1. Madubin da ke lanƙwasa yana da tsawon mai da hankali na santimita 10. Bayyana yadda hoton ya samo asali sannan a tantance nisan hoton da girmansa idan nisan abin daga madubin da ke da lanƙwasa ya kai santimita 20.
Tattaunawa
An san cewa:
Tsawon madubi mai lanƙwasa (f) = -10 cm
Madogarar madubin da ke da santsi ba ta da kyau domin kuwa ba a wuce hasken madubin da ke da santsi ta hanyar haske ko kuma ta kama-da-wane ba.
Nisa (s) na abu = 20 cm
Amsa:
Hoton samuwar inuwar abubuwa :
Nisa tsakanin inuwa:
1/s' = 1/f – 1/s = -1/10 – 1/20 = -2/20 – 1/20 = -3/20
s' = -20/3 = -6,7 cm
Nisa tsakanin inuwar da inuwar ba ta da kyau, ma'ana inuwar ta kama-da-wane ce ko kuma hasken bai ratsa inuwar ba.
Nisa tsakanin hoton da na'urar ta kai santimita 20 ya fi ƙasa da santimita 6,7.
Ƙara girman hoto:
M = -s'/s = -(-6,7)/20 = 6,7/20 = sau 0,3
Girman inuwar ya ninka girman inuwar sau 0,3.
Girman hoto mai kyau yana nufin hoton yana tsaye. Ana juya hoton idan girman hoton ya kasance mara kyau.
2. An sanya wani abu mai tsayin santimita 10 a gaban madubi mai lanƙwasa wanda tsawonsa ya kai santimita 20. A tantance tsayin hoton idan nisan abin da ke gaban madubin ya kai santimita 10, santimita 30, santimita 40, da santimita 50.
Tattaunawa
An san cewa:
Tsawon madubi mai lanƙwasa (f) = -20 cm
Madogarar madubi mai lanƙwasa ba ta da kyau saboda hasken ba ya ratsa ta wurin da ke bayan madubin.
Radius na lanƙwasa madubi mai lanƙwasa (R) = 2f = 2(20) = 40 cm
Tsawon abu (h) = 10 cm
Amsa:
a) Nisa mai zurfi (f) = -20 cm da nisan abu (s) = 10 cm
Nisa ta hoto (s'):
1/s' = 1/f – 1/s = -1/20 – 1/10 = -1/20 – 2/20 = -3/20
s' = -20/3 = -6,7
Nisa mara kyau ta hoto yana nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Ƙara girman hoto (M):
M = -s'/s = -(-6,7)/10 = 6,7/10 = sau 0,67
Girman hoton yana da kyau, ma'ana hoton yana tsaye.
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Tsawon inuwar (h'):
M = h'/h
h' = h M = (10 cm)(0,67) = 6,7 cm
Hoton (h') yana ƙasa da abin (h) da santimita 10 da santimita 6,7.
b) Nisa mai zurfi (f) = -20 cm da nisan abu (s) = 30 cm
Nisa ta hoto (s'):
1/s' = 1/f – 1/s = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
s' = -60/5 = -12
Nisa mara kyau ta hoto yana nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Ƙara girman hoto (M):
M = -s'/s = -(-12)/30 = 12/30 = sau 0,4
Girman hoton yana da kyau, ma'ana hoton yana tsaye.
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Tsawon inuwar (h'):
M = h'/h
h' = h M = (10 cm)(0,4) = 4 cm
Hoton (h') yana ƙasa da abin (h) da santimita 10 da santimita 4.
c) Nisa mai zurfi (f) = -20 cm da nisan abu (s) = 40 cm
Nisa ta hoto (s'):
1/s' = 1/f – 1/s = -1/20 – 1/40 = -2/40 – 1/40 = -3/40
s' = -40/3 = -13,3
Nisa mara kyau ta hoto yana nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Ƙara girman hoto (M):
M = -s'/s = -(-13,3)/40 = 13,3/40 = sau 0,3
Girman hoton yana da kyau, ma'ana hoton yana tsaye.
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Tsawon inuwar (h'):
M = h'/h
h' = h M = (10 cm)(0,3) = 3 cm
Hoton (h') yana ƙasa da abin (h) da santimita 10 da santimita 3.
d) Nisa mai zurfi (f) = -20 cm da nisan abu (s) = 50 cm
Nisa ta hoto (s'):
1/s' = 1/f – 1/s = -1/20 – 1/50 = -5/100 – 2/100 = -7/100
s' = -100/7 = -14,3
Nisa mara kyau ta hoto yana nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Ƙara girman hoto (M):
M = -s'/s = -(-14,3)/50 = 14,3/50 = sau 0,3
Girman hoton yana da kyau, ma'ana hoton yana tsaye.
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Tsawon inuwar (h'):
M = h'/h
h' = h M = (10 cm)(0,3) = 3 cm
Hoton (h') yana ƙasa da abin (h) da santimita 10 da santimita 3.
3. Abu yana da nisan santimita 20 a gaban madubi mai lanƙwasa. Idan hoton da aka yi ya ninka tsayin abu sau 1/5, a tantance a) nisan hoton, b) tsawon mai da hankali, c) yanayin hoton.
Tattaunawa
An sani :
Nisa (s) na abu = 20 cm
Tsawon hoto (h') = 1/5 h = 0,2 h
Tsayin inuwar (h) = h
Jawab :
a) Nisa ta hoto (s')
Tsarin ƙara girman inuwa:
M = h'/h = 0,2h/h = sau 0,2
Girman hoton da kyau yana nufin hoton yana tsaye.
Girman hoton (M) bai kai 1 ba, ma'ana girman hoton ya ragu.
Nisa ta hoto (s'):
Lissafin nisan hoton ta amfani da dabarar ƙara girman hoton M = -s'/s
-s' = Ms
s' = – M s = -(0,2)(20 cm) = -4 cm
Nisa mara kyau na hoto yana nufin hoton yana kama da na kama-da-wane. Hoton yana bayan madubi kuma hasken ba ya wucewa ta cikinsa.
b) Tsawon maƙasudi (f)
Nisa mai zurfi (f):
1/f = 1/s + 1/s' = 1/20 – 1/4 = 1/20 – 5/20 = -4/20
f = -20/4 = -5 cm
Tsawon abin da aka mayar da hankali a kai ba shi da kyau saboda hasken ba ya ratsa wurin da madubin ke haskakawa.
c) Sifofin inuwa
Halayen inuwa:
- Tsaye
– Ragewa yana nufin girman inuwar ya fi ƙasa da girman abin
– Na'urar kama-da-wane tana nufin inuwar ba ta wucewa ta cikin hasken ba saboda tana bayan madubin da ke da santsi.
Tambayoyin madubi masu ratsa zuciya
1. Madubin da ke da lanƙwasa yana da radius na lanƙwasa na 24 cm. Kayyade nisan hoton, girman hoton, tsayin hoton da halayen hoton idan abin ya kai 6 cm daga madubin kuma abin ya kai 3 cm tsayi.
Maɓallin amsawa:
(a) Nisa tsakanin hotuna = s'= -4 cm
(b) Girman hoton = M = 2/3
(c) Tsayin inuwa = h' = 2 cm
(d) Halayen hoton: kama-da-wane, a tsaye, girmansa ya ragu.
2. Nisa tsakanin abu da madubin da ke da santsi mai tsawon santimita 8 shine santimita 12. Idan tsayin abu shine santimita 4, a tantance: (a) nisan hoton, (b) girman hoton, (c) tsayin hoton da halayen hoton.
Maɓallin amsawa:
(a) Nisa tsakanin hotuna = s'= -4,8 cm
(b) Girman hoton = M = 0,4
(c) Tsayin inuwa = h' = 1,6 cm
(d) Halayen hoton: kama-da-wane, a tsaye, girmansa ya ragu.
3. Wani abu mai tsawon santimita 5 yana da nisan santimita 15 a gaban madubin mai lanƙwasa wanda ke nuna haske. Idan tsawon madubin mai lanƙwasa ya kai santimita 5, a tantance: (a) nisan hoton, (b) girman hoton, (c) tsayin hoton, (d) halayen hoton.
Maɓallin amsawa:
(a) Nisa tsakanin hotuna = s'= -3,75 cm
(b) Girman hoton = M = 0,25
(c) Tsayin inuwa = h' = 1,25 cm
(d) Halayen hoton: kama-da-wane, a tsaye, girmansa ya ragu.
4. Nisa tsakanin abin da ke gaban madubin mai lanƙwasa shine 10 cm kuma hoton da aka samar shine 1/2 tsawon abin. A tantance: (a) nisan hoton, (b) tsawon madubin mai lanƙwasa, (c) halayen hoton.
Maɓallin amsawa:
(a) Nisa tsakanin hotuna = s'= -5 cm
(b) Tsawon madubi mai lanƙwasa = f = -10 cm
(c) Halayen hoton: kama-da-wane, a tsaye, girmansa ya ragu.
