1. Dhererka muraayadda qaloocan waa 10 cm, masaafada shayguna waa 20 cm. Go'aami (a) masaafada sawirka (b) weyneynta sawirka
La yaqaan:
Dhererka diiradda (f) = -10 cm
Calaamadda laga jaray waxay muujinaysaa in barta diiradda ee muraayadda qaloocan ay tahay mid dalwad ah
Masaafada shayga ( d o ) = 20 cm
Xalka:
Samaynta sawirka iyadoo la adeegsanayo muraayad qaloocan:
Masaafada sawirka (d i ):
1/ d i = 1/f – 1/ d o = -1/10 – 1/20 = -2/20 – 1/20 = -3/20
d i = -20/3 = -6.7 cm
Calaamadda laga jaray waxay muujinaysaa in sawirku yahay mid casri ah.
Weyneynta sawirka:
m = – d i / d o = -(-6.7)/20 = 6.7/20 = 0.3
m = 0,3 jeer ka yar shayga.
Calaamadda dheeraadka ah waxay muujinaysaa in sawirku kor u kacayo.
2. Shay dhererkiisu yahay 10-cm ayaa la dhigayaa hortiisa muraayad qaloocan oo dhererkeedu yahay 20 cm. Go'aami dhererka sawirka haddii masaafada shaygu tahay (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm
La yaqaan:
Dhererka diiradda ee muraayadda qaloocan (f) = -20 cm
Calaamadda laga jaray waxay muujinaysaa in barta diiradda la saarayo ay tahay mid casri ah
Gacanka qalooca ( r ) = 2 f = 2(20) = 40 cm
Dhererka shayga (h) = 10 cm
Xalka:
a) dhererka diiradda (f) = -20 cm iyo masaafada shayga (d o ) = 10 cm
Masaafada sawirka (d i ) :
1/ d i = 1/f – 1/ d o = -1/20 – 1/10 = -1/20 – 2/20 = -3/20
d i = -20/3 = -6.7
Calaamadda laga jaray waxay muujinaysaa in sawirku yahay mid casri ah ama sawirku uu ka dambeeyo muraayadda.
Weyneynta sawirka ( m ):
m = – d i / d o = -(-6.7)/10 = 6.7/10 = 0.67
Calaamadda dheeraadka ah waxay muujinaysaa in sawirku uu toosan yahay.
Sawirku waa 0.67 ka yar yahay shayga.
Dhererka sawirka (h i ):
m = h i / h o
h i = h o m = (10 cm)(0.67) = 6.7 cm
b) dhererka diiradda (f) = -20 cm iyo masaafada shayga ( d o ) = 30 cm
Masaafada sawirka ( d i ):
1/ d i = 1/f – 1/ d o = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
d i = -60/5 = -12
Calaamadda laga jaray waxay muujinaysaa in sawirku yahay mid casri ah ama sawirku uu ka dambeeyo muraayadda.
Weyneynta sawirka ( m ):
m = – d i / d o = -(-12)/30 = 12/30 = 0.4
Calaamadda dheeraadka ah waxay muujinaysaa in sawirku uu toosan yahay.
Sawirka ayaa 0,4 jeer ka yar shayga.
Dhererka sawirka (h i ):
m = h i / h o
h i = h o m = (10 cm)(0.4) = 4 cm
c) Dhererka diiradda (f) = -20 cm iyo masaafada shayga ( d o ) = 40 cm
Masaafada sawirka ( d i ):
1/ d i = 1/f – 1/ d o = -1/20 – 1/40 = -2/40 – 1/40 = -3/40
d i = -40/3 = -13.3
Calaamadda laga jaray waxay muujinaysaa in sawirku yahay mid casri ah ama sawirku uu ka dambeeyo muraayadda qaloocan.
Weyneynta sawirka ( m ):
m = – d i / d o = -(-13.3)/40 = 13.3/40 = 0.3
Calaamadda dheeraadka ah waxay muujinaysaa in sawirku uu toosan yahay.
Sawirku waa 0.3 ka yar yahay shayga.
Dhererka sawirka ( h i ) :
m = h i / h o
h i = h o m = (10 cm)(0.3) = 3 cm
d) Dhererka diiradda (f) = -20 cm iyo masaafada shayga ( d o ) = 50 cm
Masaafada sawirka ( d i ):
1/ d i = 1/f – 1/ d o = -1/20 – 1/50 = -5/100 – 2/100 = -7/100
d i = -100/7 = -14.3
Calaamadda laga jaray waxay muujinaysaa in sawirku yahay mid casri ah ama sawirku uu ka dambeeyo muraayadda qaloocan.
Weyneynta sawirka ( m ):
m = – d i / d o = -(-14.3)/50 = 14.3/50 = 0.3
Calaamadda dheeraadka ah waxay muujinaysaa in sawirku uu toosan yahay.
Sawirku waa 0.3 ka yar yahay shayga.
Dhererka sawirka (h i ) :
m = h i / h o
h i = h o m = (10 cm)(0.3) = 3 cm
3. Shayga saaran waa 20 cm hortiisa muraayadda qaloocan . Haddii dhererka sawirku yahay 1/5 jibaar dhererka shayga, go'aami ( a) dhererka sawirka b) dhererka diiradda c) sifooyinka sawirka
La yaqaan:
Masaafada shayga ( d o ) = 20 cm
Dhererka sawirka (h i ) = 1/5 saac = 0.2 saac
Dhererka shayga (h) = h
Xalka:
a) masaafada sawirka ( d i )
Qaacidda weyneynta sawirka :
m = h i / h o = 0.2h / h = 0.2
Calaamadda dheeraadka ah waxay muujinaysaa in sawirku uu toosan yahay.
Sawirku waa 0.2 ka yar yahay shayga.
Masaafada sawirka ( d i ):
– d i = md o
d i = – m d o = -(0.2)(20 cm) = -4 cm
Calaamadda laga jaray waxay muujinaysaa in sawirku yahay mid casri ah ama sawirku uu ka dambeeyo muraayadda qaloocan.
b) Dhererka diiradda ( f)
Dhererka diiradda (f):
1/f = 1/ d o + 1/ d i = 1/20 – 1/4 = 1/20 – 5/20 = -4/20
f = -20/4 = -5 cm
Calaamadda laga jaray waxay muujinaysaa in barta diiradda la saarayo ay tahay mid casri ah.
c) Astaamaha sawirka:
- Toosan
- Yar
- dalwad
4. Iftiinka oo ku dhaca muraayad qaloocan oo barbar socota dhidibka ayaa la arki doonaa….
A. dhanka barta diiradda ee muraayadda
B. sida laga soo bilaabo barta dhexe ee muraayadda
C. iyada oo loo marayo bartamaha qalooca muraayadda
D. oo ku toosan muraayadda diyaaradda
Solution
Dhibaatadu waxay ku jirtaa sawirka hoose.
Jawaabta saxda ah waa B.
5. Baaskiil wade wuxuu arkaa sawirka mooto gadaasheeda 1/6 jibaar cabbirkeedii asalka ahaa marka masaafada u dhaxaysa mootada iyo mootada ay tahay 30 mitir. Go'aami gacanka qalooca muraayadda dambe…
A. 7.14 mitir
B. 8.57 mitir
C. 12.00 mitir
D. 24.00 mitir
La yaqaan:
Weyneynta sawirka (M) = 1/6 jeer
Masaafada walxaha (d) = 30 mitir
La Rabay: Gacanka qalooca ee muraayadda aragtida dambe (R)
Xalka:
Xisaabi masaafada sawirka (d')
Maadaama la yaqaanay weyneynta sawirka (M) iyo masaafada (yada) shayga, masaafada sawirka waxaa lagu ogaan karaa iyadoo la isticmaalayo qaacidada weyneynta sawirka:
Calaamad taban waxay ka dhigan tahay in sawirku yahay mid casri ah. Sawirku wuxuu 5 mitir ka dambeeyaa muraayadda qaloocan.
Xisaabi dhererka diiradda (f)
Maadaama masaafada shayga (d) iyo masaafada sawirka (d'), markaa dhererka diiradda waxaa lagu xisaabin karaa iyadoo la adeegsanayo qaacidada muraayadda:
Gacanka qalooca (R)
Gacanka qalooca muraayadda qalooca leh waa labanlaab dhererka diiradda muraayadda qalooca leh.
R = 2 f = 2 (6 mitir) = 12 mitir
Gacanka qalooca muraayadda qalooca leh waa 12 mitir.
Jawaabta saxda ah waa C.
6. Muraayadda qaloocan waxaa loo doortay muraayadda gadaal ee mootada sababtoo ah sifooyinka sawirka uu muraayaddu soo saarto waa…
A. dhab ah, toosan, la yareeyay
B. dhab ah, toosan, la ballaariyay
C. dadban, toosan, la yareeyay
D. dadban, toosan, la ballaariyay
Xalka:
Iyada oo lagu saleynayo labada sawir ee kor ku xusan, waxaa lagu soo gabagabeyn karaa in sifooyinka sawirku ay yihiin kuwo casri ah, toosan, la yareeyay.
Jawaabta saxda ah waa C.
7. Shay wuxuu 12 cm ka hor yahay muraayad qaloocan oo leh gacan 6 cm ah. Astaamaha sawirka waa…
A. dhab ah, rogan masaafo dhan 12 cm
B. dhab ah, toosan masaafad dhan 4 cm
C. qof ahaan, toosan masaafad dhan 2.4 cm
D. dalwad, rogrogmi karta masaafad dhan 6 cm
La yaqaan:
Masaafada shayga (d) = 12 cm
Dhexroorka muraayadda qaloocan (r) = 6 cm.
Dhererka muraayadda qaloocan ( f) = 6 cm / 2 = -3 cm
Dhererka muraayadda qaloocan waxaa loo calaamadeeyay taban sababtoo ah waa mid casri ah. Macmal ah sababtoo ah iftiin ma dhaafo.
La Raadinayo: Sifooyinka sawirka
Xalka:
Masaafada sawirka (d'):
1/d' = 1/f – 1/d = -1/3 – 1/12 = -4/12 – 1/12 = -5/12
d' = -12/5 = -2.4 cm
Masaafada sawirka ee la saxiixay ee taban waxay ka dhigan tahay in sawirku yahay mid dalwad ah.
Weyneynta sawirka (m):
m = -d' / d = -(-2.4) / 12 = 2.4 / 12 = 0.2 jeer
Weyneynta sawirka ee calaamadaysan ee togan waxay la macno tahay in sawirku toosan yahay weyneynta sawirkuna ay tahay 0.2 macnaheedu waa cabbirka sawirku wuu ka yar yahay cabbirka shayga (la dhimay).
Jawaabta saxda ah waa C.
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