3 Tusaalooyin su'aalo muraayado qaloocan leh
1. Muraayad wareegsan wuxuu leeyahay dherer diiradda saaraya 5 cm. Sharax sameynta sawirka ka dibna go'aami masaafada sawirka iyo weyneynta sawirka haddii masaafada shayga laga soo bilaabo muraayadda qaloocan ay tahay 10 cm.
Dood
Waa la ogyahay in:
Dhererka muraayadda qaloocan (f) = 5 cm
Diiradda muraayadda qaloocan waa mid togan sababtoo ah barta diiradda ee muraayadda qaloocan waa meesha iftiinku ka gudbo ama uu yahay mid dhab ah.
Masaafada shayga (yada) = 10 cm
Jawaab:
Sawirka sameynta hooska walxaha :
Masaafada hooska:
1/s' = 1/f – 1/s = 1/5 – 1/10 = 2/10 – 1/10 = 1/10
s' = 10/1 = 10 cm
Masaafada hoosku waa 10 cm.
Weyneynta Sawirka:
M = -s'/s = -10/10 = -1 jeer
Weynaynta 1 macnaheedu waa in cabbirka hoosku uu la mid yahay cabbirka shayga.
Weynaynta sawirka taban macnaheedu waa in sawirku rogrogay. Sawirku waa toosan yahay haddii weynaynta sawirku tahay mid togan.
2. Shay dhererkiisu yahay 5 cm ayaa la hor dhigayaa muraayad qaloocan oo leh gacan qalooc ah oo ah 20 cm. Go'aami dhererka sawirka haddii masaafada u dhaxaysa shaygu ay tahay 5 cm, 15 cm, 20 cm, iyo 30 cm.
Dood
Waa la ogyahay in:
Kala-goysyada muraayadda qaloocan (R) = 20 cm
Dhererka diiradda muraayadda qaloocan (f) = R/2 = 20/2 = 10 cm
Diiradda muraayadda qaloocan waa mid togan sababtoo ah iftiinka iftiinku wuxuu dhex maraa barta diiradda.
Dhererka shayga (h) = 5 cm
Jawaab:
a) Masaafada diiradda (f) = 10 cm iyo masaafada shayga (yada) = 5 cm
Masaafada sawirka(yada):
1/s' = 1/f – 1/s = 1/10 – 1/5 = 1/10 – 2/10 = -1/10
s' = -10/1 = -10 cm
Masaafada sawirka taban macnaheedu waa in sawirku yahay mid casri ah ama sawirku wuxuu ka dambeeyaa muraayadda qaloocan halkaas oo iftiinka iftiinku uusan dhex marin sawirka.
Weyneynta Sawirka (M):
M = -s'/s = -(-10)/5 = 10/5 = 2 jeer
Weyneynta sawirka waa mid togan, taasoo la micno ah in sawirku uu toosan yahay.
Dhererka hooska (h'):
M = h'/saacaddii
h' = h M = (5 cm)(2) = 10 cm
Sawirka (h') wuxuu 10 cm ka sarreeyaa shayga (h) oo ah 5 cm.
b) Masaafada diiradda (f) = 10 cm iyo masaafada shayga (yada) = 15 cm
Masaafada sawirka(yada):
1/s' = 1/f – 1/s = 1/10 – 1/15 = 3/30 – 2/30 = 1/30
s' = 30/1 = 30 cm
Masaafada hooska togan waxay ka dhigan tahay in hoosku yahay mid dhab ah ama hoosku uu hor yaal muraayadda qaloocan halkaas oo iftiinka iftiinku uu dhex maro hooska.
Weyneynta Sawirka (M):
M = -s'/s = -30/15 = -2 jeer
Weyneynta sawirka oo leh calaamad taban waxay la macno tahay in sawirku rogmanayo.
Weyneynta sawirka waxay ka weyn tahay 1, taasoo la micno ah in cabbirka sawirku ka weyn yahay cabbirka shayga.
Dhererka hooska (h'):
M = h'/saacaddii
h' = h M = (5 cm)(2) = 10 cm
Sawirka (h') wuxuu 10 cm ka sarreeyaa shayga (h) oo ah 5 cm.
c) Masaafada diiradda (f) = 10 cm iyo masaafada shayga (yada) = 20 cm
Masaafada sawirka(yada):
1/s' = 1/f – 1/s = 1/10 – 1/20 = 2/20 – 1/20 = 1/20
s' = 20/1 = 20 cm
Masaafada hooska togan waxay ka dhigan tahay in hoosku yahay mid dhab ah ama hoosku uu hor yaal muraayadda qaloocan halkaas oo iftiinka iftiinku uu dhex maro hooska.
Weyneynta Sawirka (M):
M = -s'/s = -20/20 = -1 jeer
Weyneynta sawirka oo leh calaamad taban waxay la macno tahay in sawirku rogmanayo.
Weynaynta 1 macnaheedu waa in cabbirka sawirku uu la mid yahay cabbirka shayga.
Dhererka hooska (h'):
M = h'/saacaddii
h' = h M = (5 cm)(1) = 5 cm
Sawirka (h') 5 cm waa isla dhererka shayga (h) 5 cm.
d) Masaafada diiradda (f) = 10 cm iyo masaafada shayga (yada) = 30 cm
Masaafada sawirka(yada):
1/s' = 1/f – 1/s = 1/10 – 1/30 = 3/30 – 1/30 = 2/30
s' = 30/2 = 15 cm
Masaafada hooska togan waxay ka dhigan tahay in hoosku yahay mid dhab ah ama hoosku uu hor yaal muraayadda qaloocan halkaas oo iftiinka iftiinku uu dhex maro hooska.
Weyneynta Sawirka (M):
M = -s'/s = -15/30 = -0,5 jeer
Weyneynta sawirka oo leh calaamad taban waxay la macno tahay in sawirku rogmanayo.
Qiimaha weyneynta waa ka yar yahay 1, taasoo la micno ah in cabbirka sawirku ka yar yahay cabbirka shayga.
Dhererka hooska (h'):
M = h'/saacaddii
h' = h M = (5 cm)(0,5) = 2,5 cm
Sawirka (h') wuxuu 2,5 cm ka hooseeyaa shayga (h) 5 cm.
3. Sawirka casriga ah ee uu sameeyay muraayad qaloocan ayaa afar jeer ka weyn shayga. Haddii wareegga muraayaddu yahay 20 cm, markaa masaafada shayga hortiisa muraayadda waa…
Dood
Waa la garanayaa :
Weyneynta Sawirka (M) = 4
Kala-baxa muraayadda (R) = 20 cm
Masaafada diiradda (f) = R/2 = 20/2 = 10 cm
La weydiiyay Masaafada shayga (yada)
Jawab :
M = – s' / s
4 = – s' / s
– s' = 4 ilbiriqsi
s' = – 4 ilbiriqsi
1/f = 1/s + 1/s'
1/10 = 1/2 + 1/4s
4/40 = 4/4s + 1/4s
4/40 = 5/4s
(4)(4) = (5)(40)
16 ilbiriqsi = 200
s = 12,5 cm
Masaafada shayga ee muraayadda horteeda waa 12,5 cm.
Su'aalo muraayad isku dhafan
1. Shay dhererkiisu yahay 3 cm wuxuu ku yaal masaafo dhan 3 cm oo ka horreysa dusha sare ee muraayadda qaloocan ee iftiimisa iftiinka. Haddii dhererka diiradda muraayadda qaloocan uu yahay 6 cm, go'aami: (a) masaafada sawirka, (b) weynaynta sawirka, (c) dhererka sawirka, (d) sifooyinka sawirka.
Furaha jawaabta:
(a) s' = – 6 cm
(b) M = 2
(c) h' = 6 cm
(d) sifooyinka sawirka: dalwad, toosan, la ballaariyay
2. Masaafada shay u jirta muraayad qaloocan oo leh gacan qalooc ah 16 cm waa 12 cm. Haddii dhererka shaygu yahay 4 cm, go'aami: (a) masaafada sawirka, (b) weynaynta sawirka, (c) dhererka sawirka, (d) sifooyinka sawirka.
Furaha jawaabta:
(a) s' = 24 cm
(b) M = -2
(c) h' = -8 cm
(d) sifooyinka sawirka: dhab ah, rogmaday, la ballaariyay
3. Shay wuxuu u jiraa 20 cm muraayad qaloocan oo dhererkeedu yahay 5 cm. Go'aami: (a) masaafada sawirka, (b) weyneynta sawirka, (c) dhererka sawirka haddii dhererka shaygu yahay 5 cm, (d) sifooyinka sawirka.
Furaha jawaabta:
(a) s' = 6,7 cm
(b) M = -1/3
(c) h' = -5/3 cm
(d) sifooyinka sawirka: dhab ah, rogmaday, cabbirkiisu yar yahay
4. Sawirka casriga ah ee uu sameeyay muraayad qaloocan ayaa laba jibaar ka weyn cabbirka shayga. Haddii dhererka diiradda muraayadda qaloocan uu yahay 20 cm, markaa masaafada shayga hortiisa muraayadda qaloocan waa…
Furaha jawaabta:
(a) s = 10 cm
