Focal Length thiab Radius ntawm Curvature ntawm Lub Lens Formula
Hauv kev kho qhov muag, lub lens yog ib lub cuab yeej siv los ua kom lub teeb ci thiab tsim cov duab. Cov lens muaj ntau yam duab thiab qhov loj me, tab sis feem ntau, lawv tuaj yeem muab faib ua ob hom tseem ceeb: convex lens thiab concave lens. Kev nkag siab txog kev ua haujlwm ntawm cov lens yog qhov tseem ceeb hauv ntau yam kev siv, los ntawm cov tsom iav mus rau telescopes thiab microscopes. Ib qho tseem ceeb ntawm kev nkag siab txog cov lens yog lawv qhov ntev focal thiab radius ntawm curvature. Tsab xov xwm no yuav tham txog cov qauv tseem ceeb ntsig txog qhov ntev focal thiab radius ntawm curvature, nrog rau lawv cov ntawv thov hauv lub neej txhua hnub.
Nkag Siab Txog Qhov Ntev Ntawm Qhov Muag Thiab Radius Ntawm Qhov nkhaus
Qhov ntev ntawm lub lens yog qhov deb ntawm qhov chaw nruab nrab ntawm lub lens thiab qhov chaw nruab nrab, uas yog qhov chaw uas cov teeb ci sib luag rau lub axis tseem ceeb ntawm lub lens sib sau ua ke tom qab dhau los ntawm lub lens. Qhov ntev ntawm lub lens feem ntau yog cim los ntawm tsab ntawv **f**.
Lub Radius of Curvature yog lub radius ntawm lub voos xwmfab uas nws qhov chaw sib xws rau qhov chaw ntawm lub lens. Txhua lub lens muaj ob qhov chaw nkhaus, yog li muaj ob lub radii ntawm curvature koom nrog, uas feem ntau yog cim los ntawm R1 thiab R2 rau thawj thiab thib ob qhov chaw.
Cov Qauv Ntsuas Ntev Focal Lens Nyias
Cov mis tseem ceeb uas cuam tshuam txog qhov ntev ntawm lub lens rau lub vojvoog ntawm qhov nkhaus hauv lub lens nyias yog muab los ntawm Thin Lens Equation lossis Lens Maker's Formula:
\[ \frac{1}{f} = (n – 1) \left( \frac{1}{R1} – \frac{1}{R2} \right) \]
Qhov twg:
- f yog qhov ntev ntawm lub lens
-n yog qhov ntsuas refractive ntawm cov khoom siv lens
- R1 yog lub vojvoog ntawm qhov nkhaus ntawm qhov chaw thawj zaug ntawm lub lens
- R2 yog lub vojvoog ntawm qhov nkhaus ntawm ob qho chaw ntawm lub lens
Cov Lens Convex thiab Concave
Rau lub lens convex, qhov chaw ntawm lub lens yog convex sab nraud, yog li R1 yog qhov zoo thiab R2 yog qhov tsis zoo. Ntawm qhov tod tes, rau lub lens concave, qhov chaw ntawm lub lens yog concave sab hauv, yog li R1 yog qhov tsis zoo thiab R2 yog qhov zoo. Qhov no yog qhov tseem ceeb hauv kev txiav txim siab lub cim ntawm lub vojvoog ntawm curvature thaum siv cov mis saum toj no.
Kev txiav txim siab ntawm Focal Length Formula
Tus qauv ntawm lub lens nyias yog los ntawm cov ntsiab cai yooj yim ntawm geometric optics thiab Snell txoj cai ntawm refraction. Nws cov derivation muaj ntau kauj ruam:
1. Siv Txoj Cai Snell:
Txoj cai Snell hais tias n1 sin(\theta1) = n2 sin(\theta2)), qhov twg n1 thiab n2 yog cov ntsuas refractive ntawm ob lub xov xwm sib txawv, thiab n1 thiab n2 yog cov ces kaum ntawm qhov tshwm sim thiab refraction.
2. Kev Tshawb Fawb Txog Ray Ntawm Qhov Chaw Thawj Zaug:
Rau thawj qhov chaw ntawm lub lens nrog lub vojvoog ntawm curvature R1, peb siv Snell txoj cai los xam qhov refraction ntawm lub teeb tshwm sim rau ntawm qhov chaw ntawd.
3. Kev Tshawb Fawb Txog Ray Ntawm Qhov Chaw Thib Ob:
Tom qab lub teeb ci dhau los ntawm qhov chaw thib ib, nws yuav raug refracted dua los ntawm qhov chaw thib ob nrog lub vojvoog ntawm curvature ntawm R2.
4. Kev Sib Txuas Ua Ke ntawm Ob Qhov Chaw:
Los ntawm kev sib txuas cov teebmeem refractive ntawm ob qho chaw thiab siv qhov kev kwv yees lub kaum sab xis me me (qhov twg sin (θ) ≈ θ), peb tuaj yeem tsim ib qho kab zauv uas cuam tshuam qhov ntev ntawm lub lens rau lub radii ntawm curvature ntawm ob lub lens nto.
Cov Kev Siv Tau Zoo
Qhov ntev ntawm lub lens thiab lub vojvoog ntawm qhov nkhaus ua lub luag haujlwm tseem ceeb hauv ntau yam kev siv:
1. Cov tsom iav:
Cov tsom iav siv cov iav concave lossis convex los kho qhov muag. Cov iav convex siv rau hyperopia (kev pom tsis meej ze), thaum cov iav concave siv rau myopia (kev pom tsis meej deb). Qhov ntev ntawm lub lens yuav tsum tau kho kom haum rau tus neeg qhov kev xav tau kho qhov muag.
2. Lub Koob Yees Duab:
Cov iav tsom iav tau tsim los nrog cov qhov ntev focal tshwj xeeb los txiav txim siab lub kaum sab xis ntawm qhov pom thiab qhov loj dua. Lub lens luv focal ntev (wide-angle) npog thaj chaw pom dav dua, thaum lub lens ntev focal ntev (telephoto) muab qhov loj dua.
3. Lub Tshuab Microscope thiab Lub Tshuab Telescope:
Cov tshuab microscopes siv cov lens uas muaj qhov ntev focal luv luv los ua kom cov khoom me me loj dua, thaum cov telescopes siv cov lens uas muaj qhov ntev focal ntev los saib cov khoom nyob deb xws li cov hnub qub thiab cov ntiaj teb.
4. Lub tshuab ua kom pom kev:
Cov projectors siv cov lens los tsom cov duab rau ntawm lub vijtsam. Qhov ntev ntawm lub lens projector yuav tsum tau kho kom ntseeg tau tias cov duab ntse thiab meej.
Piv txwv txog teeb meem
Yuav kom nkag siab meej txog kev siv cov mis focal length, cia peb saib cov piv txwv hauv qab no:
Lo lus nug:
Ib lub lens convex uas muaj refractive index ntawm 1,5 muaj lub vojvoog ntawm curvature ntawm 10 cm ntawm nws qhov chaw thawj zaug thiab -15 cm ntawm nws qhov chaw thib ob. Xam qhov ntev ntawm lub lens.
Kev daws teeb meem:
Siv cov qauv lens nyias:
\[ \frac{1}{f} = (n – 1) \left( \frac{1}{R1} – \frac{1}{R2} \right) \]
Nws paub tias:
– n = 1,5
– R1 = 10 cm
– R2 = -15 cm
Hloov cov nqi no rau hauv cov mis:
\[ \frac{1}{f} = (1,5 – 1) \left( \frac{1}{10} – \frac{1}{-15} \right) \]
\[ \frac{1}{f} = 0,5 \left( \frac{1}{10} + \frac{1}{15} \right) \]
\[ \frac{1}{f} = 0,5 \left( \frac{15 + 10}{150} \right) \]
\[ \frac{1}{f} = 0,5 \times \frac{25}{150} \]
\[ \frac{1}{f} = 0,5 \times \frac{1}{6} \]
\[ \frac{1}{f} = \frac{1}{12} \]
Yog li, qhov ntev f yog 12 cm.
Xaus
Qhov ntev ntawm qhov muag thiab qhov vojvoog ntawm qhov nkhaus yog cov tswv yim tseem ceeb hauv kev nkag siab txog seb cov tsom iav ua haujlwm li cas. Cov mis lens nyias muab txoj hauv kev los xam qhov ntev ntawm qhov muag raws li qhov vojvoog ntawm qhov nkhaus thiab qhov ntsuas refractive ntawm cov khoom siv lens. Kev nkag siab txog cov mis no tsis yog tsuas yog tseem ceeb hauv physics xwb tab sis kuj muaj kev siv tau zoo hauv ntau yam thev naus laus zis kho qhov muag uas peb siv txhua hnub. Txij li tsom iav mus rau lub koob yees duab, lub tshuab microscopes, thiab lub tshuab telescopes, cov ntsiab cai kho qhov muag no pab peb pom lub ntiaj teb nrog kev meej thiab meej dua.
