Samaynta sawirka oo ay samaysay muraayadda concave

Si aad u fahamto sawirka shay uu sameeyay muraayad qaloocan, hoos ka baro tusaalooyinka dhibaatooyinka iyo xalalka. Arrintan, shayga waxaa loo qaadanayaa masaafo cayiman oo u jirta muraayadda qaloocan, ka dibna sawir qaabka sawirka muraayadda qaloocan,

Masaafada sawirka ee muraayadda qaloocan iyo weynaynta sawirka oo ay samaysay muraayadda qaloocan.

Ka fiirso muraayad qaloocan oo leh dherer diiradda saaraya 20 cm. Sawir qaabaynta sawirka ka dibna go'aami masaafada sawirka iyo weynaynta sawirka haddii:

a) masaafada walxaha ay ka yar tahay masaafada dhererka diiradda (samayn)

b) walxaha waxay ku yaalliin barta dhexe ee muraayadda (do = f)

c) walxaha waxay u dhexeeyaan meelaha diiradda la saarayo iyo barta dhexe ee qalooca muraayadda (f < do)

d) walxaha ku yaal bartamaha qalooca muraayadda (do = R)

e) masaafada walxaha ay ka weyn tahay gacanka qalooca muraayadda (do > R)

La yaqaan

Dhererka diiradda ee muraayadda qaloocan (f) = 20 cm

Dhererka muraayadda qaloocan waa mid togan sababtoo ah iftiinka iftiinku wuxuu dhex maraa barta diiradda ee muraayadda qaloocan.

Gacanka qalooca (R) = 2 f = 2 (20) = 40 cm

Solution:

Masaafada walaxdu way ka yar tahay dhererka diiradda ee muraayadda qaloocan ( do <f)

Ka soo qaad in masaafada walxaha u dhaxaysa muraayaddu ay tahay 5 cm, 10 cm, iyo 15 cm.

1. Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 5 cm

Masaafada sawirka (di) :

1/di = 1/f – 1/do = 1/20 – 1/5 = 1/20 – 4/20 = -3/20

di = -20/3 = -6.7 cm

Masaafada sawirka ( di ) waxay leedahay calaamad taban oo macnaheedu yahay in hoosku yahay mid casri ah, ama sawirku wuxuu ka dambeeyaa muraayad qaloocan oo iftiinka iftiinku aanu dhex marin sawirka.

Masaafada sawirka ( di ) 6.7 cm ayaa ka weyn masaafada shayga ( do ) 5 cm

Weyneynta sawirka (M) :

M = -di / do = -(-6.7)/5 = 6.7 / 5 = 1.3 jeer

Weyneynta toosan ee sawirka (M) waxay dhaaftay 1 taasoo la micno ah in cabbirka sawirku ka weyn yahay cabbirka shayga.

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad togan, taasoo la micno ah in sawirku uu toosan yahay.

2. Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 10 cm

Masaafada sawirka ( di ) :

1/di = 1/f – 1/do = 1/20 – 1/10 = 1/20 – 2/20 = -1/20

di = -20/1 = -20 cm

Masaafada sawirka ( di ) waxay leedahay calaamad taban oo macnaheedu yahay in sawirku yahay mid casri ah, ama sawirku wuxuu ka dambeeyaa muraayadda qaloocan halkaas oo iftiinka iftiinku uusan dhex marin sawirka.

Masaafada sawirka ( di ) 20 cm ayaa ka weyn masaafada shayga ( do ) 10 cm

Weyneynta Sawirka (M) :

M = -di / do = -(-20)/10 = 20/10 = 2 jeer

Weyneynta toosan ee sawirka (M) waxay dhaaftay 1 macnaheedu waa in cabbirka sawirku uu ka weyn yahay cabbirka shayga

Weyneynta toosan ee hooska (M) waxay leedahay calaamad togan, taasoo la micno ah in sawirku uu toosan yahay.

3. Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 15 cm

Masaafada sawirka ( di ) :

1/di= 1/f – 1/do = 1/20 – 1/15 = 3/60 – 4/60 = -1/60

di = -60/1 = -60 cm

Masaafada sawirka ( di ) waxay leedahay calaamad taban oo macnaheedu yahay in sawirku yahay mid casri ah, ama sawirku wuxuu ka dambeeyaa muraayad qaloocan oo iftiinka iftiinku aanu dhex marin sawirka.

Masaafada sawirka ( di ) 60 cm ayaa ka weyn masaafada shayga ( do ) 15 cm

Weyneynta Sawirka (M) :

M = -di / do = -(-60)/15 = 60/15 = 4 jeer

Weyneynta toosan ee sawirka (M) waxay dhaaftay 1 taasoo la micno ah in cabbirka hoosku ka weyn yahay cabbirka shayga.

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad togan, taasoo la micno ah in sawirku uu toosan yahay.

Walxaha ku yaal barta dhexe ee muraayadda qaloocan ( do = f)

Walxaha ku yaal barta dhexe ee muraayadda qaloocan, sidaas darteed masaafada shayga (do) = dhererka diiradda (f) = 20 cm

Masaafada sawirka ( di ):

1/di = 1/f – 1/do = 1/20 – 1/20 = 0

at = 0

Weyneynta sawirka (M):

M = di / samee = 0

Haddii masaafada shayga ( do ) ay la mid tahay dhererka diiradda muraayadda (f) markaa ma jiro sawir uu muraayaddu samaysay.

Shayga wuxuu u dhexeeyaa barta diiradda iyo bartamaha qalooca muraayadda qalooca leh (f < do < R)

Ka soo qaad in masaafada shayga u jirta muraayaddu ay tahay 25 cm, 30 cm, iyo 35 cm.

1) Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 25 cm

Masaafada sawirka ( di ) :

1/di = 1/f – 1/do = 1/20 – 1/25 = 5/100 – 4/100 = 1/100

di = 100/1 = 100 cm

Masaafada sawirka (di) waxaa lagu calaamadeeyay mid togan taasoo la macno ah in sawirku yahay mid dhab ah, ama sawirku wuxuu hor yaallaa muraayad qaloocan oo iftiinka iftiinku uu dhex maro sawirka.

Masaafada sawirka (di) 100 cm ayaa ka weyn masaafada shayga (do) 25 cm

Weyneynta sawirka (M) :

M = -di / do = -(100)/25 = -4 jeer

Weyneynta toosan ee sawirka (M) waxay dhaaftay 1 taasoo la micno ah in cabbirka sawirku ka weyn yahay cabbirka shayga.

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad taban oo macnaheedu yahay in sawirku rogmanayo.

2) Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 30 cm

Masaafada sawirka ( di ) :

1/di = 1/f – 1/do = 1/20 – 1/30 = 3/60 – 2/60 = 1/60

di = 60/1 = 60 cm

Masaafada sawirka (di) waxaa lagu calaamadeeyay mid togan taasoo la macno ah in sawirku yahay mid dhab ah, ama sawirku wuxuu hor yaallaa muraayad qaloocan oo iftiinka iftiinku uu dhex maro sawirka.

Masaafada sawirka (di) 60 cm ayaa ka weyn masaafada shayga (do) 30 cm

Weyneynta toosan ee sawirka (M) :

M = -di / do = -60/30 = -2 jeer

Weyneynta toosan ee sawirka (M) waxay dhaaftay 1 macnaheedu waa in cabbirka sawirku uu ka weyn yahay cabbirka shayga

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad taban oo macnaheedu yahay in sawirku rogmanayo.

3) Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 35 cm

Masaafada sawirka ( di ) :

1/di = 1/f – 1/do = 1/20 – 1/35 = 7/140 – 4/140 = 3/140

di = 140/3 = 46.7 cm

Masaafada sawirka (di) waxaa lagu calaamadeeyay togan taasoo la macno ah in sawirku yahay mid dhab ah, ama sawirku wuxuu ku yaal hore ee muraayadda qaloocan halkaas oo iftiinka iftiinku uu dhex maro sawirka.

Masaafada sawirka (di) 46.7 cm ayaa ka weyn masaafada shayga (do) 35 cm

Weyneynta toosan ee sawirka (M) :

M = -di / do = -46.7 / 35 = -1.3 jeer

Weyneynta toosan ee sawirka (M) waxay dhaaftay 1 taasoo la micno ah in cabbirka sawirku uu ka weyn yahay cabbirka shayga.

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad taban oo macnaheedu yahay in sawirku rogmanayo.

Shayga ku yaal bartamaha qalooca muraayadda qalooca leh (do = R)

Shay ku yaal bartamaha qalooca muraayadda qalooca sidaas darteed masaafada shayga (yada) = gacanka qalooca muraayadda (R) = 40 cm

Masaafada sawirka ( di ):

1/di = 1/f – 1/do = 1/20 – 1/40 = 2/40 – 1/40 = 1/40

di = 40/1 = 40 cm

Masaafada sawirka (di) waxaa lagu calaamadeeyay mid togan taasoo la macno ah in sawirku yahay mid dhab ah, ama sawirku wuxuu ku yaal hore ee muraayad qaloocan halkaas oo iftiinka iftiinku uu dhex maro sawirka.

Masaafada sawirka (di) 40 cm waxay la mid tahay masaafada shayga (do) 40 cm

Weyneynta toosan ee sawirka (M):

M = -di / samee = -40/40 = -1

Weyneynta toosan ee sawirka (M) waxay la mid tahay 1 macnaheedu waa in cabbirka sawirku uu la mid yahay cabbirka shayga.

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad taban oo macnaheedu yahay in sawirku rogmanayo.

Masaafada shayga ayaa ka weyn gacanka qalooca muraayadda qalooca leh (do > R)

Ka soo qaad in masaafada walxaha u dhaxaysa muraayaddu ay tahay 45 cm, 50 cm iyo 60 cm.

1) Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 45 cm

Masaafada sawirka ( di ) :

1/di = 1/f – 1/do = 1/20 – 1/45 = 9/180 – 4/180 = 5/180

di = 180/5 = 36 cm

Masaafada sawirka (di) waxaa lagu calaamadeeyay togan taasoo la macno ah in sawirku yahay mid dhab ah, ama sawirku wuxuu ku yaal hore ee muraayadda qaloocan halkaas oo iftiinka iftiinku uu dhex maro sawirka.

Masaafada sawirka (di) 36 cm way ka yar tahay masaafada shayga (do) 45 cm

Weyneynta toosan ee sawirka (M) :

M = -di / do = -(36)/45 = -0.8 jeer

Weyneynta toosan ee sawirka (M) waxay ka yar tahay 1 taasoo la micno ah in cabbirka sawirku uu ka yar yahay cabbirka shayga.

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad taban oo macnaheedu yahay in sawirku rogmanayo.

2) Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 50 cm

Masaafada sawirka ( di ) :

1/di = 1/f – 1/do = 1/20 – 1/50 = 5/100 – 2/100 = 3/100

di = 100/3 = 33.3 cm

Masaafada sawirka (di) waxaa lagu calaamadeeyay togan taasoo la macno ah in sawirku yahay mid dhab ah, ama sawirku wuxuu ku yaal hore ee muraayadda qaloocan halkaas oo iftiinka iftiinku uu dhex maro sawirka.

Masaafada sawirka (di) 33 cm way ka yar tahay masaafada shayga (do) 50 cm.

Weyneynta toosan ee sawirka (M) :

M = -di / do = -33/50 = -0.7 jeer

Weyneynta toosan ee sawirka (M) waxay ka yar tahay 1 macnaheedu waa in cabbirka sawirku uu ka yar yahay cabbirka shayga.

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad taban, taasoo la micno ah in sawirku rogmanayo.

3) Dhererka diiradda (f) = 20 cm iyo haddii masaafada shayga (do) = 60 cm

Masaafada sawirka ( di ) :

1/di = 1/f – 1/do = 1/20 – 1/60 = 3/60 – 1/60 = 2/60

di = 60/2 = 30 cm

Masaafada sawirka (di) waxaa lagu calaamadeeyay mid togan taasoo la macno ah in sawirku yahay mid dhab ah, ama sawirku wuxuu ku yaal hore ee muraayad qaloocan halkaas oo iftiinka iftiinku uu dhex maro sawirka.

Masaafada sawirka (di) 30 cm way ka yar tahay masaafada shayga (do) 60 cm

Weyneynta toosan ee sawirka ( M) :

M = -di / do = -30/60 = -0.5 jeer

Weyneynta toosan ee sawirka (M) waxay ka yar tahay 1 taasoo la micno ah in cabbirka sawirku uu ka yar yahay cabbirka shayga.

Weyneynta toosan ee sawirka (M) waxay leedahay calaamad taban, taasoo la micno ah in sawirku rogmanayo.