Zitsanzo ziwiri za mafunso a mandala awiri okhala ndi convex-concave
1. Lenzi yozungulira ili ndi kutalika kwa masentimita 30 ndipo lenzi yozungulira ili ndi kutalika kwa masentimita 20 komwe kumayikidwa pafupi pomwe mtunda pakati pa ma lenzi awiriwo ndi masentimita 150. Ngati chinthucho chili ndi masentimita 40 patsogolo pa lenzi yozungulira, dziwani mtunda wa chithunzicho ndi kukula kwa chithunzicho chopangidwa ndi lenziyo. mandala ozungulira dani mandala opindika koma!
Zokambirana
Amadziwika kuti:
Kutalika kwa lenzi yozungulira (f)1) = +30 cm
Utali wa lenzi yozungulira ndi wabwino chifukwa kuwala kumadutsa pakati pa lenzi yozungulira.
Kutalika kwa lenzi yopingasa (f)2) = -20 cm
Utali wa lenzi yopingasa ndi woipa chifukwa kuwala sikudutsa pakati pa lenzi yopingasa.
Mtunda pakati pa magalasi awiri (l) = 150 cm
Mtunda wa chinthucho kuchokera ku lenzi yozungulira (s)1) = 40 cm
Mtunda wa chinthucho ndi wabwino chifukwa kuwala kumadutsa mu chinthucho.
Yankho:
a) Mtunda wa mthunzi
Mtunda wa chithunzi chopangidwa ndi lenzi yozungulira (mtunda woyamba wa chithunzi):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/30 – 1/40 = 4/120 – 3/120 = 1/120
s1' = 120/1 = 120 cm
Chithunzi choyamba chili pa mtunda wa masentimita 120 kuchokera pa lenzi yozungulira.
Mtunda wa chithunzi choyamba ndi wabwino, kutanthauza kuti chithunzi choyamba ndi chenicheni chifukwa chithunzicho chimadutsa ndi kuwala.
Mtunda wa chithunzi chopangidwa ndi lenzi yopingasa (mtunda womaliza wa chithunzi):
Chithunzi chopangidwa ndi lenzi yozungulira chimaonedwa ngati chinthu ndi lenzi yozungulira. Mtunda wa chithunzi/chinthu choyamba kuchokera ku lenzi yozungulira2) = mtunda pakati pa magalasi awiri (l) - mtunda wa chithunzi choyamba kuchokera ku magalasi ozungulira (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
Chithunzi chomaliza chili pa 12 cm kuchokera pa lenzi yokhotakhota.
Mtunda wa chithunzi chomaliza ndi woipa, zomwe zikutanthauza kuti chithunzi chomaliza ndi chabodza kapena chabodza chifukwa kuwala sikudutsa mu chithunzicho.
b) Kukula kwa chithunzicho
Kukula kwa chithunzicho ndi lenzi yozungulira:
m1 = -s1'/s1 = -120 cm/40 cm = -3 nthawi
Lenzi yozungulira imapangitsa kukula kwa chithunzi kukhala kwakukulu kawiri kuposa kukula kwa chinthucho.
Kukula kwa chithunzicho ndi chizindikiro chotsutsa kumatanthauza kuti chithunzicho chatembenuzidwa.
Kukula kwa chithunzicho ndi lenzi yopingasa:
m2 = -s2'/s2 = -(-12 cm)/30 cm = 12/30 = kawiri
Lenzi yachiwiri yozungulira imakulitsa chinthucho (chithunzi cha lenzi yozungulira) ndi nthawi 0,4.
Kukula konse kwa chithunzicho ndi:
m = (m1)m2) = (-3)(0,4) = -1,2 nthawi
Kukula kwa chithunzi chomaliza ndi kokulirapo ka 1,2 kuposa kukula kwa chinthucho kapena kutalika kwa chithunzi chomaliza ndi kokulirapo ka 1,2 kuposa kutalika kwa chinthucho. Kukula konse kolakwika kumatanthauza kuti chithunzicho chasinthidwa.
2. Mtunda pakati pa lenzi yozungulira ndi yopingasa ndi 120 cm. Lenzi yopingasa ili ndi kutalika kwa 50 cm ndipo lenzi yopingasa ili ndi kutalika kwa 100 cm. Chinthu chili 100 cm patsogolo pa lenzi yopingasa. Dziwani mtunda wa chithunzi ndi kukula kwa chithunzi chopangidwa ndi ma lenzi awiriwa!
Zokambirana
Ndizodziwika kuti :
Mtunda pakati pa magalasi awiri (l) = 120 cm
Kutalika kwa lenzi yozungulira (f)1) = 50 cm
Utali wa lenzi yozungulira ndi wabwino chifukwa kuwala kumadutsa pakati pa lenzi yozungulira.
Kutalika kwa lenzi yopingasa (f)2) = -100 cm
Utali wa lenzi yopingasa ndi woipa chifukwa kuwala sikudutsa pakati pa lenzi yopingasa.
Mtunda wa chinthucho kuchokera ku lenzi yozungulira (s)1) = 100 cm
Mtunda wa chinthucho ndi wabwino chifukwa kuwala kwa kuwala kumabwera kudzera mu chinthucho.
Yankhani :
a) Mtunda wa mthunzi
Mtunda wa chithunzi chopangidwa ndi lenzi yozungulira (mtunda woyamba wa chithunzi):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/50 – 1/100 = 2/100 – 1/100 = 1/100
s1' = 100/1 = 100 cm
Chithunzi choyamba chili pa 100 cm kumanja kwa lenzi yozungulira.
Mtunda wa chithunzi choyamba ndi wabwino, kutanthauza kuti chithunzi choyamba ndi chenicheni chifukwa chithunzicho chimadutsa ndi kuwala.
Mtunda wa chithunzi chopangidwa ndi lenzi yopingasa (mtunda womaliza wa chithunzi):
Chithunzi chopangidwa ndi lenzi yozungulira chimaonedwa ngati chinthu ndi lenzi yozungulira. Mtunda wa chithunzi/chinthu choyamba kuchokera ku lenzi yozungulira2) = mtunda pakati pa magalasi awiriwa - mtunda wa chithunzi choyamba kuchokera ku magalasi ozungulira = 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
Chithunzi chomaliza chili pa 16,7 cm kuchokera pa lenzi yokhotakhota.
Mtunda womaliza wa chithunzi ndi woipa, zomwe zikutanthauza kuti chithunzi chomaliza ndi chabodza kapena chabodza chifukwa kuwala sikudutsa mu chithunzicho (chithunzi chomaliza chili kumanzere kwa lenzi yokhotakhota).
b) Kukula kwa chithunzicho
Kukula kwa chithunzicho ndi lenzi yozungulira:
m1 = -s1'/s1 = -100 cm/100 cm = -1 nthawi
Lenzi yozungulira imapangitsa kukula kwa chithunzi kukhala kofanana ndi kukula kwa chinthucho.
Kukula kwa chithunzicho ndi chizindikiro chotsutsa kumatanthauza kuti chithunzicho chatembenuzidwa.
Kukula kwa chithunzicho ndi lenzi yopingasa:
m2 = -s2'/s2 = -(-16,7 cm)/20 cm = 16,7/20 = kawiri
Lenzi yopingasa imachepetsa kukula kwa chinthu (chinthu = chithunzi cha lenzi yopingasa) ndi nthawi 0,8.
Kukula konse kwa chithunzicho ndi:
m = (m1)m2) = (-1)(0,8) = -0,8 nthawi
Kukula kwa chithunzi chomaliza ndi kochepa ka 0,8 kuposa kukula kwa chinthucho kapena kutalika kwa chithunzi chomaliza ndi kochepera ka 0,8 kuposa kutalika kwa chinthucho. Kukula konse kolakwika kumatanthauza kuti chithunzicho chasinthidwa.
Mafunso a ma lenzi awiri okhala ndi concave-convex
1. Lenzi yozungulira yokhala ndi kutalika kwa 10 cm ndi lenzi yozungulira yokhala ndi kutalika kwa 40 cm imayikidwa pafupi pomwe mtunda pakati pa ma lenzi awiriwo ndi 100 cm. Ngati mtunda wa chinthu chomwe chili patsogolo pa lenzi yozungulira ndi 20 cm, dziwani mtunda wa chithunzi ndi kukula kwa chithunzi chomwe chimapangidwa ndi ma lenzi ozungulira ndi ozungulira!
Kiyi yoyankhira:
(a) mtunda womaliza wa chithunzi = s2' = -26,7 cm.
(b) kukula konse kwa chithunzi = m = nthawi 0,33
