2 Mienzaniso yemibvunzo ine magirazi maviri akajeka
1. Magirazi maviri akamoneredzwa, rimwe nerimwe rine urefu hwemasendimita makumi maviri nemakumi matatu, anoiswa pedyo nepedyo, daro riri pakati pemagirazi maviri akamoneredzwa riri masendimita makumi manomwe. Chinhu chiri pamberi pegirazi rekutanga riri masendimita makumi matatu. Sarudza daro remufananidzo uye kukura kwemufananidzo wakaumbwa nemagirazi maviri. lenzi yakamoneredzwa iyo!
Kukurukurirana
Zvinozivikanwa kuti:
Kureba kwegirazi rekutanga re convex (f)1) = +20 cm
Kureba kwegirazi rechipiri rine convex (f)2) = +30 cm
Hurefu hwegirazi re convex hwakanaka nekuti chiedza chinopfuura nepakati pegirazi re convex.
Kureba pakati pemagirazi maviri e convex (l) = 50 cm
Kureba kwechinhu kubva pane lenzi yekutanga ye convex (s)1) = 30 cm
Kureba kwechinhu kwakarurama nekuti chiedza chinobva muchinhu chacho.
Mhinduro:
a) Nharaunda yemumvuri
Kureba kwemufananidzo kunoumbwa ne lenzi yekutanga ine convex (kureba kwemufananidzo wekutanga):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s1' = 60/1 = 60 cm
Mufananidzo wekutanga uri 60 cm kubva pane lenzi ine convex 1.
Kureba kwemufananidzo wekutanga kwakanaka, zvichireva kuti mufananidzo wekutanga ndewechokwadi, zvichireva kuti uripo zvechokwadi nekuti chiedza chinopfuura nepamufananidzo.
Kureba kwemufananidzo kunoumbwa ne lenzi yechipiri ine convex (kureba kwemufananidzo wekupedzisira):
Mufananidzo unoumbwa ne lenzi yekutanga ine convex unoonekwa sechinhu ne lenzi yechipiri ine convex. Kureba kwemufananidzo/chinhu chekutanga kubva kune lenzi yechipiri ine convex (s)2) = chinhambwe chiri pakati pemagirazi maviri akapinza - chinhambwe chemufananidzo wekutanga kubva kune lenzi yekutanga yakapinza = 70 cm - 60 cm = 10 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= 1/30 – 1/10 = 1/30 – 3/30 = -2/30
s2' = -30/2 = -15 cm
Mufananidzo wekupedzisira uri 15 cm kubva pane lenzi yechipiri ine convex.
Daro remufananidzo wekupedzisira harina kunaka, zvichireva kuti mufananidzo wekupedzisira hauna kunaka nekuti mufananidzo haupfuuri nepakati nechiedza (mufananidzo wekupedzisira uri kuruboshwe rwelenzi yechipiri ine convex).
b) Kukura kwemufananidzo
Kukura kwemufananidzo ne lenzi yekutanga ye convex:
m1 = -s1'/s1 = -60 cm/30 cm = -2 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 yechipiri ine convex:
m2 = -s2'/s2 = -(-15 cm)/10 cm = 15/10 = 1,5 kanomwe
Lenzi yechipiri ine convex inokudza chinhu (mufananidzo welenzi yekutanga ine convex) nekaviri.
Kukura kwese kwemufananidzo ndekwekuti:
m = (m1)(m)2) = (-2)(1,5) = -3 kanomwe
Saizi yemufananidzo wekupedzisira yakakura ka3 kupfuura saizi yechinhu kana kuti kukwirira kwemufananidzo wekupedzisira kwakakwira ka3 kupfuura kukwirira kwechinhu. Kukura kwese kwese hakuna kunaka zvichireva kuti mufananidzo wakapindurwa. (mufananidzo wekupedzisira wakapindurwa saka mufananidzo wekupedzisira unofanira kunge uri kuruboshwe rwelenzi yechipiri yakatenderedzwa).
2. Kureba pakati pemagirazi maviri akachinjika i100 cm. Magirazi maviri akachinjika rimwe nerimwe ane urefu hwemasentimita makumi maviri nehafu (focal lengths) uye masendimita makumi masere (80 cm). Chinhu chiri pamberi pegirazi rekutanga iri 30 cm. Sarudza daro remufananidzo uye kukura kwemufananidzo wakaumbwa nemagirazi maviri akachinjika!
Kukurukurirana
Zvinozivikanwa :
Kureba pakati pemalenzi maviri (l) = 100 cm
Kureba kwegirazi rekutanga re convex (f)1) = 20 cm
Kureba kwegirazi rechipiri rine convex (f)2) = 80 cm
Hurefu hwegirazi re convex hwakanaka nekuti chiedza chinopfuura nepakati pegirazi re convex.
Kureba kwechinhu kubva pane lenzi yekutanga ye convex (s)1) = 30 cm
Kureba kwechinhu kwakarurama nekuti chiedza chinobva muchinhu chacho.
Jawab :
a) Nharaunda yemumvuri
Kureba kwemufananidzo kunoumbwa ne lenzi yekutanga ine convex (kureba kwemufananidzo wekutanga):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s1' = 60/1 = 60 cm
Mufananidzo wekutanga uri 60 cm kubva pane lenzi ine convex 1.
Kureba kwemufananidzo wekutanga kwakanaka, zvichireva kuti mufananidzo wekutanga ndewechokwadi, zvichireva kuti uripo zvechokwadi nekuti chiedza chinopfuura nepamufananidzo.
Kureba kwemufananidzo kunoumbwa ne lenzi yechipiri ine convex (kureba kwemufananidzo wekupedzisira):
Mufananidzo unoumbwa ne lenzi yekutanga ine convex unoonekwa sechinhu ne lenzi yechipiri ine convex. Kureba kwemufananidzo/chinhu chekutanga kubva kune lenzi yechipiri ine convex (s)2) = chinhambwe chiri pakati pemagirazi maviri akapinza - chinhambwe chemufananidzo wekutanga kubva kune lenzi yekutanga yakapinza = 100 cm - 60 cm = 40 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= 1/80 – 1/40 = 1/80 – 2/80 = -1/80
s2' = -80/1 = -80 cm
Mufananidzo wekupedzisira uri 80 cm kubva pane lenzi yechipiri ine convex.
Daro remufananidzo wekupedzisira harina kunaka, zvichireva kuti mufananidzo wekupedzisira hauna kunaka nekuti mufananidzo haupfuuri nepakati nechiedza (mufananidzo wekupedzisira uri kuruboshwe rwelenzi yechipiri ine convex).
b) Kukura kwemufananidzo
Kukura kwemufananidzo ne lenzi yekutanga ye convex:
m1 = -s1'/s1 = -60 cm/30 cm = -2 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 yechipiri ine convex:
m2 = -s2'/s2 = -(-80 cm)/40 cm = 80/40 = 2 kanomwe
Lenzi yechipiri ine convex inokudza chinhu (mufananidzo welenzi yekutanga ine convex) nekaviri.
Kukura kwese kwemufananidzo ndekwekuti:
m = (m1)(m)2) = (-2)(2) = -4 kanomwe
Saizi yemufananidzo wekupedzisira yakakura ka4 pane saizi yechinhu kana kuti kukwirira kwemufananidzo wekupedzisira kwakakwira ka4 pane kukwirira kwechinhu. Kukura kwese kwese hakuna kunaka zvichireva kuti mufananidzo wakapindurwa (mufananidzo wekupedzisira wakapindurwa saka mufananidzo wekupedzisira unofanira kunge uri kuruboshwe rwelenzi yechipiri yakatenderedzwa).
Mibvunzo ine magirazi maviri akakombama
1. Magirazi maviri akapinza rimwe nerimwe rine urefu hwe40 cm uye 20 cm anoiswa pedyo nepedyo apo daro riri pakati pemagirazi maviri akapinza riri 100 cm. Sarudza daro remufananidzo uye kukura kwese kwemufananidzo wakaumbwa nemagirazi maviri akapinza pachinhu chiri 120 cm pamberi pegirazi rekutanga rakapinza!
Kiyi yemhinduro:
(a) daro rekupedzisira remufananidzo = s2' = 40
(b) kukura kwese kwemufananidzo = m = 0,5
2. Chinhu chiri 10 cm kuruboshwe rwelenzi ine denderedzwa remasendimita makumi maviri. Kurudyi kwelenzi ine denderedzwa remasendimita makumi mashanu (50 cm). Kana daro riri pakati pelenzi mbiri iri 120 cm, sarudza daro remufananidzo uye kukura kwemufananidzo wakaumbwa nelenzi mbiri dzine denderedzwa remasendimita!
Kiyi yemhinduro:
(a) daro rekupedzisira remufananidzo = s2' = 133 cm
(b) kukura kwese kwemufananidzo = m = -1,7 times. Negative zvinoreva kuti mufananidzo wakapindurwa.
