1. Chinhu chinoiswa 10 cm kubva pagirazi rakakombama . Kureba kwefocal i5 cm. Sarudza (a) Daro remufananidzo ( b) kukura kwemufananidzo
Zvinozivikanwa:
Kureba kwefocal (f) = 5 cm
Daro rechinhu ( do o ) = 10 cm
Mhinduro :
Kuumbwa kwemufananidzo negirazi rakatetepa:
Kureba kwemufananidzo:
1/ di = 1/f – 1/ do o = 1/5 – 1/10 = 2/10 – 1/10 = 1/10
d i = 10/1 = 10 cm
Kureba kwemufananidzo i10 cm.
Kukura:
m = – di i / do o = -10/10 = -1
1 zvinoreva kuti mufananidzo wacho wakafanana nechinhu chacho.
Chiratidzo chekusiya chinoratidza kuti mufananidzo wakapindurwa. Kana chiratidzo chiri chakanaka, mufananidzo wacho wakamira.
2. Chinhu chakareba masendimita mashanu chinoiswa pamberi pegirazi rakakombama rine dhayamita yekukombama ye20 cm. Sarudza kukwirira kwemufananidzo kana daro rechinhu chacho riri masendimita mashanu, gumi nemashanu, makumi maviri, makumi matatu.
Zvinozivikanwa:
Radiyo yekukombama ( r ) = 20 cm
Kureba kwefocal (f) = R/2 = 20/2 = 10 cm
Kureba kwechinhu (h o ) = 5 cm
Solution:
a) kureba kwefocal (f) = 10 cm uye daro rechinhu ( do o ) = 5 cm
Kuumbwa kwemufananidzo negirazi rakatetepa:
Kureba kwemufananidzo ( di i ):
1/ di = 1/f – 1/ do o = 1/10 – 1/5 = 1/10 – 2/10 = -1/10
d i = -10/1 = -10 cm
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi.
Kukura kwemufananidzo ( m ):
m = – di i / do o = -(-10)/5 = 10/5 = 2
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.
Kureba kwemufananidzo ( h i ):
m = h i / h o
h i = ho m = (5 cm)(2) = 10 cm
Kureba kwemufananidzo ndeye 10 cm.
b) Kureba kwefocal (f) = 10 cm uye daro rechinhu ( do o ) = 15 cm
Kuumbwa kwemufananidzo negirazi rakatetepa:
Kureba kwemufananidzo ( di i ):
1/ di = 1/f – 1/ do o = 1/10 – 1/15 = 3/30 – 2/30 = 1/30
d i = 30/1 = 30 cm
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho ndewechokwadi kana kuti mufananidzo wacho uri 30 cm pamberi pegirazi, parutivi rumwe chete nechinhu chacho.
Kukura kwemufananidzo ( m ):
m = – di i / do o = -30/15 = -2
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho wakapindurwa.
Mufananidzo wacho wakakura zvakapetwa kaviri pane chinhu chacho.
Kureba kwemufananidzo (h i ):
m = h i / h o
h i = h o m = (5 cm)(2) = 10 cm
Kureba kwemufananidzo ndeye 10 cm.
c) Kureba kwefocal (f) = 10 cm uye daro rechinhu ( do o ) = 20 cm
Kuumbwa kwemufananidzo negirazi rakatetepa:
Kureba kwemufananidzo (di i ):
1/ di = 1/f – 1/ do o = 1/10 – 1/20 = 2/20 – 1/20 = 1/20
d i = 20/1 = 20 cm
Chiratidzo chakanaka chinoratidza kuti mufananidzo wacho ndewechokwadi kana kuti mufananidzo wacho uri 20 cm pamberi pegirazi, parutivi rumwe chete nechinhu chacho.
Kukura kwemufananidzo ( m ):
m = – di i / do o = -20/20 = -1
Chiratidzo chekuramba chinoreva kuti mufananidzo wacho wapindurwa.
Kureba kwemufananidzo ( mhoro ):
m = h i / h o
h i = h m = (5 cm)(1) = 5 cm
d) Kureba kwefocal (f) = 10 cm uye daro rechinhu ( do o ) = 30 cm
Kureba kwemufananidzo ( di i ):
1/ di = 1/f – 1/ do o = 1/10 – 1/30 = 3/30 – 1/30 = 2/30
d i = 30/2 = 15 cm
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho ndewechokwadi kana kuti mufananidzo wacho uri 15 cm pamberi pegirazi, parutivi rumwe chete nechinhu chacho.
Kukura kwemufananidzo ( m) :
m = – di i / do o = -15/30 = -0.5
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho wakapindurwa.
Mufananidzo wacho mudiki ne 0.5 pane chinhu chacho.
Kureba kwemufananidzo (h i ):
m = h i / h o
h i = ho m = (5 cm)(0.5) = 2.5 cm
3. Mufananidzo wakagadzirwa negirazi rakakombama wakakura ka4 pane chinhu chacho. Kana dhayamita yekukombama iri 20 cm, sarudza daro rechinhu chiri pamberi pegirazi!
Zvinozivikanwa:
Kukura kwemufananidzo ( m ) = 4
Radiyo yekukombama ( r ) = 20 cm
Kureba kwefocal (f) = r /2 = 20/2 = 10 cm
Chinodiwa : Kureba kwechinhu ( do o )
Solution:
m = – di i / do o
4 = – di i / do o
– d i = 4 do o
di i = – 4 do o
1/f = 1/ do o + 1/ di i
1/10 = 1/ do o + 1/4 do o
4/40 = 4/4 do o + 1/4 do o
4/40 = 5/4 do o
(4)(4s) = (5)(40)
16 d o = 200
do o = 12.5 cm
Kureba kwechinhu = 12.5 cm.
4. Chinhu chakareba 1-cm chinoiswa 10 cm kubva pagirazi rakakombama rine urefu hwefocal, f = 15 cm. Sarudza:
A. Kureba kwemufananidzo?
B. Kureba kwemufananidzo?
C. Hunhu hwemufananidzo hunoumbwa negirazi rakakombama?
Zvinozivikanwa:
Kureba kwechinhu (h) = 1 cm
Daro rechinhu (do o ) = 10 cm
Kureba kwegirazi rakakombama (f) = 15 cm
Solution:
A. Kureba kwemufananidzo (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
Chiratidzo chekuramba chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi.
B. Kureba kwemufananidzo (h i )
Kukura kwemufananidzo (M):
M = -d i /d o = h i /h o
M = -(-30)/10 = 30/10 = katatu
Kureba kwemufananidzo (h i ):
M = h i / h o
3 = h i / 1 cm
h i = 3 (1 cm)
h i = 3 cm
Kureba kwemufananidzo i3 cm. Chiratidzo chekuwedzera chinoratidza kuti mufananidzo uri kumusoro.
C. Hunhu hwemufananidzo:
Zviri pachena, kumusoro, hombe kupfuura chinhu
5. Kukura kwemufananidzo, zvichienderana nemufananidzo uri pazasi.
Zvinozivikanwa:
Daro rechinhu (do o ) = 60 cm
Kureba kwefocal (f) = 20 cm
Zvinodiwa: Kukura kwemufananidzo (M)
Solution:
Kureba kwemufananidzo:
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
Kukura kwemufananidzo (M):
M = di i / do o = 30 cm / 60 cm = 1/2 kanomwe
6. Kana chinhu chacho chakaiswa 6 cm kubva pagirazi rakakombama, daro remufananidzo i12 cm sezvakaratidzwa mumufananidzo uri pazasi. Ndeipi daro remufananidzo kana chinhu chacho chikabviswa panzvimbo yekutanga 1 cm kubva pagirazi.
Zvinozivikanwa:
Daro rechinhu (do o ) = 6 cm
Daro remufananidzo (d i ) = 12 cm
Zvinodiwa: kana daro rechinhu (do o ) = 7 cm saka daro remufananidzo ndiro …
Solution:
1/f = 1/do + 1/di = 1/6 + 1/12 = 2/12 + 1/12 = 3/12
f = 12/3 = 4 cm
Kureba kwefocal kuri pachena, zvichireva kuti focal point ndeyechokwadi kana kuti mwaranzi inopfuura nepakati pepoint.
Kureba kwemufananidzo:
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. Chiremba wemazino anotarisa uye anoongorora mazino emurwere achishandisa girazi rine 8 cm radius. Kuti buri rionekwe zvakajeka nachiremba, daro riri pakati pemazino emurwere negirazi nderei?
A. pasi pe 4 cm pamberi pegirazi rakakombama
B. pasi pe 4 cm pamberi pegirazi rakamonana
C. anopfuura 4 cm pamberi pegirazi rakakombama
D. anopfuura 4 cm pamberi pegirazi rakatenderedza
Zvinozivikanwa:
Nharaunda yegirazi (r) = 8 cm
Kureba kwegirazi (f) = r / 2 = 8 / 2 = 4 cm
Chinodiwa: Daro riri pakati pemazino emurwere negirazi
Solution:
Girazi rinoshandiswa igirazi rakakombama kana kuti girazi rakakombama? Kuti buri rezino rionekwe zvakajeka nachiremba, girazi rinoshandiswa rinofanira kukwanisa kuwedzera mufananidzo wezino uye mufananidzo unofanira kumira wakamira. Magirazi akakombama anogara achiburitsa mifananidzo yakakombama uye saizi yemufananidzo idiki pane saizi yechinhu. Kusiyana neizvi, girazi rakakombama rinogona kugadzira mufananidzo wakamira kana daro rechinhu (d) riri diki pane urefu hwefocal (f). Kana daro rechinhu rakakura pane urefu hwefocal (f) saka girazi rakakombama rinoburitsa mufananidzo wakakombama.
Kureba kwegirazi rakakombama (f) i4 cm, saka mazino emurwere anofanira kunge ari pasi pe4 cm pamberi pegirazi rakakombama.
Mhinduro chaiyo ndeinoti A.
8. Girazi rakakombama rine denderedzwa re 24 cm. Kana chinhu chacho chikaiswa 20 cm pamberi pegirazi, sarudza hunhu hwemufananidzo.
A. Chaiyo, yakatwasuka uye yakakura
B. Chaicho, chakapindurwa uye chakakudzwa
C. Zviri pachena, zvakamira uye zvakakura
D. Zviri paindaneti, zvakapindurwa uye zvidiki
Zvinozivikanwa:
Nharaunda yekukombama (r) = 24 cm
Kureba kwefocal (f) = R/2 = 24/2 = +12 cm
Kureba kwegirazi rakakombama kwakanaka kana kuti kwechokwadi nekuti chiedza chinopfuura nepakati pegirazi.
Kureba kwechinhu (d) = 20 cm
Zvinodiwa: Hunhu hwemufananidzo
Solution:
Mufananidzo uri wechokwadi here kana kuti uri wechokwadi? Verenga daro remufananidzo (s'):
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
Kureba kwemufananidzo kwakasainwa kuti kwakanaka zvinoreva kuti mufananidzo wacho ndewechokwadi nekuti unopfuudzwa nechiedza.
Mufananidzo wakakura here? Wakatwasuka here kana kuti wakapindurwa? Kutanga verenga kukura kwemufananidzo (M):
M = -d' / d = -30/20 = -1.5
M > 1 zvinoreva kuti mufananidzo wakura, M ine chiratidzo chekuramba zvinoreva mufananidzo wakapindurwa. Saka hunhu hwemufananidzo ndehwechokwadi, hwakapindurwa, hwakakura.
Mhinduro chaiyo ndeiyi B.
9. Girazi rakatenderera rinoburitsa mufananidzo wakakura kashanu pane chinhu chiri pachikirini, chiri kure nemamita mashanu kubva pane chinhu chacho. Girazi iri…..
A. dendere rakakombama rine hurefu hwepakati hwe25/24 m
B. convex ine urefu hwefocal hwe25/24 m
C. dendere rakakombama rine hurefu hwepakati hwe 24/25 m
D. convex ine urefu hwefocal hwe 24/25 m
Zvinozivikanwa:
Kukura kwemufananidzo (M) = kashanu
Kureba pakati pechinhu nemufananidzo = mamita mashanu
Solution:
Saizi yemufananidzo unogadzirwa negirazi rakapinza inogara iri diki pane saizi yechinhu chacho, saka, girazi iri girazi rakapinza.
Kureba kwechinhu (d) = x
Kureba kwemufananidzo (d') = x + 5
Kukura kwemufananidzo (M) = kashanu
Fomura yekukudza mufananidzo:
Fomura yehurefu hwefocal (f):
Mhinduro chaiyo ndeinoti A.
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