2 Mienzaniso yemibvunzo ine magirazi maviri ane convex-concave
1. Lenzi ine denderedzwa remasentimita makumi matatu (30 cm) uye lenzi ine denderedzwa remasentimita makumi maviri (20 cm) iri pedyo pedyo apo daro riri pakati pemalenzi maviri iri 150 cm. Kana chinhu chacho chiri 40 cm pamberi pelenzi ine denderedzwa remasentimita, sarudza daro remufananidzo uye kukura kwemufananidzo wakagadzirwa nelenzi. lenzi yakamoneredzwa dhani lenzi yakakombama iyo!
Kukurukurirana
Zvinozivikanwa kuti:
Hurefu hwegirazi re convex (f)1) = +30 cm
Hurefu hwegirazi re convex hwakanaka nekuti chiedza chinopfuura nepakati pegirazi re convex.
Kureba kwegirazi remukati (f)2) = -20 cm
Hurefu hwegirazi re concave hunenge husina kunaka nekuti chiedza hachipfuuri nepakati pegirazi re concave.
Kureba pakati pemalenzi maviri (l) = 150 cm
Kureba kwechinhu kubva kune lenzi ye convex (s)1) = 40 cm
Kureba kwechinhu chacho kwakanaka nekuti chiedza chinopfuura nepakati pechinhu chacho.
Mhinduro:
a) Nharaunda yemumvuri
Kureba kwemufananidzo unoumbwa ne lenzi ye convex (kureba kwemufananidzo wekutanga):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/30 – 1/40 = 4/120 – 3/120 = 1/120
s1' = 120/1 = 120 cm
Mufananidzo wekutanga uri 120 cm kubva pane lenzi ine convex.
Kureba kwemufananidzo wekutanga kwakanaka, zvichireva kuti mufananidzo wekutanga ndewechokwadi nekuti mufananidzo wacho unopfuudzwa nechiedza.
Kureba kwemufananidzo wakagadzirwa ne lenzi yakakombama (kureba kwemufananidzo wekupedzisira):
Mufananidzo unogadzirwa ne lenzi ine convex unoonekwa sechinhu ne lenzi ine concave. Kureba kwemufananidzo/chinhu chekutanga kubva kune lenzi ine concave (s)2) = chinhambwe chiri pakati pemalenzi maviri (l) - chinhambwe chemufananidzo wekutanga kubva kune lenzi ine convex (s)1') = 150 cm – 120 cm = 30 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= -1/20 – (1/30) = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
s2' = -60/5 = -12 cm
Mufananidzo wekupedzisira uri 12 cm kubva pane lenzi yakakombama.
Daro remufananidzo wekupedzisira harina kunaka, zvichireva kuti mufananidzo wekupedzisira hauna kunaka nekuti chiedza hachipfuuri nepamufananidzo.
b) Kukura kwemufananidzo
Kukura kwemufananidzo ne lenzi ine convex:
m1 = -s1'/s1 = -120 cm/40 cm = -3 ka3
Lenzi ine convex inoita kuti saizi yemufananidzo ive yakakura kakapetwa katatu kupfuura saizi yechinhu chacho.
Kukura kwemufananidzo nechiratidzo chekuramba zvinoreva kuti mufananidzo wacho wapindurwa.
Kukura kwemufananidzo ne lenzi yakatetepa:
m2 = -s2'/s2 = -(-12 cm)/30 cm = 12/30 = 0,4 kanomwe
Lenzi yechipiri ine convex inokudza chinhu (mufananidzo we lenzi ine convex) nekanenge ka0,4.
Kukura kwese kwemufananidzo ndekwekuti:
m = (m1)(m)2) = (-3)(0,4) = -1,2 kanomwe
Saizi yemufananidzo wekupedzisira yakakura ka1,2 pane saizi yechinhu kana kuti kukwirira kwemufananidzo wekupedzisira kwakakwira ka1,2 pane kukwirira kwechinhu. Kukura kwese kwemufananidzo kunoreva kuti mufananidzo wakapindurwa.
2. Kureba pakati pegirazi rakamonana negirazi rakamonana i120 cm. Girazi rakamonana rine urefu hwe50 cm uye girazi rakamonana rine urefu hwe100 cm. Chinhu chiri 100 cm pamberi pegirazi rakamonana. Sarudza daro remufananidzo uye kukura kwemufananidzo wakaumbwa nemagirazi maviri!
Kukurukurirana
Zvinozivikanwa :
Kureba pakati pemalenzi maviri (l) = 120 cm
Hurefu hwegirazi re convex (f)1) = 50 cm
Hurefu hwegirazi re convex hwakanaka nekuti chiedza chinopfuura nepakati pegirazi re convex.
Kureba kwegirazi remukati (f)2) = -100 cm
Hurefu hwegirazi re concave hunenge husina kunaka nekuti chiedza hachipfuuri nepakati pegirazi re concave.
Kureba kwechinhu kubva kune lenzi ye convex (s)1) = 100 cm
Kureba kwechinhu kwakarurama nekuti chiedza chinobva muchinhu chacho.
Jawab :
a) Nharaunda yemumvuri
Kureba kwemufananidzo unoumbwa ne lenzi ye convex (kureba kwemufananidzo wekutanga):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/50 – 1/100 = 2/100 – 1/100 = 1/100
s1' = 100/1 = 100 cm
Mufananidzo wekutanga uri 100 cm kurudyi rwe lenzi ine convex.
Kureba kwemufananidzo wekutanga kwakanaka, zvichireva kuti mufananidzo wekutanga ndewechokwadi nekuti mufananidzo wacho unopfuudzwa nechiedza.
Kureba kwemufananidzo wakagadzirwa ne lenzi yakakombama (kureba kwemufananidzo wekupedzisira):
Mufananidzo unogadzirwa ne lenzi ine convex unoonekwa sechinhu ne lenzi ine concave. Kureba kwemufananidzo/chinhu chekutanga kubva kune lenzi ine concave (s)2) = chinhambwe chiri pakati pemagirazi maviri - chinhambwe chemufananidzo wekutanga kubva kune lenzi yakapinza = 120 cm - 100 cm = 20 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= -1/100 – 1/20 = -1/100 – 5/100 = -6/100
s2' = -100/6 = -16,7 cm
Mufananidzo wekupedzisira uri 16,7 cm kubva pane lenzi yakakombama.
Daro remufananidzo wekupedzisira harina kunaka, zvichireva kuti mufananidzo wekupedzisira hausi wechokwadi kana kuti wenhema nekuti chiedza hachipfuuri nepamufananidzo (mufananidzo wekupedzisira uri kuruboshwe rwegirazi rakakombama).
b) Kukura kwemufananidzo
Kukura kwemufananidzo ne lenzi ine convex:
m1 = -s1'/s1 = -100 cm/100 cm = -1 ka3
Lenzi ine convex inoita kuti saizi yemufananidzo ive yakafanana nehukuru hwechinhu.
Kukura kwemufananidzo nechiratidzo chekuramba zvinoreva kuti mufananidzo wacho wapindurwa.
Kukura kwemufananidzo ne lenzi yakatetepa:
m2 = -s2'/s2 = -(-16,7 cm)/20 cm = 16,7/20 = 0,8 kanomwe
Lenzi yakakombama inoderedza saizi yechinhu (chinhu = mufananidzo welenzi yakakombama) nekanenge ka0,8.
Kukura kwese kwemufananidzo ndekwekuti:
m = (m1)(m)2) = (-1)(0,8) = -0,8 kanomwe
Saizi yemufananidzo wekupedzisira idiki ka0,8 pane saizi yechinhu kana kuti kukwirira kwemufananidzo wekupedzisira kwakaderera ka0,8 pane kukwirira kwechinhu. Kukura kwese kwemufananidzo kunoreva kuti mufananidzo wakapindurwa.
Mibvunzo ine magirazi maviri akakombama
1. Lenzi ine denderedzwa ine urefu hwe 10 cm uye lenzi ine denderedzwa ine urefu hwe 40 cm zvinoiswa pedyo nepedyo apo daro riri pakati pemalenzi maviri iri 100 cm. Kana daro rechinhu chiri pamberi pelenzi ine denderedzwa riri 20 cm, sarudza daro remufananidzo uye kukura kwemufananidzo unoumbwa nemalenzi ane denderedzwa ne denderedzwa!
Kiyi yemhinduro:
(a) daro rekupedzisira remufananidzo = s2' = -26,7 cm.
(b) kukura kwese kwemufananidzo = m = 0,33 times
