Domin fahimtar hoton wani abu da madubi mai lanƙwasa ya samar , a kula da wannan misali tambaya da tattaunawa. A cikin wannan tambayar, ana ɗauka cewa abin yana da wani nisa daga madubin mai lanƙwasa, sannan a bayyana yadda hoton abin yake ta hanyar madubin mai lanƙwasa , nisan hoton daga madubin mai lanƙwasa da kuma girman hoton da madubin mai lanƙwasa ya samar.
A ce madubi mai lanƙwasa yana da radius na lanƙwasa na santimita 30. Bayyana yadda hoton ya samo asali, sannan a tantance nisan hoton da girmansa idan:
a) nisan abu ya fi ƙanƙanta fiye da tsawon mai da hankali (s < f)
b) nisan abin yayi daidai da tsawon mai da hankali (s = f)
c) nisan abu ya fi tsayin mai da hankali kuma ya fi ƙanƙanta da radius na lanƙwasa madubi (f < s < r)
d) nisan da ke tsakanin abu da radius na lanƙwasa madubi (s = R)
e) nisan abu ya fi radius na lanƙwasa madubin (s > R)
Tattaunawa
An sani :
Radius na lanƙwasa madubi mai lanƙwasa (R) = 30 cm
Tsawon madubi mai lanƙwasa (f) = R/2 = 30/2 = -15 cm
Madogarar madubin mai lanƙwasa tana bayan madubin mai lanƙwasa inda hasken bai ratsa ta wurin madubin mai lanƙwasa ba, don haka ana ba wa madubin mai lanƙwasa alama mara kyau.
Jawab :
Nisa tsakanin abu da abin ya fi ƙanƙanta fiye da tsawon madubin da ke da lanƙwasa (s < f)
A ce nisan abin daga madubin shine 5 cm da 10 cm.
1) Nisa mai zurfi (f) = -15 cm kuma idan nisan abu (s) = 5 cm
Nisa tsakanin hotuna (s) :
1/s' = 1/f – 1/s = -1/15 – 1/5 = -1/15 – 3/15 = -4/20
s' = -20/4 = -5 cm
Nisa (s') na hoton ba shi da kyau, ma'ana hoton yana kama da na kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin inuwar (s') 5 cm daidai yake da nisan abin (s) 5 cm
Girman hoto mai layi (M) :
M = -s'/s = -(-5)/5 = 5/5 = sau 1
Girman hoton layi (M) 1 yana nufin girman hoton yayi daidai da girman abin.
Girman hoton layi (M) yana da kyau, ma'ana hoton a tsaye yake.
2) Nisa mai zurfi (f) = -15 cm kuma idan nisan abu (s) = 10 cm
Nisa tsakanin hotuna (s) :
1/s' = 1/f – 1/s = -1/15 – 1/10 = -2/30 – 3/30 = -5/30
s' = -30/5 = -6 cm
Nisa (s') na hoton ba shi da kyau, ma'ana hoton yana kama da na kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da na'urar (s') 6 cm ya fi ƙasa da nisan abu (s) 10 cm
Girman hoto mai layi (M) :
M = -s'/s = -(-6)/10 = 6/10 = sau 0,6
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da kyau, ma'ana hoton a tsaye yake.
Nisa tsakanin abu da tsawon madubin da ke kewaye da shi iri ɗaya ne da tsawon mai da hankali (s = f)
Tsawon maƙasudi (f) = nisan abu (s) = 15 cm.
Nisa tsakanin hotuna (s) :
1/s' = 1/f – 1/s = -1/15 – 1/15 = -2/15
s' = -15/2 = -7,5 cm
Alamar da ba ta dace ba ta nuna nisan hoton (s') na nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da na'urar (s') 7,5 cm ya fi ƙasa da nisan abu (s) 15 cm
Girman hoto mai layi (M) :
M = -s'/s = -(-7,5)/15 = 7,5/15 = sau 0,5
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da kyau, ma'ana hoton a tsaye yake.
Nisa tsakanin abu da abin ya fi tsayin da aka mayar da hankali kuma ya fi ƙanƙanta fiye da radius na lanƙwasa na madubin da ke lanƙwasa (f < s < R)
A ce nisan abin daga madubin shine 20 cm da 25 cm.
1) Nisa mai zurfi (f) = -15 cm kuma idan nisan abu (s) = 20 cm
Nisa tsakanin hotuna (s) :
1/s' = 1/f – 1/s = -1/15 – 1/20 = -4/60 – 3/60 = -7/60
s' = -60/7 = -8,6 cm
Alamar da ba ta dace ba ta nuna nisan hoton (s') na nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da na'urar (s') 8,6 cm ya fi ƙasa da nisan abu (s) 20 cm
Girman hoto mai layi (M) :
M = -s'/s = -(-8,6)/20 = 8,6/20 = sau 0,4
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da kyau, ma'ana hoton a tsaye yake.
2) Nisa mai zurfi (f) = -15 cm kuma idan nisan abu (s) = 25 cm
Nisa tsakanin hotuna (s) :
1/s' = 1/f – 1/s = -1/15 – 1/25 = -25/375 – 15/375 = -35/375
s' = -375/35 = -10,7 cm
Nisa ('s') na hoton ba shi da kyau, ma'ana hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da na'urar (s') 10,7 cm ya fi ƙasa da nisan abu (s) 25 cm
Girman hoto mai layi (M) :
M = -s'/s = -(-10,7)/25 = 10,7/25 = sau 0,4
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da kyau, ma'ana hoton a tsaye yake.
Nisa tsakanin abu da radius na lanƙwasa na madubin da ke lanƙwasa (s = R)
Radius na lanƙwasa madubi (R) = nisan abin (s) = 30 cm.
Nisa tsakanin hotuna (s) :
1/s' = 1/f – 1/s = -1/15 – 1/30 = -2/30 – 1/30 = -3/30
s' = -30/3 = -10 cm
Alamar da ba ta dace ba ta nuna nisan hoton (s') na nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da na'urar (s') 10 cm ya fi ƙasa da nisan abu (s) 30 cm
Girman hoto mai layi (M) :
M = -s'/s = -(-10)/30 = sau 1/3
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da kyau, ma'ana hoton a tsaye yake.
Nisa tsakanin abu ya fi radius na lanƙwasa na madubin convex (s > R) girma.
A ce nisan abin daga madubin shine 40 cm da 50 cm.
1) Nisa mai zurfi (f) = -15 cm kuma idan nisan abu (s) = 40 cm
Nisa tsakanin hotuna (s) :
1/s' = 1/f – 1/s = -1/15 – 1/40 = -8/120 – 3/120 = -11/120
s' = -120/11 = -10,9 cm
Alamar da ba ta dace ba ta nuna nisan hoton (s') na nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da na'urar (s') 10,9 cm ya fi ƙasa da nisan abu (s) 40 cm
Girman hoto mai layi (M) :
M = -s'/s = -(-10,9)/40 = 10,9/40 = sau 0,3
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da kyau, ma'ana hoton a tsaye yake.
2) Nisa mai zurfi (f) = -15 cm kuma idan nisan abu (s) = 50 cm
Nisa tsakanin hotuna (s) :
1/s' = 1/f – 1/s = -1/15 – 1/50 = -10/150 – 3/150 = -13/150
s' = -150/13 = -11,5 cm
Alamar da ba ta dace ba ta nuna nisan hoton (s') na nufin cewa hoton yana kama-da-wane ko kuma hoton yana bayan madubin da ke da lanƙwasa inda hasken bai ratsa ta hoton ba.
Nisa tsakanin hoton da na'urar (s') 11,5 cm ya fi ƙasa da nisan abu (s) 50 cm
Girman hoto mai layi (M) :
M = -s'/s = -(-11,5)/50 = 11,5/50 = sau 0,2
Girman hoton layi (M) ya fi 1 ƙanƙanta, ma'ana girman hoton ya fi ƙanƙanta girman abin.
Girman hoton layi (M) yana da kyau, ma'ana hoton a tsaye yake.
