Tambayoyi da dabarun misalai na ƙara girman gilashin girma
1. Wani mai bincike yana duba ganyen ta amfani da ruwan tabarau mai lanƙwasa mai tsawon 25/3 cm a matsayin gilashin ƙara girma. Wace magana ce daidai?
(1) Girman kusurwa daidai yake da 4 idan hoton ƙarshe na abin yana da nisan santimita 25.
(2) Girman kusurwa daidai yake da 3 idan hoton ƙarshe na abin yana a ƙarshen iyaka.
(3) Ƙarfin ruwan tabarau mai lanƙwasa shine Diopters 12
(4) Nisa tsakanin ainihin hoton shine 25/3 cm idan nisan abin shine 50/3 cm.
Tattaunawa
(1) Tsarin girman kusurwar gilashin ƙara girma lokacin da hoton ƙarshe yake a wani nisa (ido yana da matsakaicin wurin zama)
M = N / f + 1
M = kusurwar ƙara girman gilashin, N = kusa da wurin ido na yau da kullun (25 cm), f = tsawon mai da hankali na gilashin ƙara girman
M = 25: 25/3 + 1 = 25 x 3/25 + 1 = 3 + 1 = 4
Bayani na 1 gaskiya ne
(2)
Tsarin girman kusurwar gilashin ƙara girma lokacin da hoton ƙarshe yake a ƙarshen lokaci (mafi ƙarancin wurin zama na ido)
M = N / f
M = kusurwar ƙara girman gilashin, N = kusa da wurin ido na yau da kullun (25 cm), f = tsawon mai da hankali na gilashin ƙara girman
Girman kusurwar gilashin ƙara girma:
M = 25: 25/3 = 25 x 3/25 = 3
Bayani na 2 gaskiya ne
(3) Ƙarfin ruwan tabarau mai lanƙwasa
P = 1/f = 1: 25/3 = 1 x 3/25 = 3/25 Diopters
Bayani na 3 ba daidai ba ne
(4) Nisa ta ainihin hoto
1/s' = 1/f – 1/s
1/s' = 1:25/3 – 1:50/3
1/s' = 1×3/25 – 1×3/50
1/s' = 3/25 – 3/50
1/s' = 6/50 – 3/50
1/s' = 3/50
s' = 50/3
Bayani na 4 ba daidai ba ne
Tushen tambaya:
Tambayoyin Kimiyyar Kimiyyar SBMPTN
Kamar yadda aka bayyana a cikin maudu'in gilashin ƙara girman, abu yana bayyana ƙarami idan aka gan shi daga nesa mai nisa kuma yana bayyana babba idan aka gan shi daga nesa mai kusa. Bambancin girman abubuwan da ido ya gani yana faruwa ne sakamakon bambancin kusurwar da aka samu tsakanin ido da abu. Lokacin da abu ya yi nisa da ido, kusurwar da ke tsakanin ido da abu ya fi ƙanƙanta don haka hoton da aka samar a kan idon ido shi ma ya fi ƙanƙanta. Akasin haka, lokacin da abin yake kusa da ido, kusurwar da ke tsakanin ido da abu ya fi girma don haka hoton da aka samar a kan idon ido shi ma ya fi girma. Mafi kusanci da ido, mafi girman kusurwar da ke tsakanin ido da abu don haka hoton da aka samar a kan idon ido shi ma ya fi girma. Ya kamata a lura cewa kusancin kusa da idon mutum na yau da kullun shine 25 cm don haka nisan da ke tsakanin ido da abu ba zai iya zama ƙasa da 25 cm ba. Za a iya kammala da cewa kusurwar da ke tsakanin idon mutum na yau da kullun da abu, tana da matsakaicin ƙima lokacin da nisan da ke tsakanin ido da abu ya kai 25 cm.
Idan bayan an kusanto da shi zuwa nisan santimita 25 daga idon da aka saba, ba za a iya ganin abu a sarari ba, to ya zama dole a gilashin ƙara girman don taimakawa ido ya ga abin. Gilashin ƙara girma ko ƙaramin na'urar ƙara girma yana aiki don faɗaɗa kusurwar da ke tsakanin ido da abin. Ikon gilashin ƙara girma na faɗaɗa hoton abu yana bayyana ta hanyar kusurwar ƙara girma (M) na gilashin ƙara girmaGilashin ƙara girman fuska mai girman fuska 2x tabbas ya fi gilashin ƙara girman fuska mai girman fuska 1x. Ƙara girman fuska ya bambanta da ƙara girman fuska mai layi; don fahimtar bambancin, da fatan za a yi nazarin batun. Ƙara girman kusurwa (M) da ƙara girman layi (m).
Fahimtar Girman Kusurwar Girman Girma
Girman kusurwa (M) na gilashin ƙara girma shine rabon kusurwar da ke tsakanin ido da hoton abin (θ') lokacin da aka kalli abin ta gilashin ƙara girma, zuwa kusurwar da ke tsakanin ido da abin (θ) lokacin da aka kalli abin kai tsaye daga inda idon yake a zahiri. A lissafi:
M = θ' / θ
Tsarin Gabaɗaya don Girman Kusurwar Girma
An yi cikakken bayani game da dabarar girman kusurwa a sashe mai zuwa. Domin taimaka muku fahimta, duba hoton da ke ƙasa.
A cikin hoto na 1, ana kallon abin kai tsaye daga inda idon yake..
N = kusa da wurin ido na yau da kullun
θ = kusurwa tsakanin ido da ƙarshen abu biyu
h = tsayin abin.
A hoto na 2, an ga abin ta gilashin ƙara girma..
s = tazara tsakanin abu da ruwan tabarau
θ' = kusurwa tsakanin madauki da ƙarshen abu biyu
h = tsayin abu
Idan kusurwar ƙarama ce to tangent θ ≈ θ
θ = h / N
θ' = h / s
Tsarin gaba ɗaya don ƙara girman kusurwa (M) na gilashin ƙara girman girma:
Bayani: M = girman kusurwa, N = kusa da wurin ido na yau da kullun, s = nisa tsakanin abu da gilashin ƙara girma. Wannan shine dabarar gabaɗaya don ƙara girma kusurwar gilashin ƙara girma. Ana kiranta dabarar gabaɗaya saboda nisan da ke tsakanin abu da gilashin ƙara girma (s) ba takamaiman ƙima bane amma yana iya zama kowace ƙima.
Tsarin ƙara girman gilashin ƙara girma idan ido ya fi dacewa da shi
Idan, lokacin kallon abu ta amfani da gilashin ƙara girma, idon mai kallo ya fi dacewa da shi fa? Idan idon ya fi dacewa da shi, nisan hoton ba shi da iyaka. Domin hoton ya yi nisa sosai, nisan da ke tsakanin abu da gilashin ƙara girma dole ne ya kasance iri ɗaya da tsawon gilashin ƙara girma (kwatanta bayanin da ke cikin batun). gilashin ƙara girma ko loupe). Ka lura da hoton da ke ƙasa.
A cikin hoto na 3, ana kallon abin kai tsaye daga inda idon yake..
N = kusa da wurin ido na yau da kullun
θ = kusurwa tsakanin ido da ƙarshen abu biyu
h = tsayin abin.
A cikin hoto na 4, an kalli abin ta hanyar gilashin ƙara girma inda idon mai kallo yake da ƙarancin dacewa..
s = nisan da ke tsakanin abu da ruwan tabarau = f = tsawon gilashin ƙara girma
θ' = kusurwa tsakanin madauki da ƙarshen abu biyu
h = tsayin abu
Idan kusurwar ƙarama ce to tangent θ ≈ θ
Tsarin ƙara girman kusurwa (M) na gilashin ƙara girman idan ido ya fi dacewa da shi:
Bayani: M = girman kusurwa, N = kusa da wurin ido na yau da kullun, f = tsawon mai da hankali na gilashin ƙara girma.
Wannan lissafi ya nuna cewa girman kusurwa (M) na gilashin ƙara girma yana daidai da tsayin haske (f) na gilashin ƙara girma. Girman tsayin haske na gilashin ƙara girma, ƙaramin girman kusurwa. Akasin haka, ƙaramin tsawon haske na gilashin ƙara girma, girman girman kusurwa. Gilashin ƙara girma ainihin ruwan tabarau ne mai lanƙwasa, saboda haka ya fi kyau a yi amfani da ruwan tabarau mai lanƙwasa mai ƙaramin tsayin haske ko ruwan tabarau mai lanƙwasa mai ƙaramin radius na lanƙwasa don girman kusurwar gilashin ƙara girma ya yi girma.
Tsarin ƙara girman gilashin ƙara girma lokacin da ido yake a matsakaicin matsayi
Idan, lokacin kallon abu ta amfani da gilashin ƙara girman hoto, idon mai kallo ya fi dacewa da shi fa? Idan idon ya fi dacewa da shi, nisan hoton da gilashin ƙara girman hoto ya samar iri ɗaya ne da kusancin ido na yau da kullun. Hoton yana kama da na kama-da-wane, don haka nisan hoton (s') mara kyau ne.
Idan nisan hoton (s') yayi daidai da kusancin ido na al'ada (N) to nisan abu (s):
Idan kusurwar ƙarama ce to tangent θ ≈ θ
Tsarin ƙara girman kusurwa (M) na gilashin ƙara girman idan ido yana da matsakaicin daidaito:
Bayani: M = girman kusurwa, N = kusa da wurin ido na yau da kullun, f = tsawon mai da hankali na gilashin ƙara girma.
Bandingkan dabarar ƙara girman kusurwar gilashin girma lokacin da idon yake a mafi ƙarancin wurin zama dengan dabarar ƙara girman kusurwar gilashin girma lokacin da idon yake a matsakaicin wurin zamaDangane da waɗannan dabarun guda biyu, za a iya kammala da cewa kusurwar ƙara girman gilashin ƙara girma ta fi girma idan idon yana cikin matsakaicin daidaito. Don haka, idan ka lura da ƙaramin rubutu ta amfani da gilashin ƙara girma, rubutun zai bayyana mafi girma lokacin da idon yake a matsakaicin daidaito.
