Sterrekunde

Vergelyking om afstand tussen objektief en okularis te vind

Vergelyking om afstand tussen objektief en okularis te vind


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Ek het 'n tuisgemaakte astronomiese teleskoop met 'n lens van 100 cm en 'n okular van 5 cm. As u 'n voorwerp in oneindigheid bekyk, is die afstand tussen okular en objektief 105 cm. Hoe kon ek dus afstand bereken tussen objektief en okularis vir en ver voorwerp? Byvoorbeeld, 'n planeet 1 AE vanaf die aarde, hoeveel moet die afstand tussen objektief en okulêr wees?


Astronomiese voorwerpe is so ver weg dat hulle dieselfde punt as 'n voorwerp op oneindige afstand fokus. In werklikheid kan enige voorwerp wat meer as honderd meter daarvandaan is, as 'n oneindige afstand beskou word.

Oorweeg die fokusafstandvergelyking om dit te kwantifiseer:

$ frac {1} {f} = frac {1} {d_o} + frac {1} {d_i} $

As die brandpuntafstand = 1m is, en die voorwerpafstand $ d_o $ = 1AU = $ 150 keer 10 ^ 9 $ m

Die beeldafstand ($ d_i $) sal 10000000000001 cm wees (minder as een atoom anders)


1 A.U. is dieselfde as oneindigheid. Die verskil ten opsigte van die oculair se posisie is oneindig klein, u kan dit nie meet nie. Enigiets verder as 'n paar kilometer verder is amper 'in die oneindigheid'.

Ongeag dit - uit die praktyk om teleskope te ontwerp en te bou, bied berekeninge u slegs 'n beginpunt. U doen wiskunde en die afstand is 105 cm. Maar in die praktyk sal lense afwyk van die ideale brandpuntsafstand. Selfs as hulle nie op 'n sekere temperatuur afwyk nie, plaas dit in 'n koue omgewing, en die brandpuntsafstand sal 'n fraksie van mm verander.

Neem die berekeninge as vertrekpunt en bou die instrument sodanig dat die posisie van die okulêr fyn verstel kan word. Daar is 'n toestel genaamd focuser wat sulke fyn aanpassings moontlik maak. Of vertrou eenvoudig op wrywing om die okulêr heen en weer te beweeg totdat die beeld die beste lyk, en hou dit daar.

As u die instrument in die praktyk gebruik, vergeet u die ideale afstand. Wat u sal doen, is om die posisie van die okulêr aan te pas totdat die beeld die beste lyk. U sal dit doen elke keer as u waarneem, en dikwels verskeie kere tydens dieselfde waarneming.


As u wiskunde wil hê, kyk na die dun lensvergelyking en pas dit op die objektiewe lens toe.

f = brandpuntlengte van die lens

o = afstand van lens tot voorwerp

i = afstand van lens tot beeld

Dan is die dun lensvergelyking:

1 / f = 1 / i + 1 / o i = 1 / (1 / f - 1 / o)

As o = oneindigheid, dan is i = f.

Maar wat gebeur as o = 1 A.U.?

i = 1 / (1/1 - 1 / (1,5 * 10 ^ 11)) = 1,0000000000067 meter

Die verskil is ongeveer 6,7 * 10 ^ -12 meter. Dit is kleiner as 'n atoom.


Oogstukprojeksie met c-monteerlens

Oogstukprojeksie met die ENVIS-objektieflens is uiteraard 'n baie gewilde manier om nagvisie-sterrekunde te doen.

Ek het 'n Mod-3C en wonder of dit die moeite werd is om 'n c-monteerlens met 'n ander brandpuntsafstand te gebruik. Soos ek dit verstaan, kan u die effektiewe brandpuntvermindering van die ENVIS / oculairkombinasie bereken deur die ENVIS-brandpuntsafstand (27mm) te deel deur die oogpunt se fokuspunt. Vir die Tele Vue 55mm plossl-projeksiestelsel sou dit ongeveer 27/55 = 0,49x wees, wat die f-verhouding van die OTA basies verminder met 2. Met die 67mm-kit word die effektiewe f-verhouding nog verder verminder.

Maar wat sou gebeur as u 'n k-lens met korter brandpuntlengte gebruik in plaas van die ENVIS-doelwit? Iets soos hierdie 12mm Tamron-lens:

Sal u uiteindelik die effektiewe f-verhouding met 12/55 = 0,21x verminder? En wat is die impak van die 27 mm Mod 3-oogstuk op dit alles?

# 2 a__l

Ek dink daar sal probleme met vignettering en afstand tussen NV-lens en okularis wees. Miskien is Eye Relief vir TV55 (38mm) genoeg, miskien nie. U moet seker maak.
Ek gebruik tans 'n Zeiss Tevidon 24mm f / 1.4 met die TV67 en het effense vignettering. Met TV 55 is dit beter, maar meer afwykings. Ek het sopas 'n Nikkor 24mm (F bajonet) f / 2 gekoop en sal daarmee eksperimenteer.

# 3 a__l

Zeiss is 'n goeie lens, miskien selfs beter as Envis, maar moet dit langs mekaar kyk.
Ek hou ook van Nikkor, maar tot dusver het ek meer fokuslengtes.

Geredigeer deur a__l, 21 Maart 2021 - 21:02.

# 4 Bottervlieg

Oogstukprojeksie met die ENVIS-lens is uiteraard 'n baie gewilde manier om nagvisie-sterrekunde te doen.

Nee. Dit lyk miskien wiskundig as 'n onderskeid, maar daar is 'n groot verskil in die regte wêreld. Hier is 'n uittreksel uit die televisie-beeldvormingsmetode-bladsy onder die afokaal afdeling:

'N Alternatiewe manier om die effektiewe brandpuntlengte te bepaal, beskou die kameralens en die okularis as 'n relais. Aan die hand van die voorbeeld hierbo gee die 50 mm-kameralens met die 10 mm-okularis 5x aflosvergroting. Die objektiewe brandpuntlengte van 5x600mm teleskoop lewer 'n fokuspunt van 3000mm.

Die praktiese verskil is dat 'n okular baie elemente het wat saamwerk om 'n goed gekorrigeerde veld te maak. Dieselfde met die doel van die NV-toestel. 'N Lukrake koppeling van 'n okular en 'n kameralens wat op 'n ewekansige plek 'n beeld vorm, lei gewoonlik tot baie klein bruikbare velde met vullis aan die rande, hoofsaaklik omdat die okulariteit gebruik word, afwesig met spesifikasies. Vullis in vullis buite, veral as dit verskerp word.

Selfs toe dit nog algemeen gebruik is, was die projeksie van die oculair hoofsaaklik gereserveer vir planete omdat dit klein is.


Sal u uiteindelik die effektiewe f-verhouding met 12/55 = 0,21x verminder? En wat is die impak van die 27mm Mod 3-oogstuk op dit alles?

Dink aan uittreepupil om u lewe baie makliker te maak. Elke lens wat u op u NV-toestel plaas, het 'n opening wat die toegangspupil genoem word. Die opening beperk die hoeveelheid uittreepupil wat dit kan hanteer. Wanneer die uitgangspupil ooreenstem met die toegangspupil, is die effektiewe f / verhouding van die hele stelsel die f / verhouding van die lens wat u op die NV-toestel plaas. Wanneer die uitgangspupilent kleiner is as die toegangspupil, gaan die effektiewe f / verhouding UP in dieselfde verhouding as die gebiede deursnee van die uitgangsleerling na die toegangsleerling.

As ek dus 'n 22 mm-uittreepupil kan hanteer, maar slegs 'n 11 mm-uittreepupilie lewer, gebruik ek 'n kwart van die beskikbare area. Die effektiewe f / verhouding van die stelsel is vier twee keer dié van die lens wat jy op die NV-toestel plaas.

Dit is alles relatief tot dusver. Om die werklike effektiewe f / verhouding te verkry, moet u weet wat die werklike f / verhouding is van die lens wat u op die NV-toestel plaas. As ons aanvaar dieselfde ingangspupil, dan is 'n 12 mm-brandpuntlengte 2,25 keer vinniger as 'n 27 mm-lens.

Die f / verhouding van 'n 22 mm toegangspupil met 'n brandpunt van 12 mm is f / 0,54.

As dit absurd klink, dan is dit. As u kyk na die spesifikasies van die lens waaraan u gekoppel het, het dit f / verhoudings tussen f / 1.4 en f / 16, as gevolg van die zoom. Die vinnigste werklike effektiewe f / verhouding van 'n stelsel met hierdie lens kan NOOIT onder f / 1.4 daal nie. As u probeer vinniger te gaan, pas die uitgangspupil net nie in die ingangspupil nie, en verminder u die effektiewe diafragma wat net genoeg is om die lens se f / verhouding te bereik.

Net soos by enige gewone okularis, is die vergroting van die NV-toestel nog steeds: omvang brandpunt / oogpunt brandpunt. Net soos by enige gewone okularis, styg die beeldskaal met 'n faktor van 2,25 (27/12) terwyl die totale lig met 2,25 ^ 2 verminder.


Vergelyking om afstand tussen objektief en okularis te vind - Sterrekunde

Lenskombinasies: teleskope

Die reëls vir straalsporing het 'n eenvoudige gevolg vir lenskombinasies: as twee lense een na die ander aangebring word, word die beeld wat deur die eerste lens gevorm word, die voorwerp vir die tweede lens. 'N Mens kan die dun lensvergelyking twee keer toepas om die beeld te vind wat gevorm word deur die stelsel van twee dun lense. Met elke toepassing moet u p en q vanaf die toepaslike lens meet en die f vir die lens gebruik. U moet ook die tekenkonvensies vir voorwerpposisie p en beeldposisie q onthou (teenoorgestelde!) HERSIEN die dun lensvergelyking, indien nodig. Kyk na u begrip van hierdie idees deur die volgende nuttige feite af te lei: twee lense op dieselfde plek - hoofsaaklik op mekaar - het 'n effektiewe brandpuntsafstand f wat gehoorsaam

[Let op, dit is NIE WAAR as die lense op verskillende plekke is nie!]

Een van die eenvoudigste en mees bruikbare lenskombinasies is die astronomiese teleskoop (hieronder). Die lens aan die linkerkant word die objektief genoem en die lens aan die regterkant word die okularis genoem (die lens waarmee u u oog sou opsit). Die voorwerp is oneindig, en die beeld is ook oneindig! Wat baat dit? wonder jy dalk. Kyk na die hoeke in die simulasie hieronder. Kies veral die "bron" heel links deur daarop te klik en sleep dan die strale om hul hoek te verander. U sal sien dat die teleskoop die hoeke vergroot - en as u nadink oor hoe ons sien, sal u besef dat dit is wat ons intuïtief met vergroting bedoel.

'N Ander manier om hieroor na te dink, is om 'n "oog" heel regs by te voeg om deur die teleskoop te kyk. Die oog is 'n derde lens en 'n "retina". Die voorwerp vir hierdie derde lens is die beeld wat deur die tweede lens gevorm word, dus as die beeld op oneindig is, sal dit mooi op die retina gerig wees (die ontspanne oog kan maklik beelde van dinge ver vorm). Kies weer die bron en sleep die strale om om te sien hoe die hoek in die retina posisioneer. Die oog sien die beeld van verre sterre as punte, en hul hoekskeiding word vergroot. As die oog na 'n vaste sterrebeeld van sterre kyk, sou die sterrebeeld deur die teleskoop omgekeer lyk of nie? Verduidelik noukeurig!

Hoe ver moet die twee lense van mekaar af wees om 'n teleskoop te maak? Vind qo en ble (in die notasie van die dun lensvergelyking) waar die subskripsies o en e onderskeidelik na die objektief en die okularis verwys. Die afstand tussen die lense is net die som daarvan qo + ble . Toon aan dat dit f iso+ fe , waar die intekenare o en e weer verwys na die doel en die okularis. Gebruik ook die hoofstraal deur die middel van elke lens om die hoekvergroting van die teleskoop af te lei: M = - fo/ fe . (Gebruik 'n klein hoek benadering. Die minusteken is 'n tekenkonvensie soos vir die beeld wat deur 'n enkele lens gevorm word, wat te doen het met die vraag of die beeld omgekeer of regs na bo is.)

'N Galilese teleskoop is net soos die teleskoop hierbo, behalwe dat die okularis 'n negatiewe lens is. U kan 'n fokuspunt van die okularis deur die lens in die applet hierbo sleep om dit aan die verkeerde kant te bring en sodoende 'n Galilese teleskoop te maak. Natuurlik sal u die okularis op die regte plek moet plaas, soortgelyk aan die fokus van 'n regte teleskoop. Hoe lank is die teleskoop nou? Wat is die vergroting daarvan? Is die beeld regs op of omgekeer? Hoe verskil die analise van die Galilese teleskoop as die astronomiese teleskoop, hoegenaamd?

Maak 'n astronomiese teleskoop op 'n optiese spoor wat geskik is om byvoorbeeld na verre voorwerpe te kyk. Bestudeer die eienskappe daarvan kwantitatief aan die hand van die teorie van meetkundige optika. Skryf 'n duidelike beskrywing daarvan met sketse en gebruik u antwoorde op die vrae hierbo

Herhaal dit met 'n Galilese teleskoop. Skryf 'n duidelike en kwantitatiewe beskrywing.

U sal dalk belangstel in wat Galileo gesê het oor sy metodes om kwantitatiewe metings met die teleskoop te maak. Hy het geen duidelike teorie oor geometriese optika gehad nie, maar hy het geweet dat die teleskoop die hoeke vergroot. Hier is sy beskrywing in sy geheel, uit sy boek The Starry Messenger uit 1610:

"Laat ABCD die buis wees en E die oog van die waarnemer wees. As daar dan geen lense in die buis was nie, bereik die strale die voorwerp FG langs die reguitlyne ECF en EDG. Maar as die lense geplaas is, sal die strale gaan langs die gebreekte lyne ECH en EDI sodat hulle nader aan mekaar gebring word, en die wat voorheen vrylik op die voorwerp FG gerig was, bevat nou slegs die gedeelte daarvan HI. Die verhouding van die afstand EH tot die lyn HI wat dan gevind is, een kan deur middel van 'n sinetafel die grootte bepaal van die hoek wat deur die voorwerp HI by die oog gevorm word, wat ons slegs 'n paar minute boog sal vind. As ons nou dun plate op die lens-CD pas, sommige deurboor met groter en sommige met kleiner openinge, as ons nou een plaat en nou 'n ander oor die lens plaas, kan ons na willekeur verskillende hoeke vorm wat meer of minder minute boog ondertrek, en op hierdie manier kan ons die intervalle tussen sterre wat maar 'n paar minute uitmekaar, met geen groter fout as een of twee minute. En tot nou toe is dit voldoende dat ons hierdie sake liggies aangeraak het en skaars meer as dit genoem het, aangesien ons by 'n ander geleentheid die hele teorie van hierdie instrument sal verduidelik. "


Inhoud

Verskeie eienskappe van 'n okulêr sal waarskynlik vir 'n gebruiker van 'n optiese instrument interessant wees as ons okulariste vergelyk en besluit watter okulêr by hul behoeftes pas.

Ontwerpafstand tot toegangspupil. Redigeer

Oogstukke is optiese stelsels waar die toegangspupiel altyd buite die stelsel geleë is. Dit moet ontwerp word vir optimale prestasies vir 'n spesifieke afstand tot hierdie toegangspeil (dws met minimum afwykings vir hierdie afstand). In 'n brekende astronomiese teleskoop is die toegangspupil identies aan die doelwit. Dit kan 'n paar voet van die okular af geleë wees, terwyl die ingangspupil met 'n mikroskoopoogstuk naby die agterste fokusvlak van die objektief is, slegs enkele sentimeter van die okulêr af. Mikroskoop-ooglede kan anders as teleskoop-ooglede reggestel word, maar die meeste is ook geskik vir die gebruik van die teleskoop.

Elemente en groepe Redigeer

Elemente is die individuele lense, wat kan voorkom as eenvoudige lense of 'enkels' en sementdublette of (selde) drieling. Wanneer lense in pare of drieë saamgesement word, word die gekombineerde elemente genoem groepe (van lense).

Die eerste oculare het slegs 'n enkele lenselement gehad wat baie verwronge beelde gelewer het. Twee en drie-element-ontwerpe is kort daarna uitgevind en het vinnig standaard geword vanweë die verbeterde beeldkwaliteit. Vandag het ingenieurs wat deur rekenaargesteunde opstelprogrammatuur bygestaan ​​is, okulêrs ontwerp met sewe of agt elemente wat buitengewoon groot, skerp aansigte lewer.

Interne weerkaatsing en verstrooiing

Interne weerkaatsings, soms 'verstrooiing' genoem, laat die lig wat deur 'n okular gaan, versprei en verminder die kontras van die beeld wat deur die okularis geprojekteer word. As die effek besonder sleg is, word 'spookbeelde' gesien, wat 'spook' genoem word. Vir baie jare is eenvoudige oculairontwerpe met 'n minimum aantal interne lug-tot-glas-oppervlaktes verkies om hierdie probleem te vermy.

Een oplossing om te strooi, is om dun filmbedekkings oor die oppervlak van die element te gebruik. Hierdie dun bedekkings is slegs een of twee golflengtes diep en werk om weerkaatsings en verstrooiing te verminder deur die breking van die lig wat deur die element beweeg, te verander. Sommige bedekkings kan ook lig absorbeer wat nie deur die lens gelei word nie, in 'n proses genaamd totale interne weerkaatsing, waar die lig wat op die film val, vlak is.

Chromatiese aberrasie Wysig

Sywaarts of dwars chromatiese aberrasie word veroorsaak omdat die breking by glasoppervlakke verskil vir lig van verskillende golflengtes. Blou lig, gesien deur 'n oogstukelement, fokus nie op dieselfde punt nie, maar op dieselfde as as rooi lig. Die effek kan 'n ring met vals kleur rondom puntbronne van lig skep en lei tot 'n algemene vaagheid van die beeld.

Een oplossing is om die aberrasie te verminder deur verskeie elemente van verskillende soorte glas te gebruik. Achromatte is lensgroepe wat twee verskillende golflengtes van lig op dieselfde fokus bring en vals kleure sterk verminder. Glas met lae verspreiding kan ook gebruik word om chromatiese aberrasie te verminder.

Langs chromatiese aberrasie is 'n uitgesproke effek van optiese teleskoopdoelstellings, omdat die brandpuntsafstand so lank is. Mikroskope, waarvan die fokuslengte oor die algemeen korter is, ly nie onder hierdie effek nie.

Brandpuntafstand

Die brandpuntsafstand van 'n okular is die afstand vanaf die hoofvlak van die okular waar parallelle ligstrale na 'n enkele punt saamtrek. Wanneer dit gebruik word, bepaal die brandpuntlengte van 'n okularis, gekombineer met die brandpuntlengte van die teleskoop- of mikroskoopoogmerk, waarop dit vas is, die vergroting. Dit word gewoonlik in millimeter uitgedruk as slegs na die okular verwys word. Wanneer 'n stel okulêre op 'n enkele instrument verwissel word, verwys sommige gebruikers egter liewer om elke okulêr te identifiseer aan die hand van die vergroting.

Die hoekvergroting vir 'n teleskoop MA geproduseer deur die kombinasie van 'n bepaalde okular en objektief, kan bereken word met die volgende formule:

Vergroting neem dus toe as die brandpuntlengte van die okular korter is of die fokuspunt langer is. Byvoorbeeld, 'n okular van 25 mm in 'n teleskoop met 'n brandpunt van 1200 mm sal voorwerpe 48 keer vergroot. 'N Okular van 4 mm in dieselfde teleskoop sal 300 keer vergroot.

Amateure sterrekundiges verwys gewoonlik na teleskoopoogspeile volgens hul brandpuntlengte in millimeter. Dit wissel gewoonlik van ongeveer 3 mm tot 50 mm. Sommige sterrekundiges verkies egter om die resulterende vergrotingskrag eerder as die brandpunt te spesifiseer. Dit is dikwels geriefliker om vergroting in waarnemingsverslae uit te druk, aangesien dit 'n onmiddellike indruk gee van watter siening die waarnemer eintlik gesien het. Vanweë die afhanklikheid daarvan van die spesifieke teleskoop wat gebruik word, is vergrotingskrag alleen sinloos vir die beskrywing van 'n teleskoopoogstuk.

Vir 'n saamgestelde mikroskoop is die ooreenstemmende formule

Volgens konvensie word mikroskopiese ooglede gewoonlik gespesifiseer deur krag in plaas van brandpuntafstand. Mikroskoop-okulêre krag P E < displaystyle P _ < mathrm >> en objektiewe krag P O < displaystyle P _ < mathrm >> word gedefinieer deur

dus uit die vroeëre uitdrukking vir die hoekvergroting van 'n saamgestelde mikroskoop

Die totale hoekvergroting van 'n mikroskoopbeeld word dan eenvoudig bereken deur die okulêre krag met die objektiewe krag te vermenigvuldig. Byvoorbeeld, 'n 10 × okular met 'n 40 × -objek sal die beeld 400 keer vergroot.

Hierdie definisie van lensvermoë berus op 'n arbitrêre besluit om die hoekvergroting van die instrument te verdeel in afsonderlike faktore vir die okularis en die doel. Histories het Abbe mikroskoop-okulêre verskillend beskryf, in terme van die hoekvergroting van die oogstuk en 'aanvanklike vergroting' van die doel. Alhoewel dit gemaklik vir die optiese ontwerper was, blyk dit minder gerieflik te wees vanuit die oogpunt van praktiese mikroskopie en is dit gevolglik verlaat.

Moderne instrumente gebruik dikwels doelstellings wat opties gekorrigeer word vir 'n oneindige buislengte eerder as 160 mm, en dit vereis 'n hulpkorreksielens in die buis.

Ligging van fokusvlak

In sommige okulariteitsvorme, soos Ramsden-okulêre (hieronder in meer besonderhede beskryf), gedra die okulêr hom as 'n vergrootglas en is die fokusvlak buite die okularis voor die veldlens geleë. Hierdie vliegtuig is dus toeganklik as 'n plek vir 'n traliedraad of mikrometer dwarsdrade. In die Huygeniaanse okularis is die fokusvlak tussen die oog- en veldlense binne die okulêr geleë en is dit dus nie toeganklik nie.

Gesigveld wysig

Die gesigsveld, dikwels afgekort FOV, beskryf die oppervlakte van 'n teiken (gemeet as 'n hoek vanaf die ligging) wat gesien kan word as u deur 'n okular kyk. Die gesigsveld wat deur 'n okular gesien word, hang af van die vergroting wat bereik word wanneer dit aan 'n bepaalde teleskoop of mikroskoop gekoppel is, en ook van die eienskappe van die okular self. Oogstukke word onderskei deur hul veldstop, wat die smalste diafragma is wat die lig deur die okular moet binnedring om die veldlens van die okulêr te bereik.

As gevolg van die gevolge van hierdie veranderlikes, verwys die term "gesigsveld" byna altyd na een van die twee betekenisse:

Werklike gesigsveld Die hoekgrootte van die hoeveelheid lug wat deur 'n okular gesien kan word wanneer dit met 'n bepaalde teleskoop gebruik word, wat 'n spesifieke vergroting lewer. Dit wissel gewoonlik tussen 0,1 en 2 grade. Blykbare gesigsveld Dit is 'n maatstaf van die hoekgrootte van die beeld wat deur die okular gesien word. Met ander woorde, dit is hoe groot die prentjie verskyn (anders as die vergroting). Dit is konstant vir elke gegewe okular met vaste brandpuntlengte en kan gebruik word om te bereken wat die werklike gesigsveld is wanneer die okular saam met 'n gegewe teleskoop gebruik word. Die meting wissel van 30 tot 110 grade.

Dit is algemeen dat gebruikers van 'n okularis die werklike gesigsveld wil bereken, omdat dit aandui hoeveel van die lug sigbaar sal wees as die okular saam met hul teleskoop gebruik word. Die gemaklikste metode om die werklike gesigsveld te bereken, hang af van of die oënskynlike gesigsveld bekend is.

As die oënskynlike gesigsveld bekend is, die werklike gesigsveld kan bereken word uit die volgende benaderde formule:

Die brandpuntafstand van die teleskoopdoelwit is die deursnee van die objektiewe maal die brandpuntverhouding. Dit stel die afstand voor waarop die spieël of objektiewe lens die lig op 'n enkele punt sal laat saamtrek.

Die formule is akkuraat tot 4% of beter tot 40 ° sigbare gesigsveld en het 'n fout van 10% vir 60 °.

As die oënskynlike gesigsveld onbekend is, die werklike gesigsveld kan ongeveer gevind word met behulp van:

Die tweede formule is eintlik akkurater, maar die grootte van die veldstop word gewoonlik nie deur die meeste vervaardigers gespesifiseer nie. Die eerste formule sal nie akkuraat wees as die veld nie plat is nie, of hoër is as 60 °, wat algemeen is vir die ultra-wye oogstukontwerp.

Die bostaande formules is benaderings. Die ISO 14132-1: 2002-standaard bepaal hoe die presiese oënskynlike hoek van die berekening (AAOV) bereken word vanuit die werklike beeldhoek (AOV).

As 'n diagonale of Barlow-lens voor die okularis gebruik word, kan die oogveld se oogveld effens beperk wees. Dit kom voor wanneer die voorste lens 'n smaller veldstop het as die okulêr, wat veroorsaak dat die obstruksie aan die voorkant as 'n kleiner veldstop voor die okularis optree. Die presiese verhouding word gegee deur

Hierdie formule dui ook aan dat, vir 'n okularontwerp met 'n gegewe oënskynlike gesigsveld, die loopdeursnee die maksimum brandpuntlengte vir daardie okulêr sal bepaal, aangesien geen veldstop groter as die loop self kan wees nie. Byvoorbeeld, 'n Plössl met 45 ° sigbare gesigsveld in 'n 1,25 duim vat sou 'n maksimum brandpuntlengte van 35 mm lewer. [1] Alles wat langer benodig verg groter vat of die sig word deur die rand beperk, wat die gesigsveld effektief minder as 45 ° maak.

Vatdiameter Wysig

Oogstukke vir teleskope en mikroskope word gewoonlik omgeruil om die vergroting te verhoog of te verlaag, en om die gebruiker in staat te stel om 'n tipe met sekere prestasie-eienskappe te kies. Om dit toe te laat, het die okulêre standaard standaard "loopdiameters".

Teleskoopoogspeelkuns Redigeer

Daar is ses standaard loopdiameters vir teleskope. Die loopgroottes (gewoonlik uitgedruk in duim [ aanhaling nodig ]) is:

  • 0,965 in. (24,5 mm) - Dit is die kleinste standaard loopdeursnee en word gewoonlik in speelgoedwinkels en winkelsentrumteleskope aangetref. Baie van hierdie ooglede wat sulke teleskope bevat, is plastiek, en sommige het selfs plastieklense. Hoogwaardige teleskoopoogstaak met hierdie loopgrootte word nie meer vervaardig nie, maar u kan steeds Kellner-soorte koop.
  • 1,25 in. (31,75 mm) - Dit is die gewildste deursnee van die teleskoop-okulêre vat. Die praktiese boonste limiet vir brandpuntsafstande vir oculare met 1,25 "-vate is ongeveer 32 mm. Met langer brandpuntsafstand dring die kante van die loop self in die aansig in en beperk die grootte daarvan. Met brandpunslengtes langer as 32 mm, is die beskikbare gesigsveld beskikbaar. val onder 50 °, wat die meeste amateurs beskou as die minimum aanvaarbare breedte. Hierdie loopgroottes is geskroef om filters van 30 mm te neem.
  • 2 in. (50,8 mm) - Die groter loopgrootte in 2 "-oogspeletjies help om die brandpuntlengte te beperk. Die boonste limiet van die brandpuntlengte met 2" -okulare is ongeveer 55 mm. Die kompromie is dat hierdie okulariste gewoonlik duurder is, nie in sommige teleskope pas nie, en dat dit swaar genoeg is om die teleskoop te laat kantel. Hierdie loopgroottes is geskroef om filters van 48 mm (of selde 49 mm) te neem.
  • 2.7 in. (68,58 mm) - 2,7 "-oogspeletjies word deur 'n paar vervaardigers vervaardig. Dit laat effens groter gesigsvelde toe. Baie fyn fokusers aanvaar hierdie okularis.
  • 3 in. (76,2 mm) - Die nog groter loopgrootte in 3 "-oogspeletjies maak voorsiening vir uiterste brandpuntsafstande en meer as 120 ° -aansig vir die oog. Die nadele is dat hierdie okulare ietwat skaars, uiters duur is, tot 5 kg gewig, en dat slegs enkele teleskope het fokusers wat groot genoeg is om dit te aanvaar. Hul groot gewig veroorsaak balanseringsprobleme in Schmidt-Cassegrains onder 10 duim, refraktors onder 5 duim en weerkaatsers onder 16 duim. Ook as gevolg van hul groot veldstop, sonder groter sekondêre spieëls. die meeste weerkaatsers en Schmidt-Cassegrains het 'n ernstige vignettering met hierdie okulêre vervaardigers. Makers van hierdie okulêrs sluit in Explore Scientific en Siebert Optics. Teleskope wat hierdie okulare kan aanvaar, word gemaak deur Explore Scientific en Orion Telescopes en Binoculars.
  • 4 in. (102 mm) - Hierdie oculare is skaars en word slegs algemeen in sterrewagte gebruik. Dit word deur baie min vervaardigers vervaardig en die vraag daarna is laag.

Mikroskoop-ooglede Redigeer

Oogstukke vir mikroskope het loopdiameters gemeet in millimeter soos 23,2 mm en 30 mm.

Oogverligting Wysig

Die oog moet op 'n sekere afstand agter die ooglens van 'n okular gehou word om beelde behoorlik daardeur te sien. Hierdie afstand word die oogverligting genoem. 'N Groter oogverligting beteken dat die optimale posisie verder van die okulariteit af is, wat dit makliker maak om 'n beeld te sien. As die oogverligting egter te groot is, kan dit ongemaklik wees om die oog vir 'n lang tyd in die regte posisie te hou, en daarom het sommige oogstukke met 'n lang oogverligting koppies agter die ooglens om die waarnemer te help om die korrekte waarnemingsposisie. Die oog pupil moet saamval met die uitgang pupil, die beeld van die ingang pupil, wat in die geval van 'n astronomiese teleskoop ooreenstem met die voorwerp glas.

Oogverligting wissel gewoonlik van ongeveer 2 mm tot 20 mm, afhangende van die konstruksie van die oogstuk. Oogstukke met lang brandpuntsafstand het gewoonlik genoeg oogverligting, maar kort oogpunte vir brandpuntsafstand is meer problematies. Tot onlangs, en nog steeds baie algemeen, het ooglede met 'n kort fokuspunt 'n kort oogverligting. Goeie ontwerpriglyne stel 'n minimum van 5-6 mm voor om die wimpers van die waarnemer te akkommodeer om ongemak te voorkom. Moderne ontwerpe met baie lenselemente kan egter hiervoor regstel, en die bekyk met hoë krag word gemakliker. Dit is veral die geval vir brildraers, wat tot 20 mm oogverligting benodig om hul bril te akkommodeer.

Tegnologie het mettertyd ontwikkel en daar is 'n verskeidenheid oculare ontwerpe vir gebruik met teleskope, mikroskope, geweerbesienswaardighede en ander toestelle. Sommige van hierdie ontwerpe word hieronder in meer besonderhede beskryf.

Negatiewe lens of "Galilese" wysig

Die eenvoudige negatiewe lens wat voor die fokus van die doelwit geplaas word, het die voordeel dat dit 'n regop beeld bied, maar met 'n beperkte gesigsveld wat beter geskik is vir lae vergroting. Daar word vermoed dat hierdie tipe lens in sommige van die eerste brekingsteleskope wat in ongeveer 1608 in Nederland verskyn het, gebruik is. Dit is ook gebruik in Galileo Galilei se 1609-teleskoopontwerp, wat hierdie soort okularisering die naam geeGalileërHierdie soort okularis word steeds gebruik in baie goedkoop teleskope, verkykers en in 'n operaglas.

Konvekse lens Redigeer

'N Eenvoudige konvekse lens wat na die fokus van die objektiewe lens geplaas word, bied die kyker 'n vergrote omgekeerde beeld. Hierdie konfigurasie is moontlik in die eerste brekingsteleskope uit Nederland gebruik en is voorgestel as 'n manier om 'n veel wyer gesigsveld en groter vergroting in teleskope te hê in Johannes Kepler se boek uit 1611 Dioptrice. Aangesien die lens na die fokusvlak van die doelwit geplaas word, is dit ook toegelaat om 'n mikrometer op die fokusvlak te gebruik (wat gebruik word om die hoekgrootte en / of afstand tussen voorwerpe waargeneem te word).

Huygens Edit

Huygens-ooglede bestaan ​​uit twee plano-konvekse lense, met die vlakke sye na die oog, geskei deur 'n luggaping. Die lense word die ooglens en die veldlens genoem. Die fokusvlak is tussen die twee lense geleë. Dit is in die laat 1660's deur Christiaan Huygens uitgevind en was die eerste saamgestelde (multi-lens) okular. [2] Huygens het ontdek dat twee lense in die lug gebruik kan word om 'n okular met 'n nul dwarschromatiese afwyking te maak. As die lense van glas met dieselfde Abbe-nommer gemaak word, wat gebruik moet word met 'n ontspanne oog en 'n teleskoop met 'n oneindig verre doel, word die skeiding gegee deur:

Hierdie oculare werk goed met die teleskope met baie lang brandpuntlengtes (op Huygens-dag is dit gebruik met lang-brandpuntteleskope vir enkele elemente, nie-achromatiese brekingsteleskope, insluitend baie lang brandpuntteleskope). Hierdie optiese ontwerp word nou as verouderd beskou, aangesien die okularis met die korter brandpuntlengte van vandag onder kort oogverligting, hoë beeldvervorming, chromatiese afwyking en 'n baie skaars gesigsveld ly. Aangesien dit goedkoop is om hierdie okularis te vervaardig, kan dit dikwels op goedkoop teleskope en mikroskope gevind word. [3]

Omdat Huygens-ooglede nie sement bevat om die lenselemente vas te hou nie, gebruik die teleskoopgebruikers hierdie okulêrs soms in die rol van 'sonprojeksie', dit wil sê om 'n beeld van die son vir lang tydperke op 'n skerm te projekteer. Gesementeerde ooglede word tradisioneel beskou as moontlik kwesbaar vir hittebeskadiging deur die intense ligkonsentrasies.

Ramsden Edit

Die Ramsden-okular bestaan ​​uit twee plano-konvekse lense van dieselfde glas en soortgelyke brandpuntsafstand, wat minder as een brandpuntlengte van mekaar geplaas is, 'n ontwerp wat deur die astronomiese en wetenskaplike instrumentvervaardiger Jesse Ramsden in 1782 geskep is. Die lensskeiding wissel tussen verskillende ontwerpe , maar is gewoonlik iewers tussen 7/10 en 7/8 van die brandpuntsafstand van die ooglens, die keuse is 'n afweging tussen oorblywende dwars-chromatiese afwyking (teen lae waardes) en teen hoë waardes wat die gevaar van die veldlens inhou raak aan die fokusvlak as dit gebruik word deur 'n waarnemer wat met 'n noue virtuele beeld werk, soos 'n byziende waarnemer, of 'n jong persoon wie se akkommodasie in staat is om 'n noue virtuele beeld te hanteer (dit is 'n ernstige probleem as dit met 'n mikrometer gebruik word) kan skade aan die instrument veroorsaak).

'N Skeiding van presies 1 brandpuntsafstand is ook nie aan te beveel nie, aangesien dit die stof op die veldlens ontstellend in fokus maak. Die twee geboë oppervlaktes wys na binne. The focal plane is thus located outside of the eyepiece and is hence accessible as a location where a graticule, or micrometer crosshairs may be placed. Because a separation of exactly one focal length would be required to correct transverse chromatic aberration, it is not possible to correct the Ramsden design completely for transverse chromatic aberration. The design is slightly better than Huygens but still not up to today's standards.

It remains highly suitable for use with instruments operating using near-monochromatic light sources bv. polarimeters.

Kellner or "Achromat" Edit

In a Kellner eyepiece an achromatic doublet is used in place of the simple plano-convex eye lens in the Ramsden design to correct the residual transverse chromatic aberration. Carl Kellner designed this first modern achromatic eyepiece in 1849, [4] also called an "achromatized Ramsden". Kellner eyepieces are a 3-lens design. They are inexpensive and have fairly good image from low to medium power and are far superior to Huygenian or Ramsden design. The eye relief is better than the Huygenian and worse than the Ramsden eyepieces. [5] The biggest problem of Kellner eyepieces was internal reflections. Today's anti-reflection coatings make these usable, economical choices for small to medium aperture telescopes with focal ratio f/6 or longer. The typical apparent field of view is 40–50°.

Plössl or "Symmetrical" Edit

The Plössl is an eyepiece usually consisting of two sets of doublets, designed by Georg Simon Plössl in 1860. Since the two doublets can be identical this design is sometimes called a symmetrical eyepiece. [6] The compound Plössl lens provides a large 50° or more oënskynlike field of view, along with relatively large FOV. This makes this eyepiece ideal for a variety of observational purposes including deep-sky and planetary viewing. The chief disadvantage of the Plössl optical design is short eye relief compared to an orthoscopic since the Plössl eye relief is restricted to about 70–80% of focal length. The short eye relief is more critical in short focal lengths below about 10 mm, when viewing can become uncomfortable especially for people wearing glasses.

The Plössl eyepiece was an obscure design until the 1980s when astronomical equipment manufacturers started selling redesigned versions of it. [7] Today it is a very popular design on the amateur astronomical market, [8] where the name Plössl covers a range of eyepieces with at least four optical elements.

This eyepiece is one of the more expensive to manufacture because of the quality of glass, and the need for well matched convex and concave lenses to prevent internal reflections. Due to this fact, the quality of different Plössl eyepieces varies. There are notable differences between cheap Plössls with simplest anti-reflection coatings and well made ones.

Orthoscopic or "Abbe" Edit

The 4-element orthoscopic eyepiece consists of a plano-convex singlet eye lens and a cemented convex-convex triplet field lens achromatic field lens. This gives the eyepiece a nearly perfect image quality and good eye relief, but a narrow apparent field of view — about 40°–45°. It was invented by Ernst Abbe in 1880. [3] It is called "orthoscopic"of"orthographic" because of its low degree of distortion and is also sometimes called an "ortho" or "Abbe".

Until the advent of multicoatings and the popularity of the Plössl, orthoscopics were the most popular design for telescope eyepieces. Even today these eyepieces are considered good eyepieces for planetary and lunar viewing. Due to their low degree of distortion and the corresponding globe effect, they are less suitable for applications which require an excessive panning of the instrument.

Monocentric Edit

A Monocentric is an achromatic triplet lens with two pieces of crown glass cemented on both sides of a flint glass element. The elements are thick, strongly curved, and their surfaces have a common center giving it the name "monocentric". It was invented by Hugo Adolf Steinheil around 1883. [9] This design, like the solid eyepiece designs of Robert Tolles, Charles S. Hastings, and E. Wilfred Taylor, [10] is free from ghost reflections and gives a bright contrasty image, a desirable feature when it was invented (before anti-reflective coatings). [11] It has a narrow field of view of around 25° [12] and is a favorite amongst planetary observers. [13]

Erfle Edit

An erfle is a 5-element eyepiece consisting of two achromatic lenses with extra lenses in between. They were invented during the first world war for military purposes, described in US patent by Heinrich Erfle number 1,478,704 of August 1921 and are a logical extension to wider fields of four element eyepieces such as Plössls.

Erfle eyepieces are designed to have wide field of view (about 60 degrees), but they are unusable at high powers because they suffer from astigmatism and ghost images. However, with lens coatings at low powers (focal lengths of 20 mm and up) they are acceptable, and at 40 mm they can be excellent. Erfles are very popular because they have large eye lenses, good eye relief and can be very comfortable to use.

König Edit

The König eyepiece has a concave-convex positive doublet and a plano-convex singlet. The strongly convex surfaces of the doublet and singlet face and (nearly) touch each other. The doublet has its concave surface facing the light source and the singlet has its almost flat (slightly convex) surface facing the eye. It was designed in 1915 by German optician Albert König (1871−1946) as a simplified Abbe [ aanhaling nodig ] . The design allows for high magnification with remarkably high eye relief — the highest eye relief proportional to focal length of any design before the Nagler, in 1979. The field of view of about 55° makes its performance similar to the Plössl, with the advantage of requiring one less lens.

Modern versions of Königs can use improved glass, or add more lenses, grouped into various combinations of doublets and singlets. The most typical adaptation is to add a positive, concave-convex simple lens before the doublet, with the concave face towards the light source and the convex surface facing the doublet. Modern improvements typically have fields of view of 60°−70°.

RKE Edit

An RKE eyepiece has an achromatic field lens and double convex eye lens, a reversed adaptation of the Kellner eyepiece. It was designed by Dr. David Rank for the Edmund Scientific Corporation, who marketed it throughout the late 1960s and early 1970s. This design provides slightly wider field of view than classic Kellner design and makes its design similar to a widely spaced version of the König.

According to Edmund Scientific Corporation, RKE stands for "Rank Kellner Eyepiece'" [ aanhaling nodig ] . In an amendment to their trademark application on January 16, 1979 it was given as "Rank-Kaspereit-Erfle", the three designs from which the eyepiece was derived. [14] A March 1978 Edmund Astronomy News (Vol 16 No 2) ran the headline "New Eyepiece Design Developed By Edmund" and said "The new 28mm and 15mm Rank-Kaspereit-Erfle (RKE) eyepieces are American redesigns of the famous Type II Kellner eyepiece." [15]


The Magnification Equation for a Magnifying Glass

Compared to the naked eye, a magnifying glass’ maximum angular magnification depends on how the object and the glass are held in relation to your eye. When the lens is held far from the object so that its frontal focused point is on the viewed object, the eye can see the image with angular magnification, which you can read about in this course about vision enhancement. The formula for this is:

The constant 25cm is an eye distance ‘near point’ estimate, which is the nearest distance that healthy eyes are able to focus. F here is the lens’ focal length in centimeters. In cases like this the angular magnification is independent from the distances kept between the magnifying glass and the eye. When holding the lens very close to the eye, the object is positioned nearer the lens, larger angular magnification can be obtained with this formula:

In this case, the magnifying glass alters the eye’s diopter causing it to be myopic so that there is larger angular magnification when objects are placed nearer the eyes.


Chapter 24, 25, 26

What is the apparent depth of the fish when viewed at normal incidence to the water?

Where are the object and images located?

part A Find the focal length of the lens that produces the image described in the problem introduction using the thin lens equation.

part C What is the magnification mmm of the lens?

What is the x coordinate of the object? Keep in mind that a real image and a real object should be on opposite sides of the lens.
Express your answer in centimeters, as a fraction or to three significant figures.

part J Is the lens converging or diverging?

part A Is the image inverted or upright?

part B Is the lens diverging or converging?

The image produced by the lens is real. Diverging lens produces only virtual image. The converging lens produces real image. Thus, the lens is converging.

part c
Is the image enlarged or reduced in size?

(Figure 1) shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is 1.5 cmcm along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram to answer the following questions:

Using only the ray shown, decide what type of lens this is.

Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 10.0 cm

part A Which, if any, of these people require bifocals to correct their vision?

part B Which, if any, of these people require bifocals to correct their vision?

The angular magnification produced by the telescope increases.

Which laser has its first maximum closer to the central maximum?

A green, rather than red, light source is used.

where mm is a positive integer. This is usually stated in the slightly more explicit form
λm,constructive=2d/m

part a
At Point A is the interference between the two sources constructive or destructive?

part b
At Point B is the interference between the two sources constructive or destructive?

Part C
At Point C is the interference between the two sources constructive or destructive?


The focal length of a microscope eyepiece

The question:
--------------------

The length of a microscope pipe is $L=160, m mm$,
the transverse magnification of its objective $M_o = 40 imes$
and the diameter $d_o = 5, m mm$.
As for the ocular/eyepiece, its magnification is $M_e = 10 imes$.

1. Find out the focal length of the objective $f_o$
2. At what distance from the objective must object be placed in order for a sharp image to form
3. What is the numerical aperture of the objective?
4. Where is the exit pupil of the microscope located,
if the near distance of an average person is $25, m cm$?

1. Using the transverse magnification equation for a thin lens,
the focal length of the objective can be found out to be
begin
f_o = -frac L = -frac<160, m mm> <-40>= 4, m mm,.
einde
2. Using the focal length $f_o$, if the distance of the image
formed by the objective is known to be $s_i = f_o + L$ we can solve for $s_o$ using the thin lens equation:
begin
s_o
= left(frac 1 - frac 1 ight)^<-1>
approx 4.1, m mm,.
einde
3. The numerical aperture $ m NA$ is defined as
begin
< m NA>= n_isin heta_< m max>,
einde
where $n_i$ is the refractive index of the substance surrounding the object.
Here it is assumed to be air, so $n_i approx 1$.
The maximum angle where light from a point on the lens axis can penetrate the objective lens can be found out from the diameter of the lens and the object distance:
begin
heta_ < m max>= an^<-1>left(frac<2s_o> ight) approx 0.548,
einde
so
begin
< m NA>= sinleft(0.548 ight) approx 0.52,.
einde
4. This is where I got stuck.
The definition of the exit pupil is the image of the objective as viewed through the eyepiece. For this I need the distance between the eyepiece and objective $s_ = f_o + L + f_e$, which again requires knowldge of $f_e$,
the focal length of the eyepiece, but I can't seem to figure out a way to calculate this. What I tried was to calculate teh focal length using transverse magnification:
begin
f_e = M_ex_o = M_e(L + f_o) = 1.64 m,m,
einde
and using this I calculated the distance of the exit pupil to be
begin
s_i = left(frac 1 - frac 1 ight)^ <-1>approx 18, m m,
einde
which is preposterous, as the eye would have to be placed this far from the microscope. I would not even be able to see the microscope itself from this distance without my glasses.

What I didn't try was to use the near distance of an average person $s_l = 25, m cm$ to my advantage, but I'm not sure how to go about this. I guess the microscope could be though of as a pair of correcting eyeglasses, but which part of the microscope should this function belong to?


2.1 Images Formed by Plane Mirrors

  • A plane mirror always forms a virtual image (behind the mirror).
  • The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.

2.2 Spherical Mirrors

  • Spherical mirrors may be concave (converging) or convex (diverging).
  • The focal length of a spherical mirror is one-half of its radius of curvature: (displaystyle f=R/2).
  • The mirror equation and ray tracing allow you to give a complete description of an image formed by a spherical mirror.
  • Spherical aberration occurs for spherical mirrors but not parabolic mirrors comatic aberration occurs for both types of mirrors.

2.3 Images Formed by Refraction

This section explains how a single refracting interface forms images.

  • When an object is observed through a plane interface between two media, then it appears at an apparent distance (displaystyle h_i) that differs from the actual distance (displaystyle h_o:h_i=(n_2/n_1)h_o).
  • An image is formed by the refraction of light at a spherical interface between two media of indices of refraction (displaystyle n_1) and (displaystyle n_2).
  • Image distance depends on the radius of curvature of the interface, location of the object, and the indices of refraction of the media.

2.4 Thin Lenses

  • Two types of lenses are possible: converging and diverging. A lens that causes light rays to bend toward (away from) its optical axis is a converging (diverging) lens.
  • For a converging lens, the focal point is where the converging light rays cross for a diverging lens, the focal point is the point from which the diverging light rays appear to originate.
  • The distance from the center of a thin lens to its focal point is called the focal length f.
  • Ray tracing is a geometric technique to determine the paths taken by light rays through thin lenses.
  • A real image can be projected onto a screen.
  • A virtual image cannot be projected onto a screen.
  • A converging lens forms either real or virtual images, depending on the object location a diverging lens forms only virtual images.

2.5 The Eye

  • Image formation by the eye is adequately described by the thin-lens equation.
  • The eye produces a real image on the retina by adjusting its focal length in a process called accommodation.
  • Nearsightedness, or myopia, is the inability to see far objects and is corrected with a diverging lens to reduce the optical power of the eye.
  • Farsightedness, or hyperopia, is the inability to see near objects and is corrected with a converging lens to increase the optical power of the eye.
  • In myopia and hyperopia, the corrective lenses produce images at distances that fall between the person&rsquos near and far points so that images can be seen clearly.

2.6 The Camera

  • Cameras use combinations of lenses to create an image for recording.
  • Digital photography is based on charge-coupled devices (CCDs) that break an image into tiny &ldquopixels&rdquo that can be converted into electronic signals.

2.7 The Simple Magnifier

  • A simple magnifier is a converging lens and produces a magnified virtual image of an object located within the focal length of the lens.
  • Angular magnification accounts for magnification of an image created by a magnifier. It is equal to the ratio of the angle subtended by the image to that subtended by the object when the object is observed by the unaided eye.
  • Angular magnification is greater for magnifying lenses with smaller focal lengths.
  • Simple magnifiers can produce as great as tenfold (10×) magnification.

2.8 Microscopes and Telescopes

  • Many optical devices contain more than a single lens or mirror. These are analyzed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray-tracing and thin-lens techniques developed in the previous sections apply to each lens element.
  • The overall magnification of a multiple-element system is the product of the linear magnifications of its individual elements times the angular magnification of the eyepiece. For a two-element system with an objective and an eyepiece, this is

where (displaystyle m^) is the linear magnification of the objective and (displaystyle M^) is the angular magnification of the eyepiece.

  • The microscope is a multiple-element system that contains more than a single lens or mirror. It allows us to see detail that we could not to see with the unaided eye. Both the eyepiece and objective contribute to the magnification. The magnification of a compound microscope with the image at infinity is

In this equation, 16 cm is the standardized distance between the image-side focal point of the objective lens and the object-side focal point of the eyepiece, 25 cm is the normal near point distance, (displaystyle f^) and (displaystyle f^) are the focal distances for the objective lens and the eyepiece, respectively.

  • Simple telescopes can be made with two lenses. They are used for viewing objects at large distances.
  • The angular magnification M for a telescope is given by

where (displaystyle f^) and (displaystyle f^) are the focal lengths of the objective lens and the eyepiece, respectively.


Equation to find distance between objective and eyepiece - Astronomy

THE REFRACTION OF LIGHT: LENSES AND

a. We know from the law of reflection (Section 25.2), that the angle of reflection is equal to the angle of incidence, so the reflected ray is reflected at .

b. Snell s law of refraction (Equation 26.2: can be used to find the angle of refraction. Table 26.1 indicates that the index of refraction of water is 1.333. Solving for q 2 and substituting values, we find that

13. REASONING We will use the geometry of the situation to determine the angle of incidence. Once the angle of incidence is known, we can use Snell's law to find the index of refraction of the unknown liquid. The speed of light v in the liquid can then be determined.

SOLUTION From the drawing in the text, we see that the angle of incidence at the liquid-air interface is

The drawing also shows that the angle of refraction is 90.0 . Thus, according to Snell's law (Equation 26.2: ), the index of refraction of the unknown liquid is

From Equation 26.1 ( ), we find that the speed of light in the unknown liquid is

29. REASONING AND SOLUTION If a person s eyes are very close to the surface of the water, a light ray coming from the shark will be seen even when it is refracted through an angle of 90.0 as it enters the air. In this situation, the ray strikes the water-air interface at the critical angle. The critical angle q c is given by Equation 26.4 as

where we have used n = 1.333 for the refractive index of water (see Table 26.1). The horizontal distance x of the shark from the boat is related to the depth (4.5 m) of the shark and the critical angle by trigonometry:

If the shark is farther than 5.1 m from the boat, a light ray from the shark will strike the water-air interface at an angle that is greater than the critical angle. The ray will be totally reflected back into the water, and the person will not see the shark.

33. REASONING Since the light reflected from the coffee table is completely polarized parallel to the surface of the glass, the angle of incidence must be the Brewster angle ( q B = 56.7 ) for the air-glass interface. We can use Brewster's law (Equation 26.5: ) to find the index of refraction n 2 of the glass.

SOLUTION Solving Brewster's law for n 2 , we find that the refractive index of the glass is

41. REASONING Because the refractive index of the glass depends on the wavelength (i.e., the color) of the light, the rays corresponding to different colors are bent by different amounts in the glass. We can use Snell s law (Equation 26.2: ) to find the angle of refraction for the violet ray and the red ray. The angle between these rays can be found by the subtraction of the two angles of refraction.

SOLUTION In Table 26.2 the index of refraction for violet light in crown glass is 1.538, while that for red light is 1.520. According to Snell's law, then, the sine of the angle of refraction for the violet ray in the glass is , so that

Similarly, for the red ray, , from which it follows that

Therefore, the angle between the violet ray and the red ray in the glass is

49. REASONING AND SOLUTION Equation 26.6 gives the thin-lens equation which relates the object and image distances and , respectively, to the focal length f of the lens: .

The optical arrangement is similar to that in Figure 26.27. The problem statement gives values for the focal length ( ) and the maximum lens-to-film distance ( ). Therefore, the maximum distance that the object can be located in front of the lens is

53. REASONING The ray diagram is constructed by drawing the paths of two rays from a point on the object. For convenience, we will choose the top of the object. The ray that is parallel to the principal axis will be refracted by the lens so that it passes through the focal point on the right of the lens. The ray that passes through the center of the lens passes through undeflected. The image is formed at the intersection of these two rays. In this case, the rays do not intersect on the right of the lens. However, if they are extended backwards they intersect on the left of the lens, locating a virtual, upright, and enlarged image.

a. The ray-diagram, drawn to scale, is shown below.

From the diagram, we see that the image distance is and the magnification is . The negative image distance indicates that the image is virtual. The positive magnification indicates that the image is larger than the object.

b. From the thin-lens equation [Equation 26.6: ], we obtain

The magnification equation (Equation 26.7) gives the magnification to be

59. REASONING The optical arrangement is similar to that in Figure 26.27. We begin with the thin-lens equation, [Equation 26.6: ]. Since the distance between the moon and the camera is so large, the object distance is essentially infinite, and . Therefore the thin-lens equation becomes or . The diameter of the moon's imagine on the slide film is equal to the image height h i , as given by the magnification equation (Equation 26.7: ).

When the slide is projected onto a screen, the situation is similar to that in Figure 26.28. In this case, the thin-lens and magnification equations can be used in their usual forms.

a. Solving the magnification equation for gives

The diameter of the moon's image on the slide film is, therefore, .

b. From the magnification equation, . We need to find the ratio . Beginning with the thin-lens equation, we have

Therefore, the diameter of the image on the screen is .

65. REASONING The problem can be solved using the thin-lens equation [Equation 26.6: ] twice in succession. We begin by using the thin lens-equation to find the location of the image produced by the converging lens this image becomes the object for the diverging lens.

a. The image distance for the converging lens is determined as follows:

This image acts as the object for the diverging lens. Daarom,

Thus, the final image is located .

b. The magnification equation (Equation 26.7: ) gives

Therefore, the overall magnification is given by the product .

c. Since the final image distance is negative, we can conclude that the image is .

d. Since the overall magnification of the image is negative, the image is .

e. The magnitude of the overall magnification is less than one therefore, the final image is .

69. REASONING We begin by using the thin-lens equation [Equation 26.6: ] to locate the image produced by the lens. This image is then treated as the object for the mirror.

a. The image distance from the diverging lens can be determined as follows:

The image produced by the lens is 5.71 cm to the left of the lens. The distance between this image and the concave mirror is 5.71 cm + 30.0 cm = 35.7 cm. The mirror equation [Equation 25.3: ] gives the image distance from the mirror:

b. The image is , because d i is a positive number, indicating that the final image lies to the left of the concave mirror.

c. The image is , because a diverging lens always produces an upright image, and the concave mirror produces an inverted image when the object distance is greater than the focal length of the mirror (see Figure 25.19 b ).

77. REASONING A contact lens is placed directly on the eye. Therefore, the object distance, which is the distance from the book to the lens, is 25.0 cm. The near point can be determined from the thin-lens equation [Equation 26.6: ].

a. Using the thin-lens equation, we have

In other words, at age 40, the man's near point is 40.6 cm. Similarly, when the man is 45, we have

and his near point is 52.4 cm. Thus, the man s near point has changed by .

b. With and , the focal length of the lens is found as follows:

89. REASONING The angular magnification of a compound microscope is given by Equation 26.11:

where is the focal length of the objective, is the focal length of the eyepiece, and L is the separation between the two lenses. This expression can be solved for , the focal length of the objective.

SOLUTION Solving for , we find that the focal length of the objective is

97. REASONING AND SOLUTION

a. The lens with the largest focal length should be used for the objective of the telescope. Since the refractive power is the reciprocal of the focal length (in meters), the lens with the smallest refractive power is chosen as the objective, namely, the .

b. According to Equation 26.8, the refractive power is related to the focal length f by . Since we know the refractive powers of the two lenses, we can solve Equation 26.8 for the focal lengths of the objective and the eyepiece. We find that . Similarly, for the eyepiece, . Therefore, the distance between the lenses should be

c. The angular magnification of the telescope is given by Equation 26.12 as


Eyepiece AFOV calculation

I am having some trouble with the eyepiece AFOV calculations resulting in low numbers, like 77.6 degrees for a 31mm Nagler, for example, and looking for some help in understanding this result.

I have an eyepiece spreadsheet I found online to compare eyepieces, and I noticed that the spreadsheet uses a calculated eyepiece field stop, from the published AFOV, the focal length of the eyepiece and the telescope objective lens/mirror focal length.

I want to modify the spreadsheet so that I can enter a real value for the field stop, then calculate both the apparent and true fields of view (afov and tfov) from that. So I found a list of calculations that I am trying to use, at: http://www.wilmslowa. re/formulae.htm

Magnification = Focal Length Scope / Focal Length Eyepiece

Real FoV = Apparent FoV / Magnification

RealFoV = (Eyepiece Field Stop / Focal Length Scope) * 57.3

Some quick subsitution yields a calculation for AFOV:

Apparent FoV = Real FoV * Magnification = (Eyepiece Field Stop / Focal Length Eyepiece) * 57.3

So, for the 31mm Nagler I get:

Apparent FoV = (42mm/31mm) * 57.3 = 77.6 degrees

So, what am I doing wrong? Or is the apparent field of view really 77.6 degrees for an "82 degree" 31mm Nagler? I don't think so, because all of the eyepieces for which I did this calculation, showed results that were lower than their published AFOV.

#2 gnowellsct

#3 gnowellsct

You haven't introduced the focal length of your SCOPE into the calculation using the second technique.

RealFoV = (Eyepiece Field Stop / Focal Length Scope) * 57.3

So for a Tak FS128, at 1040 mm FOCAL LENGTH OF THE SCOPE (aperture in mm times the focal ratio), so the 128 mm aperture Tak FS128 is f/8.1, 8.1*128=1036.8 mm, so you can see I've rounded a bit, but 1040mm is good nuff.

(41/1040)*57.3=2.25 degrees with the Nagler 31 (assuming your figure of 41mm is correct). Using the rough and tumble approximation,

This is pretty close to the field stop method. Televue says the Nagler 31 is actually 42mm field stop so (42/1040) * 57.3 = 2.31 so you can see that with the extra mm we have narrowed the distance between the field stop calculation and the approximation formula. The difference between field stop and approximation is 1.7 tenths of a degree or only ten arc minutes out of 2.3 degrees, so it's a pretty good approximation.

Edited by gnowellsct, 11 May 2017 - 09:46 PM.

#4 gnowellsct

Sorry, maybe I wasn't clear, but I want to encode these calculations into this extensive eyepiece spreadsheet I have. So an interactive website isn't really the kind of help I was looking for. I need to understand the underlying calculations so I can use them to modify my spreadsheet.

-Leif

Yah I put up a more detailed explanation in the second post,which you might not have seen when you wrote this.

#5 astro744

'Apparently' this difference has to do with distortion. I would like to understand it a little better myself but yes you are correct. Now try the same with the Type 4 Naglers and you will find the numbers are very close to 82 deg. In fact compare the 13NT6 and 12NT4 side by side one in each eye and the 12NT4 apparent field appears larger and the field stop diameters (17.6mm for 13NT6 and 17.1mm for 12NT4) seem to confirm this as they are very close. The true field of the 12NT4 is almost that of the 13NT6 yet there is a 1mm focal length difference so apparent field has to be larger. The percentage difference between 12 & 13 is not the same as the percentage difference between 17.1 and 17.6.

I understand distortion plays a part an am not sure of the calculation for it but I do know that when I look through the 12NT4 the apparent field appears 'apparently' larger that that of the 13NT6. Perhaps the extra eye relief and larger eye lens of the 12NT4 plays a part here but when I put them side by side with one in each eye at a blue sky the 12NT4 looks bigger and I can see the edge in both. I haven't tried reversing the eyepieces L/R as my right eye is my dominant and observing eye so I'll test again to see if it makes a difference.

#6 astro744

You haven't introduced the focal length of your SCOPE into the calculation using the second technique.

RealFoV = (Eyepiece Field Stop / Focal Length Scope) * 57.3

So for a Tak FS128, at 1040 mm FOCAL LENGTH OF THE SCOPE (aperture in mm times the focal ratio), so the 128 mm aperture Tak FS128 is f/8.1, 8.1*128=1036.8 mm, so you can see I've rounded a bit, but 1040mm is good nuff.

you get

(41/1040)*57.3=2.25 degrees with the Nagler 31 (assuming your figure of 41mm is correct). Using the rough and tumble approximation,

1040/31= 33x magnification

82 afov / 33 = 2.48.

This is pretty close to the field stop method. Televue says the Nagler 31 is actually 42mm field stop so (42/1040) * 57.3 = 2.31 so you can see that with the extra mm we have narrowed the distance between the field stop calculation and the approximation formula. The difference between field stop and approximation is 1.7 tenths of a degree or only ten arc minutes out of 2.3 degrees, so it's a pretty good approximation.

Greg N

No the OP is not calculating true field and is using the formula independent of the 'scope focal length and substituting the eyepiece focal length to work out the apparent field. There was a discussion about this a while ago and someone called it the 'pseudo' apparent field so maybe do a search for it.


Equation to find distance between objective and eyepiece - Astronomy

The Barlow Lens, invented in the nineteenth century by the British mathematician and physicist Peter Barlow (1776-1862), is a negative (concave) lens fitting inside the focuser of a telescope. Unlike the better known positive (convex) lens a negative one does not cause light passing through it to converge to a focus. On the contrary, a negative lens causes light entering it to diverge as if from a ‘virtual focus’ (Figure 1). For simplicity, in all the diagrams, the Barlow is shown as a single lens. In reality it will be comprised of two or more elements for better optical performance (particularly colour correction).

The Barlow Lens is placed a short distance inside the focus of the main telescope (Figure 2). Light entering has its path changed so that it converges less steeply. As a result the light leaving the Barlow appears to be coming from a much longer focal length telescope whilst actually moving the new focal plane back only a short distance.
Advantages and disadvantages
  • Since any eyepiece can now give two magnifications (with and without the Barlow) this potentially doubles the range of magnifications available.
  • Because of the greater focal ratio provided by the Barlow the quality of the eyepiece needed in order to give a good image is reduced. An eyepiece that was quite indifferent at say f/5 could perform much better at f/10 when paired with a 2x Barlow.
  • Short focal length eyepieces often have small eye relief which can be uncomfortable to use. When used with a Barlow, short to medium focal length eyepieces usually retain close to their original eye relief. Therefore, rather than use a short focal length eyepiece it can be more comfortable to use a longer focal length one combined with a Barlow. So for example a 20mm eyepiece with a 2x Barlow may well be easier to use than a 10mm on its own.
  • Adding an extra optical element into the optical train has the potential to degrade the image because of any imperfections of its own. As long as you use a quality Barlow this should not be a significant problem.
  • When using a Barlow with long focal length eyepieces, the eye relief can increase significantly beyond that for which the eyepiece was designed. This can result in ‘vignetting’, the falling off in light towards the edge of the field as the outer parts of the field of view are no longer able to “see” the full aperture of the objective. How important this may be to you depends on the construction of your eyepieces and on the type of observing you plan to do. If you are only interested in the centre of the field, for example when planet observing, then any vignetting at the edge is irrelevant. If however your interest is variable star observing then having a fully illuminated field is very important.
Barlow Maths
  1. f - The focal length of the Barlow Lens.
  2. d - How far inside the primary focal plane the Barlow is placed.
  3. s - How far inside the new focal plane the Barlow is placed.

Consider the case where the Barlow lens is placed a distance inside the new focal plane equal to its focal length so s=f. In this case equation (i) becomes (f/f) + 1 = 2. Thus for any 2x Barlow the length of the tube will be roughly equal to the focal length of the Barlow.

The real world

When the image is in focus the focal plane of the eyepiece and that of the objective/mirror, after travelling through the Barlow lens, are at the same position. To give the Barlow’s nominal magnification these focal planes should meet at the end of the Barlow tube. The table below gives specific details on all three. The nominal focal distance is the distance of the new focus beyond/inside the top of the Barlow tube.
Barlow 1 Barlow 2 Barlow 3
Nominal Amplification 2x 2x 4x
Focal length 80mm 70mm 25mm
Nominal focal distance 0mm 0mm 4mm beyond
Barlow 1 Barlow 2 Barlow 3
Nominal Amplification 2x 2x 4x
Eyepiece 1 (18mm beyond) 2.2x 2.3x 4.4x
Eyepiece 2 (13mm inside) 1.8x 1.8x 3.2x
Measuring the focal length

From the above it is clear that knowing a Barlow’s focal length can be useful. However, since it is a negative lens light is not brought to a focus. An internet search will turn up a number of methods, usually involving pairing the negative lens with one that is positive. This is fine if you have a suitable positive lens to use in the first place.


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