1. Shay ayaa la dhigayaa 10 cm muraayad qaloocan . Dhererka diiradda waa 5 cm. Go'aami (a) Masaafada sawirka (b) weyneynta sawirka
La yaqaan:
Dhererka diiradda (f) = 5 cm
Masaafada shayga ( d o ) = 10 cm
Xalka :
Samaynta sawirka iyadoo la adeegsanayo muraayad qaloocan:
Masaafada sawirka:
1/ d i = 1/f – 1/ d o = 1/5 – 1/10 = 2/10 – 1/10 = 1/10
d i = 10/1 = 10 cm
Masaafada sawirka waa 10 cm.
Weyneynta:
m = – d i / d o = -10/10 = -1
1 macnaheedu waa in sawirku uu la mid yahay shayga.
Calaamadda laga jaray waxay muujinaysaa in sawirku rogmanayo. Haddii calaamaddu togan tahay, sawirku waa toosan yahay.
2. Shay dhererkiisu yahay 5-cm ayaa la dhigayaa hortiisa muraayad qaloocan oo leh gacan qalooc ah oo ah 20 cm. Go'aami dhererka sawirka haddii masaafada shaygu tahay 5 cm, 15 cm, 20 cm, iyo 30 cm.
La yaqaan:
Gacanka qalooca ( r ) = 20 cm
Dhererka diiradda (f) = R/2 = 20/2 = 10 cm
Dhererka shayga (h o ) = 5 cm
Xalka:
a) dhererka diiradda (f) = 10 cm iyo masaafada shayga ( d o ) = 5 cm
Samaynta sawirka iyadoo la adeegsanayo muraayad qaloocan:
Masaafada sawirka ( d i ):
1/ d i = 1/f – 1/ d o = 1/10 – 1/5 = 1/10 – 2/10 = -1/10
d i = -10/1 = -10 cm
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 = -(-10)/5 = 10/5 = 2
Calaamadda dheeraadka ah waxay muujinaysaa in sawirku uu toosan yahay.
Dhererka sawirka ( h i ):
m = h i / h o
h i = h o m = (5 cm)(2) = 10 cm
Dhererka sawirka waa 10 cm.
b) Dhererka diiradda (f) = 10 cm iyo masaafada shayga ( d o ) = 15 cm
Samaynta sawirka iyadoo la adeegsanayo muraayad qaloocan:
Masaafada sawirka ( d i ):
1/ d i = 1/f – 1/ d o = 1/10 – 1/15 = 3/30 – 2/30 = 1/30
d i = 30/1 = 30 cm
Calaamadda dheeraadka ah waxay muujinaysaa in sawirku yahay mid dhab ah ama sawirku uu yahay 30 cm oo ku yaal muraayadda horteeda, isla dhinaca shayga.
Weyneynta sawirka ( m ):
m = – d i / d o = -30/15 = -2
Calaamadda laga jaray waxay muujinaysaa in sawirku rogmanayo.
Sawirku wuxuu 2 jeer ka weyn yahay shayga.
Dhererka sawirka (h i ):
m = h i / h o
h i = h o m = (5 cm)(2) = 10 cm
Dhererka sawirka waa 10 cm.
c) Dhererka diiradda (f) = 10 cm iyo masaafada shayga ( d o ) = 20 cm
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 = 1/20
d i = 20/1 = 20 cm
Calaamadda togan waxay muujinaysaa in sawirku yahay mid dhab ah ama sawirku uu 20 cm ka horreeyo muraayadda, isla dhinaca shayga.
Weyneynta sawirka ( m ):
m = – d i / d o = -20/20 = -1
Calaamadda taban waxay ka dhigan tahay in sawirku rogmanayo.
Dhererka sawirka ( sare ):
m = h i / h o
h i = h m = (5 cm)(1) = 5 cm
d) Dhererka diiradda (f) = 10 cm iyo masaafada shayga ( d o ) = 30 cm
Masaafada sawirka ( d i ):
1/ d i = 1/f – 1/ d o = 1/10 – 1/30 = 3/30 – 1/30 = 2/30
d i = 30/2 = 15 cm
Calaamadda lagu daray waxay muujinaysaa in sawirku yahay mid dhab ah ama sawirku uu 15 cm ka horreeyo muraayadda, isla dhinaca shayga.
Weyneynta sawirka ( m) :
m = – d i / d o = -15/30 = -0.5
Calaamadda laga jaray waxay muujinaysaa in sawirku rogmanayo.
Sawirku waa 0.5 ka yar yahay shayga.
Dhererka sawirka (h i ):
m = h i / h o
h i = h o m = (5 cm)(0.5) = 2.5 cm
3. Sawir ay samaysay muraayad qaloocan ayaa 4 jeer ka weyn shayga. Haddii gacanka qaloocan uu yahay 20 cm, go'aami masaafada shayga ee muraayadda horteeda ah!
La yaqaan:
Weyneynta sawirka ( m ) = 4
Gacanka qalooca ( r ) = 20 cm
Dhererka diiradda (f) = r /2 = 20/2 = 10 cm
La Doonayo : Masaafada shayga ( d o )
Xalka:
m = – d i / d o
4 = – d i / d o
– d i = 4 d o
d i = – 4 d o
1/f = 1/ d o + 1/ d i
1/10 = 1/ d o + 1/4 d o
4/40 = 4/4 d o + 1/4 d o
4/40 = 5/4 d o
(4)(4) = (5)(40)
16 d o = 200
d o = 12.5 cm
Masaafada shayga = 12.5 cm.
4. Shay dhererkiisu yahay 1-cm ayaa la dhigayaa 10 cm muraayad qaloocan oo leh dhererka diiradda, f = 15 cm. Go'aami:
A. Masaafada sawirka?
B. Dhererka sawirka?
C. Astaamaha sawirka oo ay samaysay muraayadda qaloocan?
La yaqaan:
Dhererka shayga (h) = 1 cm
Masaafada shayga (d o ) = 10 cm
Dhererka diiradda ee muraayadda qaloocan (f) = 15 cm
Xalka:
A. Masaafada sawirka (d i )
1/f = 1/d o + 1/d i
1/d i = 1/f – 1/d o = 1/15 – 1/10 = 2/30 – 3/30 = -1/30
d i = -30/1 = -30 cm
Calaamadda taban waxay muujinaysaa in sawirku yahay mid casri ah ama sawirku uu ka dambeeyo muraayadda.
B. Dhererka sawirka (h i )
Weyneynta sawirka (M):
M = -d i /d o = h i /h o
M = -(-30)/10 = 30/10 = 3 jeer
Dhererka sawirka (h i ):
M = h i / h o
3 = h i / 1 cm
h i = 3 (1 cm)
h i = 3 cm
Dhererka sawirku waa 3 cm. Calaamadda lagu daray waxay muujinaysaa in sawirku kor u socdo.
C. Sifooyinka sawirka:
Dalwad, kor, ka weyn shayga
5. Weyneynta sawirka, sida ku cad sawirka hoose.
La yaqaan:
Masaafada shayga (d o ) = 60 cm
Dhererka diiradda (f) = 20 cm
La Doonayo: Weyneynta Sawirka (M)
Xalka:
Masaafada sawirka:
1/f = 1/d o + 1/d i
1/d i = 1/f – 1/d o = 1/20 cm – 1/60 cm = 3/60 cm – 1/60 cm = 2/60 cm
d i = 60/2 cm = 30 cm
Weyneynta sawirka (M):
M = d i / d o = 30 cm / 60 cm = 1/2 jeer
6. Haddii shayga la dhigo 6 cm muraayad qaloocan, masaafada sawirku waa 12 cm sida ku cad sawirka hoose. Waa maxay masaafada sawirka haddii shayga laga raro meeshii asalka ahayd 1 cm muraayadda.
La yaqaan:
Masaafada shayga (d o ) = 6 cm
Masaafada sawirka (d i ) = 12 cm
La Rabay: haddii masaafada shayga (d o ) = 7 cm markaas masaafada sawirku waa ...
Xalka:
1/f = 1/do + 1/di = 1/6 + 1/12 = 2/12 + 1/12 = 3/12
f = 12/3 = 4 cm
Dhererka diiradda waa mid togan, taasoo la micno ah in barta diiradda la saarayo ay tahay mid dhab ah ama fallaaraha ay ka gudbaan barta.
Masaafada sawirka:
1/d i = 1/f – 1/d o = 1/4 – 1/7 = 7/28 – 4/28 = 3/28
d i = 28/3 = 9.3 cm
7. Dhakhtarka ilkaha ayaa fiirinaya oo hubinaya ilkaha bukaanka isagoo adeegsanaya muraayad leh gacan 8 cm ah. Si uu dhakhtarku si cad u arko godka, waa maxay masaafada u dhaxaysa ilkaha bukaanka iyo muraayadda?
A. wax ka yar 4 cm oo ku yaal muraayad qaloocan oo horteeda ah
B. wax ka yar 4 cm oo ku yaal muraayad qaloocan oo horteeda ah
C. in ka badan 4 cm oo ku yaal muraayadda qaloocan ee hore
D. in ka badan 4 cm oo ku yaal muraayadda qaloocan ee hore
La yaqaan:
Dhexroorka muraayadda (r) = 8 cm
Dhererka muraayadda (f) = r / 2 = 8 / 2 = 4 cm
La Doonayo: Masaafada u dhaxaysa ilkaha bukaanka iyo muraayadda
Xalka:
Muraayadda la isticmaalay ma muraayad qaloocan mise muraayad qaloocan? Si godka ilkaha uu si cad u arko dhakhtarku, muraayadda la isticmaalay waa inay awood u yeelataa inay ballaadhiso sawirka ilkaha sawirkuna waa inuu ahaadaa mid toosan. Muraayadda qaloocan had iyo jeer waxay soo saartaa sawirro qaloocan cabbirka sawirkuna wuu ka yar yahay cabbirka shayga. Taas beddelkeeda muraayad qaloocan waxay soo saari kartaa sawir toosan haddii masaafada shayga (d) ay ka yar tahay dhererka qaloocan (f). Haddii masaafada shaygu ay ka weyn tahay dhererka qaloocan (f) markaa muraayadda qaloocan waxay soo saartaa sawir qaloocan.
Dhererka muraayadda qaloocan (f) waa 4 cm, sidaa darteed ilkaha bukaanka waa inay ka yaraadaan 4 cm hortiisa muraayad qaloocan.
Jawaabta saxda ah waa A.
8. Muraayad qaloocan waxay leedahay gacan qalooc ah oo ah 24 cm. Haddii shayga la dhigo muraayadda horteeda 20 cm markaas go'aami sifooyinka sawirka.
A. Dhab ah, toosan oo la ballaariyay
B. Dhab ah, rogrogmay oo la ballaariyay
C. Daalac, toosan oo la ballaariyay
D. Dalwad, rogrogmi kara oo ka yar
La yaqaan:
Gacanka qalooca ( r) = 24 cm
Dhererka diiradda (f) = R/2 = 24/2 = +12 cm
Dhererka muraayadda qaloocan waa mid togan ama dhab ah sababtoo ah iftiinku wuxuu dhex maraa barta diiradda ee muraayadda.
Masaafada walxaha (d) = 20 cm
La Raadinayo: Sifooyinka sawirka
Xalka:
Sawirku ma mid casri ah baa mise waa mid dhab ah? Xisaabi masaafada sawirka:
1/d + 1/d' = 1/f
1/d' = 1/f – 1/d
1/d' = 1/12 – 1/20
1/d' = 5/60 – 3/60
1/d' = 2/60
d' = 60/2
d' = 30 cm
Masaafada sawirka ee togan ee la calaamadeeyay waxay ka dhigan tahay in sawirku yahay mid dhab ah sababtoo ah waxaa gudbiya iftiin.
Sawirka oo la weyneeyay? Toosan mise rogan? Marka hore xisaabi weyneynta sawirka (M):
M = -d' / d = -30/20 = -1.5
M > 1 macnaheedu waa sawirka waa la weyneeyay, M wuxuu leeyahay calaamad taban macnaheedu waa sawir rogrogay. Markaa sifooyinka sawirku waa kuwo dhab ah, rogrogay, weynaaday.
Jawaabta saxda ah waa B.
9. Muraayad wareegsan ayaa soo saarta sawir cabirkiisu yahay 5 jeer ka weyn shayga shaashadda ku yaal, 5 mitirna u jira shayga. Muraayaddu waa…..
A. qaloocan oo leh dhererka diiradda saaraya 25/24 m
B. qaloocsan oo leh dhererka diiradda oo ah 25/24 m
C. qaloocan oo leh dhererka diiradda saaraya 24/25 m
D. qaloocsan oo leh dhererka diiradda oo ah 24/25 m
La yaqaan:
Weyneynta sawirka (M) = 5 jeer
Masaafada u dhaxaysa shayga iyo sawirka = 5 mitir
Xalka:
Cabbirka sawirka uu soo saaro muraayadda qaloocan ayaa had iyo jeer ka yar cabbirka shayga, sidaas darteed, muraayaddu waa muraayad qaloocan.
Masaafada walxaha (d) = x
Masaafada sawirka (d') = x + 5
Weyneynta sawirka (M) = 5 jeer
Qaacidada weyneynta sawirka:
Qaacidada dhererka diiradda (f):
Jawaabta saxda ah waa A.
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