1. Kureba kwegirazi rakapinza i10 cm uye daro rechinhu i20 cm. Sarudza (a) daro remufananidzo (b) kukura kwemufananidzo
Zvinozivikanwa:
Kureba kwefocal (f) = -10 cm
Chiratidzo chekusiya chinoratidza kuti nzvimbo iri pamberi pegirazi rakatenderedzwa iri chaiyo
Daro rechinhu ( do o ) = 20 cm
Solution:
Kuumbwa kwemufananidzo negirazi rakatetepa:
Kureba kwemufananidzo (di i ):
1/ di = 1/f – 1/ do o = -1/10 – 1/20 = -2/20 – 1/20 = -3/20
d i = -20/3 = -6.7 cm
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepaindaneti.
Kukura kwemufananidzo:
m = – di i / do o = -(-6.7)/20 = 6.7/20 = 0.3
m = 0,3 nguva diki pane chinhu chacho.
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo uri kumusoro.
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2. Chinhu chakareba masendimita gumi chinoiswa pamberi pegirazi rakamonana rine urefu hwemasendimita makumi maviri. Sarudza kukwirira kwemufananidzo kana daro rechinhu chiri (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm
Zvinozivikanwa:
Kureba kwegirazi rakapinza (f) = -20 cm
Chiratidzo chekusiya chinoratidza kuti nzvimbo yakatarisana nayo iri paindaneti
Radiyo yekukombama ( r ) = 2 f = 2(20) = 40 cm
Kureba kwechinhu (h) = 10 cm
Solution:
a) kureba kwefocal (f) = -20 cm uye daro rechinhu (do o ) = 10 cm
Kureba kwemufananidzo (di i ) :
1/ di = 1/f – 1/ do o = -1/20 – 1/10 = -1/20 – 2/20 = -3/20
d i = -20/3 = -6.7
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi.
Kukura kwemufananidzo ( m ):
m = – di i / do o = -(-6.7)/10 = 6.7/10 = 0.67
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.
Mufananidzo wacho mudiki ne 0.67 pane chinhu chacho.
Kureba kwemufananidzo (h i ):
m = h i / h o
h i = h o m = (10 cm)(0.67) = 6.7 cm
b) kureba kwefocal (f) = -20 cm uye daro rechinhu ( do o ) = 30 cm
Kureba kwemufananidzo ( di i ):
1/ di = 1/f – 1/ do o = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
d i = -60/5 = -12
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi.
Kukura kwemufananidzo ( m ):
m = – di i / do o = -(-12)/30 = 12/30 = 0.4
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.
Mufananidzo wacho mudiki nekanenge ka0,4 pane chinhu chacho.
Kureba kwemufananidzo (h i ):
m = h i / h o
h i = h o m = (10 cm)(0.4) = 4 cm
c) Kureba kwefocal (f) = -20 cm uye daro rechinhu ( do o ) = 40 cm
Kureba kwemufananidzo ( di i ):
1/ di = 1/f – 1/ do o = -1/20 – 1/40 = -2/40 – 1/40 = -3/40
d i = -40/3 = -13.3
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi rakamonana.
Kukura kwemufananidzo ( m ):
m = – di i / do o = -(-13.3)/40 = 13.3/40 = 0.3
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.
Mufananidzo wacho mudiki ne 0.3 pane chinhu chacho.
Kureba kwemufananidzo ( h i ) :
m = h i / h o
h i = h o m = (10 cm)(0.3) = 3 cm
d) Kureba kwefocal (f) = -20 cm uye daro rechinhu ( do o ) = 50 cm
Kureba kwemufananidzo ( di i ):
1/ di = 1/f – 1/ do o = -1/20 – 1/50 = -5/100 – 2/100 = -7/100
d i = -100/7 = -14.3
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi rakamonana.
Kukura kwemufananidzo ( m ):
m = – di i / do o = -(-14.3)/50 = 14.3/50 = 0.3
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.
Mufananidzo wacho mudiki ne 0.3 pane chinhu chacho.
Kureba kwemufananidzo (h i ) :
m = h i / h o
h i = ho m = (10 cm)(0.3) = 3 cm
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3. Pachinhu chiri 20 cm pamberi pegirazi rakamonana . Kana kukwirira kwemufananidzo kuri 1/5 kakapetwa kukwirira kwechinhu, sarudza ( a) kureba kwemufananidzo b) kureba kwefocal c) hunhu hwemufananidzo
Zvinozivikanwa:
Daro rechinhu ( do o ) = 20 cm
Kureba kwemufananidzo (h i ) = 1/5 h = 0.2 h
Kureba kwechinhu (h) = h
Solution:
a) daro remufananidzo ( di i )
Fomura yekukudza mufananidzo :
m = h i / h o = 0.2h / h = 0.2
Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.
Mufananidzo wacho mudiki ne 0.2 pane chinhu chacho.
Kureba kwemufananidzo ( di i ):
– d i = md o
di i = – m do o = -(0.2)(20 cm) = -4 cm
Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi rakamonana.
b) Kureba kwenzvimbo yakatarisana ( f)
Kureba kwefocal (f):
1/f = 1/ do o + 1/ di = 1/20 – 1/4 = 1/20 – 5/20 = -4/20
f = -20/4 = -5 cm
Chiratidzo che "minus" chinoratidza kuti nzvimbo iri pamberi pechinhu iri paindaneti.
c) Hunhu hwemufananidzo:
- Wakarurama
- Diki
- pamhepo
4. Chiedza chinorova girazi rakatenderedza rakafanana neakisi chinozoratidzwa….
A. kuenda kunzvimbo yekutarisa girazi
B. sezviri panzvimbo yekutarisa girazi
C. nepakati pegirazi rakakombama
D. yakatarisana negirazi regirazi
mhinduro
Dambudziko iri rinoonekwa mumufananidzo uri pazasi.
Mhinduro chaiyo ndeiyi B.
5. Mutyairi webhasikoro anoona mufananidzo wemudhudhudhu uri kumashure kwawo kakapetwa kaviri pahukuru hwawo hwepakutanga kana daro riri pakati pemutyairi webhasikoro nemudhudhudhu riri mamita makumi matatu. Sarudza dhayamita yekukombama kwegirazi rekumashure…
A. 7.14 m
B. 8.57 m
C. 12.00 m
D. 24.00 m
Zvinozivikanwa:
Kukura kwemufananidzo (M) = 1/6 kanomwe
Kureba kwechinhu (d) = mamita makumi matatu
Zvinodiwa: Radius yekukombama kwegirazi rekumashure (R)
Solution:
Verenga daro remufananidzo (d')
Sezvo kukura kwemufananidzo (M) uye daro rechinhu (s) zvave zvichizivikanwa, daro remufananidzo rinogona kuzivikanwa uchishandisa fomura yekukura kwemufananidzo:
Chiratidzo chekuramba chinoreva kuti mufananidzo wacho uri wepaindaneti. Mufananidzo wacho uri pamamita mashanu kubva pagirazi rakatenderedza.
Verenga urefu hwefocal (f)
Sezvo daro rechinhu (d) uye daro remufananidzo (d'), ipapo urefu hwefocal hunogona kuverengerwa uchishandisa fomura yegirazi:
Radiyo yekukombama (R)
Radius yekukombama kwegirazi rakatenderedzwa inopetwa kaviri kureba kwegirazi rakatenderedzwa.
R = 2 f = 2 (mamita matanhatu) = mamita gumi nemaviri
Radius yekukombama kwegirazi rakatenderedzwa ine denderedzwa regirazi i12 metres.
Mhinduro chaiyo ndeinoti C.
6. Girazi rakapinza rinosarudzwa segirazi rekuona kumashure kwemudhudhudhu nekuti hunhu hwemufananidzo unogadzirwa negirazi iri…
A. chaiyo, yakatwasuka, yakaderedzwa
B. chaiyo, yakatwasuka, yakakura
C. chaiyo, yakatwasuka, yakaderedzwa
D. chaiyo, yakatwasuka, yakakura
Solution:
Zvichibva pamifananidzo miviri iri pamusoro apa zvinogona kugumiswa kuti hunhu hwemufananidzo hwakafanana, hwakamira, hwakaderedzwa.
Mhinduro chaiyo ndeinoti C.
7. Chinhu chiri 12 cm pamberi pegirazi rakamonana rine dhayamita ye6 cm. Hunhu hwemufananidzo ndehwekuti…
A. chaiyo, yakapindurwa iri chinhambwe che12 cm
B. chaiyo, yakatwasuka iri chinhambwe che 4 cm
C. chaiyo, yakatwasuka iri chinhambwe che 2.4 cm
D. chaiyo, yakapindurwa iri chinhambwe che6 cm
Zvinozivikanwa:
Kureba kwechinhu (d) = 12 cm
Nharaunda yegirazi rakatenderedzwa (r) = 6 cm.
Kureba kwegirazi rakapinza (f) = 6 cm / 2 = -3 cm
Kureba kwegirazi rakatenderedzwa kunoratidza kuti harina kunaka nekuti riri rechokwadi. Riri rechokwadi nekuti haripfuuri nechiedza.
Zvinodiwa: Hunhu hwemufananidzo
Solution:
Kureba kwemufananidzo (d'):
1/d' = 1/f – 1/d = -1/3 – 1/12 = -4/12 – 1/12 = -5/12
d' = -12/5 = -2.4 cm
Kureba kwemufananidzo kwakasainwa negative zvinoreva kuti mufananidzo wacho uri wepaindaneti.
Kukura kwemufananidzo (m):
m = -d' / d = -(-2.4) / 12 = 2.4 / 12 = 0.2 kanomwe
Kukura kwemufananidzo wakanyorwa zvakanaka kunoreva kuti mufananidzo wakamira uye kukura kwemufananidzo kuri 0.2 zvinoreva kuti saizi yemufananidzo idiki pane saizi yechinhu (yakaderedzwa).
Mhinduro chaiyo ndeinoti C.
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