Tsarin inuwar abu ta hanyar madubi mai siffar zagaye mai lanƙwasa
Pengantar
Madubin zagaye mai lanƙwasa madubi ne wanda samansa ke lanƙwasawa waje, kamar wajen wani yanki. Wannan nau'in madubin yana da nau'ikan aikace-aikacen yau da kullun, kamar a cikin madubin baya na mota da madubin tsaro a shaguna. A cikin wannan labarin, za mu tattauna yadda madubin zagaye mai lanƙwasa yake aiki, dabarar da ake amfani da ita don tantance hoton wani abu da wannan madubin ya samar, da kuma wasu misalan lissafi da aikace-aikacen aiki.
Ka'idojin Asali na Madubin Siffa Mai Lanƙwasa
Madubin zagaye mai lanƙwasa yana da halayyar nuna hasken da ke faruwa a samansa ta hanyoyi daban-daban. Wannan yana nufin cewa hasken da ke fitowa daga wannan madubin zai bazu zuwa waje. Duk da haka, idan muka miƙe hasken da ke fitowa a baya, za su bayyana kamar sun fito ne daga wani wuri guda da ake kira wurin mai da hankali (F) a bayan madubin. Wannan wurin mai da hankali shine wurin da hasken da ke shigowa ya bayyana yana taruwa bayan madubin ya nuna shi.
Halayen hoton da madubi mai lanƙwasa ya samar:
1. Hoton kama-da-wane: An ƙirƙiri hoton a bayan madubi kuma ba za a iya ɗaukarsa a allon ba.
2. Hoton da ya tsaya cak: Hoton da ya fito ya tsaya cak kamar abin da aka samo asali.
3. Hoton da aka rage: Girman hoton ya fi ƙanƙanta da ainihin girman abin.
Tsarin Madubin Convex
Babban dabarar da ake amfani da ita don nazarin hoton ta hanyar madubin zagaye mai siffar ƙwallo mai lanƙwasa ita ce dabarar madubin, wadda aka bayyana kamar haka:
\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]
Ina:
– \( f \) shine tsawon madubin da ke da ma'ana (mara kyau ga madubin da ke da ma'ana).
– \( d_o \) shine nisan abin daga madubin (positive idan abin yana gaban madubin).
– \( d_i \) shine nisan hoton daga madubin (mara kyau ga madubin da ke da lanƙwasa saboda hoton an samar da shi ne a bayan madubin).
Bugu da ƙari, muna amfani da dabarar ƙara girman hoto wanda aka bayyana kamar haka:
\[ M = – \frac{d_i}{d_o} = \frac{h_i}{h_o} \]
Ina:
– \( M \) shine girman hoton (mara kyau ga hoto mai tsayi).
– \( h_i \) shine tsayin hoton.
– \( h_o \) shine tsayin abu.
Misalin Lissafi
Bari mu dubi wasu misalan lissafin don fahimtar yadda ake amfani da dabarar madubi mai lanƙwasa a aikace.
Misali na 1: Ƙayyade Nisa Tsakanin Inuwa
A ce mun sanya wani abu a kan wani madubi mai tsawon santimita 30 a gaban madubi mai lanƙwasa mai tsawon santimita -20. Muna son mu tantance nisan hoton daga madubin.
Amfani da tsarin madubi:
\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]
\[ \frac{1}{-20} = \frac{1}{30} + \frac{1}{d_i} \]
Matakan lissafi:
1. Lissafi \( \frac{1}{30} \):
\[ \frac{1}{30} \kimanin 0.0333 \]
2. Sauya waɗannan dabi'u cikin dabarar:
\[ \frac{1}{-20} = 0.0333 + \frac{1}{d_i} \]
3. Warewa \( \frac{1}{d_i} \):
\[ \frac{1}{d_i} = \frac{1}{-20} – 0.0333 \]
\[ \frac{1}{d_i} \approx -0.05 – 0.0333 \]
\[ \frac{1}{d_i} \approx -0.0833 \]
4. Nemo \( d_i \):
\[ d_i \approx \frac{1}{-0.0833} \]
\[ d_i \approx -12 \, \text{cm} \]
Don haka, hoton ya samo asali ne daga santimita 12 a bayan madubin (mara kyau yana nuna cewa hoton yana bayan madubin).
Misali na 2: Ƙayyade Tsayin Inuwa
Idan tsayin abu (\( h_o \) ) ya kai 10 cm kuma mun riga mun san nisan hoton ( \( d_i \) ) ya kai -12 cm daga misalin da ya gabata, za mu iya tantance tsayin hoton ta amfani da dabarar ƙara girma.
Amfani da dabarar ƙara girman:
\[ M = – \frac{d_i}{d_o} = \frac{h_i}{h_o} \]
\[ M = – \frac{-12}{30} \]
\[ M = 0.4 \]
Don haka, girman hoton shine 0.4. Na gaba, zamu lissafa tsayin hoton:
\[ \frac{h_i}{h_o} = 0.4 \]
\[ h_i = 0.4 \sau 10 \]
\[ h_i = 4 \, \rubutu{cm} \]
Tsawon inuwar shine 4 cm, ƙasa da tsayin abin kuma a tsaye yake.
Aikace-aikacen Madubin Convex
Madubin Convex suna da amfani da yawa a aikace saboda keɓantattun halayensu waɗanda ke sa su zama masu amfani a yanayi daban-daban:
1. Madubin Bayan Mota
Ana amfani da madubai masu lanƙwasa a cikin madubai na baya na abin hawa don samar da faffadan ra'ayi na yankin da ke bayan motar da kuma gefen motar. Wannan yana taimaka wa direbobi su ga ƙarin abubuwan da ke kewaye da su, yana rage wuraren da ba su da makafi, da kuma inganta amincin tuƙi.
2. Madubin Kulawa
A shaguna da wuraren jama'a, galibi ana amfani da madubai masu lanƙwasa a matsayin madubai masu sa ido don faɗaɗa fagen gani. Wannan yana taimakawa wajen sa ido da hana sata ta hanyar samar da cikakken kallon yanki mai faɗi.
3. Periscope
Ana amfani da na'urorin periscopes a cikin jiragen ruwa na ƙarƙashin ruwa da wasu kayan aikin gani sau da yawa suna amfani da madubai masu lanƙwasa don faɗaɗa ra'ayin mai amfani da kuma ba su damar ganin abubuwa fiye da yadda ake gani kai tsaye.
4. Kayan Aiki na gani
Wasu kayan aikin gani kamar na'urorin hangen nesa da na'urorin hangen nesa suna amfani da madubai masu lanƙwasa a cikin tsarinsu don daidaitawa da haɓaka hoton wani abu.
Kammalawa
Madubin zagaye mai siffar convex suna da matuƙar muhimmanci wajen amfani da na'urorin gani, waɗanda ke da amfani iri-iri. Fahimtar dabarun da ake amfani da su don tantance hoton da waɗannan madubai ke samarwa yana da matuƙar muhimmanci a fannoni da dama, tun daga ƙirar abin hawa zuwa sa ido kan tsaro. Ta amfani da dabarar madubi da ƙara girmansa, za mu iya tantance matsayi, girma, da yanayin hoton da madubi mai siffar convex ke samarwa. Halaye na musamman na waɗannan madubai, kamar ikonsu na samar da faffadan fili na gani da kuma ɗaga hotuna masu raguwa, suna sa su zama masu matuƙar amfani a aikace-aikace iri-iri na yau da kullun.
