s)1') = 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
Sawirka kama dambaysta ah wuxuu 12 cm u jiraa muraayadda qaloocan.
Masaafada sawirka ugu dambeeya waa taban, taasoo la micno ah in sawirka ugu dambeeya uu yahay been abuur ama been abuur sababtoo ah iftiinka iftiinku ma dhex maro sawirka.
b) Weyneynta sawirka
Weyneynta sawirka iyadoo la adeegsanayo muraayad qaloocan:
m1 = -s1'/s1 = -120 cm/40 cm = -3 jeer
Muraayad qaloocan ayaa cabirka sawirka ka dhigaysa inuu 3 jeer ka weynaado cabbirka shayga.
Weyneynta sawirka oo leh calaamad taban waxay la macno tahay in sawirku rogmanayo.
Weyneynta sawirka iyadoo la adeegsanayo muraayad qaloocan:
m2 = -s2'/s2 = -(-12 cm)/30 cm = 12/30 = 0,4 jeer
Muraayadda labaad ee qaloocan waxay weyneysaa shayga (sawirka muraayadda qaloocan) iyadoo leh 0,4 jeer.
Wadarta weyneynta sawirka waa:
m = (m1)(m2) = (-3)(0,4) = -1,2 jeer
Cabbirka sawirka ugu dambeeya waa 1,2 jeer ka weyn cabbirka shayga ama dhererka sawirka ugu dambeeya wuxuu ka sarreeyaa 1,2 jeer dhererka shayga. Weynaynta guud ee taban macnaheedu waa in sawirku rogman yahay.
2. Masaafada u dhaxaysa muraayadda qaloocan iyo muraayadda qaloocan waa 120 cm. Muraayadda qaloocan waxay leedahay dherer diiradda saaraya oo ah 50 cm, muraayadda qaloocanna waxay leedahay dherer diiradda saaraya oo ah 100 cm. Shaygu wuxuu 100 cm ka horreeyaa muraayadda qaloocan. Go'aami masaafada sawirka iyo weynaynta sawirka ay sameeyeen labada muraayadood!
Dood
Waa la garanayaa :
Masaafada u dhaxaysa labada muraayadood (l) = 120 cm
Dhererka diiradda ee muraayadda qaloocan (f)1) = 50cm
Dhererka diiradda ee muraayadda qaloocan waa mid togan sababtoo ah iftiinka iftiinku wuxuu dhex maraa barta diiradda ee muraayadda qaloocan.
Dhererka diiradda ee muraayadda qaloocan (f)2) = -100 cm
Dhererka diiradda ee muraayadda qaloocan waa taban sababtoo ah iftiinka iftiinku ma dhex maro barta diiradda ee muraayadda qaloocan.
Masaafada shayga laga bilaabo muraayadda qaloocan (s)1) = 100cm
Masaafada shayga waa mid togan sababtoo ah iftiinka iftiinku wuxuu ka yimaadaa shayga.
Jawab :
a) Masaafada hooska
Masaafada sawirka ee ay samaysay muraayadda qaloocan (masaafada sawirka koowaad):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/50 – 1/100 = 2/100 – 1/100 = 1/100
s1' = 100/1 = 100 cm
Sawirka ugu horreeya wuxuu 100 cm u jiraa dhanka midig ee muraayadda qaloocan.
Masaafada sawirka koowaad waa mid togan, taasoo la macno ah in sawirka koowaad uu yahay mid dhab ah sababtoo ah sawirka waxaa dhex mara iftiin.
Masaafada sawirka ee uu sameeyay muraayad qaloocan (masaafada sawirka kama dambaysta ah):
Sawirka ay samaysay muraayadda qaloocan waxaa loo arkaa shay iyadoo la adeegsanayo muraayad qaloocan. Masaafada sawirka/shayga ugu horreeya uu u jiro muraayadda qaloocan (s)2) = masaafada u dhaxaysa labada muraayadood - masaafada sawirka koowaad laga bilaabo muraayadda qaloocan = 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
Sawirka kama dambaysta ah wuxuu 16,7 cm u jiraa muraayadda qaloocan.
Masaafada sawirka kama dambaysta ah waa taban, taasoo la macno ah in sawirka kama dambaysta ah uu yahay been abuur ama been abuur sababtoo ah iftiinka iftiinku ma dhex maro sawirka (sawirka kama dambaysta ah wuxuu ku yaal bidixda muraayadda qaloocan).
b) Weyneynta sawirka
Weyneynta sawirka iyadoo la adeegsanayo muraayad qaloocan:
m1 = -s1'/s1 = -100 cm/100 cm = -1 jeer
Muraayad qaloocan ayaa sababta in cabbirka sawirku uu la mid noqdo cabbirka shayga.
Weyneynta sawirka oo leh calaamad taban waxay la macno tahay in sawirku rogmanayo.
Weyneynta sawirka iyadoo la adeegsanayo muraayad qaloocan:
m2 = -s2'/s2 = -(-16,7 cm)/20 cm = 16,7/20 = 0,8 jeer
Muraayad qaloocan ayaa yareysa cabbirka shay (shay = sawirka muraayad qaloocan) iyadoo 0,8 jeer la dhimayo.
Wadarta weyneynta sawirka waa:
m = (m1)(m2) = (-1)(0,8) = -0,8 jeer
Cabbirka sawirka ugu dambeeya waa 0,8 jeer ka yar cabbirka shayga ama dhererka sawirka ugu dambeeya waa 0,8 jeer ka hooseeya dhererka shayga. Weynaynta guud ee taban macnaheedu waa in sawirku rogman yahay.
Su'aalo muraayado laba-laab ah oo isku-dhafan oo isku-dhafan
1. Muraayad qaloocan oo dhererkeedu yahay 10 cm iyo muraayad qaloocan oo dhererkeedu yahay 40 cm ayaa la dhigayaa meel isku dhow halkaasoo masaafada u dhaxaysa labada muraayadood ay tahay 100 cm. Haddii masaafada shayga hortiisa muraayadda qaloocan ay tahay 20 cm, go'aami masaafada sawirka iyo weynaynta sawirka ay sameeyeen muraayadaha qaloocan iyo kuwa qaloocan!
Furaha jawaabta:
(a) masaafada sawirka ugu dambeysa = s2' = -26,7 cm.
(b) weyneynta guud ee sawirka = m = 0,33 jeer
