1. Tsawon mai da hankali na ruwan tabarau mai lanƙwasa (ruwan tabarau masu nutsewa) 30 cm. Akwai wani abu mai tsayin cm 5 a gefen hagu na ruwan tabarau. Kayyade nisan hoton, girman hoton, tsayin hoton da halayen hoton idan abin yana da nisan cm 15 daga ruwan tabarau mai lanƙwasa.
Tattaunawa
An sani :
Tsawon maƙasudi (f) = -30 cm
Tsawon firikwensin ruwan tabarau mai siffar ƙwallo yana da kyau saboda hasken ba ya ratsawa ta cikin ruwan tabarau mai siffar ƙwallo ko kuma yana kama da na kama-da-wane.
Tsawon abu (h) = 5 cm
Nisa (s) na abu = 15 cm
An tambaya : Nisa (s') na hoto, girman hoto (M), tsayin hoto (h') da halayen hoto
Jawab :
Hoton samuwar hoton abu ta hanyar ruwan tabarau mai lanƙwasa:
Nisa ta hoto (s'):
1/s' = 1/f – 1/s = -1/30 – 1/15 = -1/30 – 2/30 = -3/30
s' = -30/3 = -10 cm
Nisa mai duhu yana nufin cewa inuwa ta kama-da-wane ce ko kuma ba ta wuce ta hasken ba.
Nisa tsakanin hoton da santimita 10 ya fi ƙasa da nisan abu da santimita 15.
Ƙara girman hoto (M):
M = -s'/s = -(-10)/15 = 10/15 = sau 2/3
Girman hoton da kyau yana nufin cewa hoton ya miƙe ko kuma ba a juya shi ba.
Girman hoton ya fi ƙanƙanta da girman abin sau 2/3.
Tsawon inuwar (h'):
M = h'/h
h' = M h = (2/3)5 = 10/3 = 3,3 cm
Tsayin inuwar yana da kyau, ma'ana inuwar tana tsaye ko ba ta juye ba.
Tsawon hoton 3,3 cm ya fi ƙanƙanta fiye da tsayin abu na 5 cm.
Halayen inuwa
Dangane da lissafin da ke sama, za a iya kammala da cewa halayen hoton wani abu da aka samar ta hanyar ruwan tabarau mai lanƙwasa sune:
- haskoki na kama-da-wane ko na haske ba sa ratsawa ta inuwa
- a tsaye ko ba a juye ba
– raguwa ko girman hoton ya fi ƙasa da girman abin
– nisan hoton ya fi ƙasa da nisan abin
2. Abu mai tsayin santimita 10 yana da santimita 60 a gaban ruwan tabarau mai lanƙwasa mai tsawon santimita 30. Lissafa nisan hoton, girman hoton, tsayin hoton da halayen hoton!
Tattaunawa
An sani :
Tsawon maƙasudi (f) = -30 cm
Tsawon firikwensin ruwan tabarau mai siffar ƙwallo yana da kyau saboda hasken ba ya ratsawa ta cikin ruwan tabarau mai siffar ƙwallo ko kuma yana kama da na kama-da-wane.
Tsawon abu (h) = 10 cm
Nisa (s) na abu = 60 cm
An tambaya : Nisa (s') na hoto, girman hoto (M), tsayin hoto (h') da halayen hoto
Jawab :
Hoton samuwar hoton abu ta hanyar ruwan tabarau mai lanƙwasa:
Nisa ta hoto (s'):
1/s' = 1/f – 1/s = -1/30 – 1/60 = -2/60 – 1/60 = -3/60
s' = -60/3 = -20 cm
Nisa mai duhu yana nufin cewa inuwa ta kama-da-wane ce ko kuma ba ta wuce ta hasken ba.
Nisa tsakanin hoton da santimita 20 ya fi ƙasa da nisan abu da santimita 60.
Ƙara girman hoto (M):
M = -s'/s = -(-20)/60 = 20/60 = sau 1/3
Girman hoton da kyau yana nufin cewa hoton ya miƙe ko kuma ba a juya shi ba.
Girman hoton ya fi ƙanƙanta da girman abin sau 1/3.
Tsawon inuwar (h'):
M = h'/h
h' = M h = (1/3)10 = 10/3 = 3,3 cm
Tsayin inuwar yana da kyau, ma'ana inuwar tana tsaye ko ba ta juye ba.
Tsawon hoton 3,3 cm ya fi ƙanƙanta fiye da tsayin abu na 10 cm.
Halayen inuwa
Dangane da lissafin da ke sama, za a iya kammala da cewa halayen hoton wani abu da aka samar ta hanyar ruwan tabarau mai lanƙwasa sune:
- haskoki na kama-da-wane ko na haske ba sa ratsawa ta inuwa
- a tsaye ko ba a juye ba
– raguwa ko girman hoton ya fi ƙasa da girman abin
– nisan hoton ya fi ƙasa da nisan abin
Matsalar ruwan tabarau mai siffar concave
1. Gilashin madubi mai siffar kusurwa yana da tsawon ma'aunin haske na 20 cm, kuma wani abu mai tsawon 10 cm yana da nisan 10 cm a gaban gilashin madubi mai siffar kusurwa. Kayyade nisan hoton, girman hoton, tsayin hoton da kuma halayen hoton!
Maɓallin amsawa:
(a) s' = -20/3 cm
(b) m = 2/3
(c) h' = 20/3 cm
(d) kaddarorin hoton: kama-da-wane, a tsaye, girman da aka rage
2. Lissafa nisan hoton, girman hoton, tsayin hoton da halayen hoton wani abu mai tsayin cm 5 da santimita 50 a gaban ruwan tabarau mai lanƙwasa mai tsawon 40 cm!
Maɓallin amsawa:
(a) s' = -22,2 cm
(b) m = 0,44
(c) h' = 2,2 cm
(d) kaddarorin hoton: kama-da-wane, a tsaye, girman da aka rage
