Cov mis rau qhov ntxoov ntxoo ntawm ib yam khoom los ntawm daim iav convex spherical
Pengantar
Daim iav puag ncig convex yog daim iav uas nws qhov chaw nkhaus tawm sab nraud, zoo li sab nraud ntawm lub pob. Hom iav no muaj ntau yam kev siv txhua hnub, xws li hauv daim iav saib tom qab tsheb thiab daim iav kev ruaj ntseg hauv khw. Hauv tsab xov xwm no, peb yuav tham txog yuav ua li cas daim iav puag ncig convex ua haujlwm, cov mis siv los txiav txim siab daim duab ntawm ib yam khoom uas tsim los ntawm daim iav no, thiab qee qhov piv txwv ntawm kev xam thiab kev siv ua haujlwm.
Cov Ntsiab Cai Tseem Ceeb ntawm Cov Iav Convex Spherical
Ib daim iav puag ncig uas zoo li lub voj voog muaj tus yam ntxwv ntawm kev cuam tshuam lub teeb ci ntsa iab rau ntawm nws qhov chaw sib txawv. Qhov no txhais tau tias cov teeb ci ntsa iab los ntawm daim iav no yuav nthuav tawm mus rau sab nraud. Txawm li cas los xij, yog tias peb nthuav cov teeb ci ntsa iab rov qab, lawv yuav zoo li lawv pib los ntawm ib qho chaw hu ua qhov chaw tsom kwm (F) tom qab daim iav. Qhov chaw tsom kwm no yog qhov chaw uas cov teeb ci ntsa iab los zoo li sib sau ua ke tom qab raug cuam tshuam los ntawm daim iav.
Cov yam ntxwv ntawm daim duab tsim los ntawm daim iav convex:
1. Duab virtual: Daim duab no yog tsim tom qab daim iav thiab tsis tuaj yeem thaij tau ntawm qhov screen.
2. Duab ncaj: Daim duab uas tshwm sim tseem ncaj zoo li cov khoom qub.
3. Duab txo qis: Qhov loj ntawm daim duab me dua qhov loj tiag tiag ntawm yam khoom.
Cov Qauv Iav Convex
Cov mis tseem ceeb siv los tshuaj xyuas cov duab los ntawm daim iav convex spherical yog daim iav mis, uas tau hais tias:
\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]
Qhov twg:
-\( f\) yog qhov ntev ntawm daim iav (tsis zoo rau daim iav convex).
- \( d_o \) yog qhov deb ntawm yam khoom ntawm daim iav (zoo yog tias yam khoom nyob rau pem hauv ntej ntawm daim iav).
- \( d_i \) yog qhov deb ntawm daim duab ntawm daim iav (tsis zoo rau daim iav convex vim tias daim duab tau tsim tom qab daim iav).
Tsis tas li ntawd xwb, peb kuj siv cov mis magnification uas tau hais tias yog:
\[ M = – \frac{d_i}{d_o} = \frac{h_i}{h_o} \]
Qhov twg:
- \( M \) yog qhov loj ntawm daim duab (tsis zoo rau daim duab ncaj).
- \( h_i \) yog qhov siab ntawm daim duab.
- \( h_o \) yog qhov siab ntawm qhov khoom.
Piv txwv kev xam
Cia peb saib qee qhov piv txwv kev xam kom nkag siab yuav ua li cas siv cov mis iav convex hauv kev xyaum.
Piv txwv 1: Txheeb xyuas qhov nrug ntawm duab ntxoov ntxoo
Xav tias peb muaj ib yam khoom tso rau 30 cm ntawm pem hauv ntej ntawm daim iav convex nrog qhov ntev focal ntawm -20 cm. Peb xav txiav txim siab qhov deb ntawm daim duab ntawm daim iav.
Siv cov qauv iav:
\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]
\[ \frac{1}{-20} = \frac{1}{30} + \frac{1}{d_i} \]
Cov kauj ruam xam:
1. Xam \( \frac{1}{30} \):
\[ \frac{1}{30} \approx 0.0333 \]
2. Hloov cov nqi no rau hauv cov mis:
\[ \frac{1}{-20} = 0.0333 + \frac{1}{d_i} \]
3. Kev Cais Tawm \( \frac{1}{d_i} \):
\[ \frac{1}{d_i} = \frac{1}{-20} – 0.0333 \]
\[ \frac{1}{d_i} \approx -0.05 – 0.0333 \]
\[ \frac{1}{d_i} \approx -0.0833 \]
4. Nrhiav \( d_i \):
\[ d_i \approx \frac{1}{-0.0833} \]
\[ d_i \approx -12 \, \text{cm} \]
Yog li, daim duab yog tsim 12 cm tom qab daim iav (qhov tsis zoo qhia tias daim duab nyob tom qab daim iav).
Piv txwv 2: Txheeb xyuas qhov siab ntawm duab ntxoov ntxoo
Yog tias qhov siab ntawm yam khoom (\(h_o \)) yog 10 cm thiab peb twb paub qhov deb ntawm daim duab (\(d_i \)) yog -12 cm los ntawm qhov piv txwv dhau los, peb tuaj yeem txiav txim siab qhov siab ntawm daim duab siv cov mis magnification.
Siv cov mis loj dua:
\[ M = – \frac{d_i}{d_o} = \frac{h_i}{h_o} \]
\[ M = – \frac{-12}{30} \]
\[ M = 0.4 \]
Yog li, qhov loj dua yog 0.4. Tom ntej no, peb xam qhov siab ntawm daim duab:
\[ \frac{h_i}{h_o} = 0.4 \]
\[ h_i = 0.4 \times 10 \]
\[ h_i = 4 \, \text{cm} \]
Qhov siab ntawm tus duab ntxoov ntxoo yog 4 cm, me dua qhov siab ntawm yam khoom thiab ncaj.
Daim Ntawv Thov Iav Convex
Cov iav convex muaj ntau yam kev siv vim lawv cov yam ntxwv tshwj xeeb uas ua rau lawv muaj txiaj ntsig zoo rau ntau yam xwm txheej:
1. Daim Iav Saib Tom Qab Tsheb
Cov iav convex siv rau hauv cov iav saib tom qab ntawm lub tsheb kom pom tau dav dua ntawm thaj chaw tom qab thiab rau sab ntawm lub tsheb. Qhov no pab cov neeg tsav tsheb pom ntau yam ntawm lawv ib puag ncig, txo cov chaw dig muag, thiab txhim kho kev nyab xeeb ntawm kev tsav tsheb.
2. Daim Iav Saib Xyuas
Hauv cov khw muag khoom thiab cov chaw pej xeem, cov iav convex feem ntau siv ua cov iav saib xyuas kom nthuav dav qhov pom. Qhov no pab txhawb kev saib xyuas thiab tiv thaiv kev tub sab los ntawm kev muab kev pom dav dav ntawm thaj chaw dav.
3. Periscope
Cov periscopes siv rau hauv cov nkoj hauv qab dej thiab qee cov cuab yeej siv kho qhov muag feem ntau siv cov iav convex los nthuav qhov pom ntawm tus neeg siv thiab tso cai rau lawv pom cov khoom dhau ntawm qhov pom ncaj qha.
4. Cov Cuab Yeej Siv Kho Qhov Muag
Qee cov cuab yeej siv kho qhov muag xws li telescopes thiab microscopes siv cov iav convex hauv lawv cov kab ke los kho thiab ua kom daim duab ntawm ib yam khoom loj dua.
Xaus
Cov iav puag ncig convex yog cov cuab yeej tseem ceeb rau kev pom kev nrog ntau yam kev siv. Kev nkag siab txog cov qauv yooj yim siv los txiav txim siab cov duab tsim los ntawm cov iav no yog qhov tseem ceeb hauv ntau qhov chaw, txij li kev tsim tsheb mus rau kev saib xyuas kev ruaj ntseg. Siv cov qauv iav thiab kev ua kom loj dua, peb tuaj yeem txiav txim siab qhov chaw, qhov loj me, thiab qhov xwm txheej ntawm cov duab tsim los ntawm daim iav convex. Cov yam ntxwv tshwj xeeb ntawm cov iav no, xws li lawv lub peev xwm los muab qhov chaw dav dav thiab cov duab tsa, txo qis, ua rau lawv muaj txiaj ntsig zoo heev hauv ntau yam kev siv txhua hnub.
