Kureba kweFocal uye Radius yeCurvature yeFomula yeLens
Mu optics, lenzi chishandiso chinoshandiswa kudzoreredza chiedza uye kugadzira mifananidzo. Ma lenzi anouya mumhando dzakasiyana-siyana uye saizi, asi kazhinji, anogona kukamurwa kuita mhando mbiri huru: ma lenzi ane convex uye ma lenzi ane concave. Kunzwisisa mashandiro anoita ma lenzi kwakakosha mumhando dzakasiyana-siyana dzekushandiswa, kubva kumagirazi emaziso kusvika kuma telescope nema microscope. Chimwe chinhu chakakosha pakunzwisisa ma lenzi ndehurefu hwawo hwe focal uye radius yekukombama. Chinyorwa chino chichakurukura mafomura akakosha ane chekuita nehurefu hwe focal uye radius yekukombama, pamwe nekushandiswa kwawo muhupenyu hwezuva nezuva.
Kunzwisisa Kureba kweFocal uye Radius yeCurvature
Kureba kwefocal idaro riri pakati penzvimbo ye optical yelens nefocal point, inova ndiyo nzvimbo iyo mwaranzi inofanana ne principal axis yelens inosangana mushure mekupfuura nepa lens. Kureba kwefocal kunowanzo fananidzirwa nebhii **f**.
Radius of Curvature iradius yebhora rekufungidzira rine pamusoro paro rinoenderana nepamusoro pe lenzi. Lenzi yega yega ine nzvimbo mbiri dzakakombama, saka kune nzvimbo mbiri dzakakombama dzinobatanidzwa, idzo dzinowanzo ratidzwa naR1 naR2 kune nzvimbo yekutanga neyechipiri.
Fomura yeKureba kweLenzi Yakatetepa
Fomura huru inobatanidza urefu hwefocal ne radius yekukombama mu lens tete inopiwa neThin Lens Equation kana kuti Lens Maker's Formula:
\[ \frac{1}{f} = (n – 1) \left( \frac{1}{R1} – \frac{1}{R2} \right) \]
Di mana:
- f ndiyo kureba kwelenzi
- n ndiyo indekisi yekutarisa refractive yezvinhu zve lenzi
- R1 ndiyo dhayamita yekukombama kwenzvimbo yekutanga yelenzi
- R2 ndiyo nharaunda yekukombama kwenzvimbo dzemalenzi ese ari maviri
Magirazi eConvex neConcave
Kune lenzi ine convex, pamusoro pe lenzi pane convex kunze, saka R1 iri positive uye R2 iri negative. Kusiyana neizvi, kune lenzi ine concave, pamusoro pe lenzi pane convex mukati, saka R1 iri negative uye R2 iri positive. Izvi zvakakosha pakuona chiratidzo che radius yekukombama pakushandisa fomura iri pamusoro.
Kutorwa kweFocal Length Formula
Equation ye lenzi diki inobva pamisimboti yekutanga ye geometric optics uye mutemo waSnell we refraction. Kutorwa kwayo kunosanganisira matanho akati wandei:
1. Kushandisa Mutemo waSnell:
Mutemo waSnell unoti \( n1 \sin(\theta1) = n2 \sin(\theta2) \), apo \( n1 \) uye \( n2 \) zviri zviratidzo zve refractive zve media mbiri dzakasiyana, uye \( \theta1 \) uye \( \theta2 \) ari ma angles e incidence ne refraction.
2. Kuongorora kweRay pamusoro pePokutanga:
Pakutangira kwelenzi ine radius of curvature R1, tinoshandisa mutemo waSnell kuti tiverenge refraction yechiedza chiri pamusoro payo.
3. Kuongorora kweRay pamusoro peChikamu Chechipiri:
Mushure mekunge mwaranzi yapfuura nepanzvimbo yekutanga, ichadzoserwa zvakare nepanzvimbo yechipiri ine radius yekukombama yeR2.
4. Kubatanidza Kubviswa kweNzvimbo Dzese:
Nekubatanidza mhedzisiro ye refractive yenzvimbo dzese mbiri uye kushandisa small angle approximation (apo sin(θ) ≈ θ), tinogona kugadzira equation inobatanidza focal length ne radii yekukombama kwenzvimbo mbiri dze lens.
Maitiro Anoshanda
Kureba kwefocal uye radius yekukombama kwelenzi zvinoita basa rakakosha mumabasa akasiyana-siyana anoshanda:
1. Magirazi:
Magirazi emaziso anoshandisa magirazi akakombama kana kuti akakombama kuti agadzirise kuona. Magirazi akakombama anoshandiswa pakuona zvakanyanya (hyperopia), nepo magirazi akakombama anoshandiswa pakuona kure (myopia). Kureba kwegirazi kunofanirwa kugadziriswa kuti kuenderane nezvinodiwa nemunhu kuti agadzirise kuona.
2. Kamera:
Magirazi ekamera akagadzirwa nehukuru hwakasiyana-siyana hwekuona kuti angle yekuona uye kukura kwacho ndeyei. Lenzi pfupi ine urefu hwakafara (yakafara) inofukidza nzvimbo yakakura yekuona, nepo lenzi refu rine urefu hwekuona (telephoto) rinopa kukura kukuru.
3. Maikorosikopu neTeresikopu:
Maikorosikopu anoshandisa magirazi ane urefu hupfupi hwefocal kuti akudze zvinhu zvidiki, nepo materesikopu achishandisa magirazi ane urefu hurefu hwefocal kuti aone zvinhu zviri kure zvakaita senyeredzi nemapuraneti.
4. Purojekita:
Mapurojekita anoshandisa malenzi kuti aise mifananidzo pachiratidziro. Hurefu hwemalenzi epurojekita hunofanira kugadziriswa kuti pave nemifananidzo yakajeka uye yakajeka.
Muenzaniso wezvinetso
Kuti tinzwisise kushandiswa kwefocal length formula, ngatitarisei muenzaniso unotevera:
Mubvunzo:
Lenzi ine denderedzwa regirazi ine refractive index ye1,5 ine radius yekukombama ye10 cm pamusoro wayo wekutanga uye -15 cm pamusoro wayo wechipiri. Verenga urefu hwefocal renzi.
Mhinduro:
Kushandisa fomura ye lenzi yakatetepa:
\[ \frac{1}{f} = (n – 1) \left( \frac{1}{R1} – \frac{1}{R2} \right) \]
Zvinozivikanwa:
– n = 1,5
– R1 = 10 cm
– R2 = -15 cm
Tsiva tsika idzi mufomura:
\[ \frac{1}{f} = (1,5 – 1) \left( \frac{1}{10} – \frac{1}{-15} \right) \]
\[ \frac{1}{f} = 0,5 \kuruboshwe( \frac{1}{10} + \frac{1}{15} \kurudyi) \]
\[ \frac{1}{f} = 0,5 \kuruboshwe( \frac{15 + 10}{150} \kurudyi) \]
\[ \frac{1}{f} = 0,5 \nguva \frac{25}{150} \]
\[ \frac{1}{f} = 0,5 \nguva \frac{1}{6} \]
\[ \frac{1}{f} = \frac{1}{12} \]
Saka, kureba kwefocal f ndeye 12 cm.
Mhedziso
Kureba kwefocal uye radius yekukombama pfungwa dzakakosha pakunzwisisa mashandiro anoita malenzi. Fomura yelenzi yakatetepa inopa nzira yekuverenga urefu hwefocal zvichibva paradius yekukombama uye refractive index yezvinhu zvelenzi. Kunzwisisa fomura iyi hakungokoshi chete mufizikisi asiwo kune mashandisirwo anoshanda mumatekinoroji akasiyana-siyana e optical atinoshandisa zuva nezuva. Kubva kumagirazi emaziso kusvika kumakamera, maikorosikopu, uye materesikopu, misimboti iyi ye optical inotibatsira kuona nyika nekujeka uye zvakadzama.
