1. Muraayad wareegsan wuxuu leeyahay dherer diiradda saaraya 10 cm. Sharax sameynta sawirka ka dibna go'aami masaafada sawirka iyo weyneynta sawirka haddii masaafada shayga laga soo bilaabo muraayadda qaloocan ay tahay 20 cm.
Dood
Waa la ogyahay in:
Dhererka diiradda muraayadda qaloocan (f) = -10 cm
Diiradda muraayadda qaloocan waa taban sababtoo ah barta diiradda ee muraayadda qaloocan iftiin ma dhex marto ama waa mid dalwad ah.
Masaafada shayga (yada) = 20 cm
Jawaab:
Sawirka sameynta hooska walxaha :
Masaafada hooska:
1/s' = 1/f – 1/s = -1/10 – 1/20 = -2/20 – 1/20 = -3/20
s' = -20/3 = -6,7 cm
Masaafada hoosku waa taban, taasoo la macno ah in hoosku yahay mid casri ah ama iftiinka iftiinku uusan dhex marin hooska.
Masaafada sawirka waa 6,7 cm ka yar masaafada shayga ee 20 cm.
Weyneynta Sawirka:
M = -s'/s = -(-6,7)/20 = 6,7/20 = 0,3 jeer
Weynaynta 0,3 waxay la macno tahay in cabbirka hoosku uu 0,3 jeer ka yar yahay cabbirka shayga.
Weynaynta sawirka togan macnaheedu waa sawirku waa toosan yahay. Sawirka waa la rogaa haddii weynaynta sawirku tahay mid taban.
2. Shay dhererkiisu yahay 10 cm ayaa la dhigayaa muraayad qaloocan oo dhererkeedu yahay 20 cm. Go'aami dhererka sawirka haddii masaafada shayga hortiisa muraayadda ay tahay 10 cm, 30 cm, 40 cm, iyo 50 cm.
Dood
Waa la ogyahay in:
Dhererka diiradda muraayadda qaloocan (f) = -20 cm
Diiradda muraayadda qaloocan waa taban sababtoo ah iftiinka iftiinku ma dhex maro barta diiradda ee ku taal muraayadda gadaasheed.
Kala-goysyada qalooca muraayadda qaloocan (R) = 2f = 2(20) = 40 cm
Dhererka shayga (h) = 10 cm
Jawaab:
a) Masaafada diiradda (f) = -20 cm iyo masaafada shayga (yada) = 10 cm
Masaafada sawirka(yada):
1/s' = 1/f – 1/s = -1/20 – 1/10 = -1/20 – 2/20 = -3/20
s' = -20/3 = -6,7
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 = -(-6,7)/10 = 6,7/10 = 0,67 jeer
Weyneynta sawirka waa mid togan, taasoo la micno ah in sawirku uu toosan yahay.
Weyneynta toosan ee sawirka (M) waxay ka yar tahay 1, taasoo la micno ah in cabbirka sawirku uu ka yar yahay cabbirka shayga.
Dhererka hooska (h'):
M = h'/saacaddii
h' = h M = (10 cm)(0,67) = 6,7 cm
Sawirka (h') wuxuu 6,7 cm ka hooseeyaa shayga (h) 10 cm.
b) Masaafada diiradda (f) = -20 cm iyo masaafada shayga (yada) = 30 cm
Masaafada sawirka(yada):
1/s' = 1/f – 1/s = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
s' = -60/5 = -12
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 = -(-12)/30 = 12/30 = 0,4 jeer
Weyneynta sawirka waa mid togan, taasoo la micno ah in sawirku uu toosan yahay.
Weyneynta toosan ee sawirka (M) waxay ka yar tahay 1, taasoo la micno ah in cabbirka sawirku uu ka yar yahay cabbirka shayga.
Dhererka hooska (h'):
M = h'/saacaddii
h' = h M = (10 cm)(0,4) = 4 cm
Sawirka (h') wuxuu 4 cm ka hooseeyaa shayga (h) 10 cm.
c) Masaafada diiradda (f) = -20 cm iyo masaafada shayga (yada) = 40 cm
Masaafada sawirka(yada):
1/s' = 1/f – 1/s = -1/20 – 1/40 = -2/40 – 1/40 = -3/40
s' = -40/3 = -13,3
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 = -(-13,3)/40 = 13,3/40 = 0,3 jeer
Weyneynta sawirka waa mid togan, taasoo la micno ah in sawirku uu toosan yahay.
Weyneynta toosan ee sawirka (M) waxay ka yar tahay 1, taasoo la micno ah in cabbirka sawirku uu ka yar yahay cabbirka shayga.
Dhererka hooska (h'):
M = h'/saacaddii
h' = h M = (10 cm)(0,3) = 3 cm
Sawirka (h') wuxuu 3 cm ka hooseeyaa shayga (h) 10 cm.
d) Masaafada diiradda (f) = -20 cm iyo masaafada shayga (yada) = 50 cm
Masaafada sawirka(yada):
1/s' = 1/f – 1/s = -1/20 – 1/50 = -5/100 – 2/100 = -7/100
s' = -100/7 = -14,3
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 = -(-14,3)/50 = 14,3/50 = 0,3 jeer
Weyneynta sawirka waa mid togan, taasoo la micno ah in sawirku uu toosan yahay.
Weyneynta toosan ee sawirka (M) waxay ka yar tahay 1, taasoo la micno ah in cabbirka sawirku uu ka yar yahay cabbirka shayga.
Dhererka hooska (h'):
M = h'/saacaddii
h' = h M = (10 cm)(0,3) = 3 cm
Sawirka (h') wuxuu 3 cm ka hooseeyaa shayga (h) 10 cm.
3. Shay wuxuu 20 cm ka hor yaallaa muraayad qaloocan. Haddii sawirka la sameeyay uu yahay 1/5 jibaar dhererka shayga, go'aami a) masaafada sawirka, b) dhererka diiradda, c) dabeecadda sawirka.
Dood
Waa la garanayaa :
Masaafada shayga (yada) = 20 cm
Dhererka sawirka (h') = 1/5 saac = 0,2 saac
Dhererka hooska (h) = h
Jawab :
a) Masaafada sawirka (yada)
Qaacidada weynaynta hooska:
M = h'/h = 0,2h/h = 0,2 jeer
Weyneynta togan ee sawirka waxay la macno tahay in sawirku uu toosan yahay.
Weyneynta sawirka (M) waa wax ka yar 1, taasoo la micno ah in sawirku uu yaraaday cabbirkiisa.
Masaafada sawirka(yada):
Xisaabi masaafada sawirka adoo isticmaalaya qaacidada weyneynta sawirka M = -s'/s
-s' = Ms
s' = – M s = -(0,2)(20 cm) = -4 cm
Masaafada sawirka taban macnaheedu waa sawirku waa mid casri ah. Sawirku wuxuu ku yaal gadaasha muraayadda mana dhex maro iftiinka.
b) Dhererka diiradda (f)
Masaafada diiradda (f):
1/f = 1/s + 1/s' = 1/20 – 1/4 = 1/20 – 5/20 = -4/20
f = -20/4 = -5 cm
Dhererka diiradda waa taban sababtoo ah barta diiradda ee muraayadda qaloocan ma dhex marto iftiinka iftiinka.
c) Sifooyinka hooska
Sifooyinka hooska:
- Toosan
– La dhimay macnaheedu waa cabbirka hoosku wuu ka yar yahay cabbirka shayga
– Macnaheedu waa in hooska aan la marin iftiinka sababtoo ah wuxuu ku yaal gadaasha muraayadda qaloocan.
Su'aalo muraayad isku dhafan
1. Muraayad qaloocan waxay leedahay gacan qalooc ah oo ah 24 cm. Go'aami masaafada sawirka, weyneynta sawirka, dhererka sawirka iyo sifooyinka sawirka haddii shaygu uu 6 cm u jiro muraayadda iyo shaygu uu yahay 3 cm dhererkiisu.
Furaha jawaabta:
(a) Masaafada sawirka = s'= -4 cm
(b) Weyneynta sawirka = M = 2/3
(c) Dhererka hooska = h' = 2 cm
(d) Sifooyinka sawirka: dalwad, toosan, cabbirkiisu yar yahay.
2. Masaafada shay u jirta muraayad qaloocan oo dhererkeedu yahay 8 cm waa 12 cm. Haddii dhererka shaygu yahay 4 cm, go'aami: (a) masaafada sawirka, (b) weynaynta sawirka, (c) dhererka sawirka iyo astaamaha sawirka.
Furaha jawaabta:
(a) Masaafada sawirka = s'= -4,8 cm
(b) Weyneynta sawirka = M = 0,4
(c) Dhererka hooska = h' = 1,6 cm
(d) Sifooyinka sawirka: dalwad, toosan, cabbirkiisu yar yahay.
3. Shay dhererkiisu yahay 5 cm wuxuu ku yaal masaafo dhan 15 cm oo ka horreysa dusha sare ee muraayadda qaloocan ee iftiimisa iftiinka. Haddii dhererka diiradda ee muraayadda qaloocan uu yahay 5 cm, go'aami: (a) masaafada sawirka, (b) weynaynta sawirka, (c) dhererka sawirka, (d) sifooyinka sawirka.
Furaha jawaabta:
(a) Masaafada sawirka = s'= -3,75 cm
(b) Weyneynta sawirka = M = 0,25
(c) Dhererka hooska = h' = 1,25 cm
(d) Sifooyinka sawirka: dalwad, toosan, cabbirkiisu yar yahay.
4. Masaafada shayga hortiisa muraayadda qaloocan waa 10 cm sawirka la sameeyayna waa 1/2 dhererka shayga. Go'aami: (a) masaafada sawirka, (b) dhererka diiradda muraayadda qaloocan, (c) sifooyinka sawirka.
Furaha jawaabta:
(a) Masaafada sawirka = s'= -5 cm
(b) Dhererka diiradda muraayadda qaloocan = f = -10 cm
(c) Sifooyinka sawirka: dalwad, toosan, cabbir yar.
