A Tedious Explanation of the Aperture

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  A Tedious Explanation of the f/stop  by Matthew ColeOur Home PageA History of Photography: The 2000sA Tedious Explaatio of !epth of   ieldPhotographers set their exposure usig a #ombiatio of shutter speeds  ad f/stops  to get the #orre#t amout of light o the film$sesor% The shutter speed regulates how log the film is exposed to light #omig through the les% The f$stop regulates how mu#h light is allowed through the les by &aryig the area of the hole the light #omes through% or ay gi&e film speed '()O* ad lightig #ombiatio there is oe #orre#t amout of light to properly expose the film% This amout of light #a be a#hie&ed with may differet #ombiatios of f$stops ad shutter speeds% !espite beig oe of the exposure #otrols i photography+ the f$stop remais a sour#e of #ofusio ad mystery to may photographers+ e&e to some who use it all the time% ( fid it iterestig that the lo#al #amera shop has pi#tures uder glass o the #outer showig a s#ee usig a rage of fo#al legths 'for a good example of this+ see my fried !a&e !ahms, -es o#al -egth Chart*+ photos showig the same s#ee prited at differet ad photos showig a a#tio s#ee shot at differet shutter speeds% All that is assumed to be of iterest ad #omprehesio to the #ustomers% /hat they don't   ha&e is a set of photos showig depth of field+ or a s#ee shot at a rage of exposure #ombiatios where the f$stop,s effe#ts are show% Maybe it ust ta1es too mu#h explaatio% /ell+ too mu#h explaatio is what this page is all about+ ad (,ll go o&er the f$stop ad espe#ially its iitially#ofusig umberig at some legth% Fill That Bucket!  My fa&orite aalogy for exposure is fillig a bu#1et with water% A bu#1et is of fixed si.e ad eeds a #ertai amout of water to fill it+ ust li1e film or a digital sesor+ whi#h is of a set sesiti&ity 'the ()O* ad eeds a #ertai amout of light to optimally #apture a image% To fill your bu#1et+ you #a pour a small stream of water for a log time or a fast stream of water for a short time% Either way+ you ed up with the same amout of water% ( photography+ the si.e of the stream of the water is aalagous to the f$stop+ the legth of time you pour is aalagous to the shutter speed+ ad the si.e of the bu#1et is aalagous to the film speed% 3roadly spea1ig+ from the bu#1et,s poit of &iew+ it does,t matter whi#h #ombiatio of stream si.e ad legth of time you #hoose as log as the right amout of water eds up #omig i% ilm is the same4 withi limits+ it is idifferet to the #ombiatio of time ad amout of light as log as the right amout of light e&etually arri&es% Shutter Speeds  )hutter speeds are a bit easier to uderstad+ so (,ll start with those% 3oth exposure #otrols ru through a se5ue#e of settigs whi#h i&ol&e doublig ad hal&ig the amout of light rea#hig the film% )hutter speeds are measured i se#ods ad fra#tios of a se#od ad so the doublig ad hal&ig is fairly selfe&idet% Oe 5uarter se#od is half as log as oehalf se#od but is twi#e as log as oeeighth% Oe se#od is twi#e as log as half a se#od ad half as log as 2 se#ods% (t,s pretty easy+ ad this wor1s through the whole se5ue#e of shutter speeds% O my old   6i1o E+ for ista#e+ the shutter speed se5ue#e is: 7 se#ods 8 se#ods 2 se#ods 9 se#od 9$2 se#od 9$8 9$7 9$9 9$;0 9$<0 9$92 9$20 9$00 9$9000Ea#h of these settigs is #learly half$double the legth of time of its immediate eighbours 'O=+ ( 1ow+ 9$9th is,t exactly  half the time of 9$7th ad 9$92th is,t exactly  half the time of 9$<0th+  but it,s #lose*% This doublig$hal&ig is thus pretty simple to #omprehed for this exposure #otrol% F/Stops f$stops are a bit more #ofusig be#ause the umbers appear so arbitrary% This is the stadard se5ue#e of f$stops from f$9%8 to f$22% Although it may ot seem ituiti&e at first+ i this se5ue#e the f$9%8 settig lets i the most light while the f$22 settig lets i the least% Also+ ea#h of these f$stops has pre#isely the same hal&ig$doublig relatioship as the shutter speed se5ue#e% 9%8 2%0 2%7 8 %< 7 99 9< 22 O the fa#e of it+ goig from f$8 to f$%< does,t soud li1e hal&ig the amout of light% /hat,s more+ %< is a larger umber ad souds li1e it ought to be more light+ ot less% 6either does f$8 to f$2%7 soud li1e doublig the amout of light% ( fa#t+ ea#h of the umbers i this se5ue#e is a hal&ig$doublig of the amout of light from its immediate eighbours+ ust li1e the shutter speed settigs are% 6ot oly that+ but it ma1es sese+ as ( shall show below% The reaso that both the hal&ig ad doublig ad the smaller umbers mea more light thigs ma1e sese is that the f/stop is a ratio % The ratio is betwee the diameter  of the aperture i the les ad the focal length  of the les% The fo#al legth is geerally measured i millimeters+ so we,ll sti#1 with those as our uit of measure% O a 0mm les+ f$2 is sayig that the diameter of the aperture is 2mm% The ratio is: 0$2 > 2% That seems pretty straightforward% A good 5uestio might be+ what is the area of that aperture? /ell+ the aperture is usually a set of fi&e to fiftee blades whi#h form a roughly #ir#ular hole+ so we,ll use the formula for the area of a #ir#le+ whi#h as (,m sure you,ll re#all is @  radius 2 % or @ (,ll use ;%989B2<% O our 0mm les+ the aperture at f$2 has a diameter of 2mm whi#h is a radius of 92%mm% The area of the aperture is thus @  92% 2 + or ;%989B2<  9<%2+ or 8B0%B s5uare millimetres% This fa#t by itself is,t all that useful% (t is  useful i relatio to the ada#et f$stops% /hat is the area of the aperture at f$2%7? /ell+ be#ause the f$stop is a ratio of the fo#al legth to diameter+ our 0mm les at f$2%7 would ha&e a diameter of 0$2%7 > 9D%7<mm% emember+ we ha&e to di&ide that by 2 to get the radius of 7%B;mm+ so the area of the #ir#le thus formed would be @  7%B; 2 + or 20% s5uare mm% oudig off a bit+ that,s about 20 s5% mm at f$2%7 ad 00 s5% mm at f$2+ a double$half relatioship% AhaF )o that,s itF The area of the hole doubles and halves + it,s ust represeted by a ratio o the lesF 6o woder it,s so dar #ofusig%  Here,s a table of the aperture areas for the #ommo f$stops for a 0mm les: f/stop Diameter of aperture mm adius of aperture mm Area of Aperture s#$ mm f$9%0 0%0 2%0 9+B<; f$9%8 ;%D 9D%B 9+002 f$2%0 2%0 92% 8B9 f$2%7 9D%B 7%B 20 f$8 92% <%; 92; f$%< 7%B 8% <; f$7 <%; ;%9 ;9 f$99 8% 2%; 9< f$9< ;%9 9%< 7 f$22 2%; 9%9 8 'As show o les* '0mm di&ided by f$stop* '9$2 the diameter* 'pi  the radius s5uared* (f you loo1 dow the #olum of figures o the right+ you #a see the 'more or less* doublig$hal&ig goig o up ad dow the #olum% Gou #a see also how the big umbers ma1e for smaller areas si#e the f$stop umber is beig di&ided ito the fo#al legth+ the hal&ed+ the s5uared+ the multiplied by @% (t,s o woder this seems obs#ure%/hy ot ust #all for the area of the aperture dire#tly? A #ouple of reasos% irst of all+ if you ha&e a 0mm les o ad say ( shot this with my 0mm at 9$92th of a se#od ad a aperture area of <; s5uare millimeters you will impart #orre#t ad exa#t iformatio that pre#isely .ero  people will uderstad% (t,s mu#h easier to say ( shot this at 9$92th at f$%<% Also+ <; s5uare millimeters is f$%< oly with a 0mm les4 if your les is a ;mm+ or a 7+ or a ;00+ the ratio #hages ad the exposure is differet% That <; s5% mm is about f$8 o the ;mm+ f$B% o the 7mm ad f$;2 o the ;00% =owig oly the area of the aperture re5uires also 1owig the legth of the les to be iformati&e as to the amout of light #omig through the les% The f$stop figure i#orporates both of these i oe useful if iitially #ofusig measure ad the les legth is immaterial% (t,s shorthad+ i effe#t% /he you say f$7+ you mea for this fo#al legth 'the f?*+ gi&e me a aperture whose area is su#h that diameter of the resultig #ir#le goes eight times ito my fo#al legth% ortuately+ the les ma1ers figure out all these thigs ad ust mar1 the f$stops o the les for us% They,re doig us a big fa&or% So% does that mean f/& is the same brightness of illumination on the film/sensor regardless of focal length of the lens' Ges% That,s why they,re so hadyF (t,s also why hadheld light meters wor1they ha&e o idea what film si.e or #amera body or les you,re usig+ but they #a tell you that 9$92th at f$7 is the #orre#t exposure 'or at least oe of a whole host of e5ui&alet exposures+ we,ll get to that later*% (t does,t matter if you set that f$7 o a 20mm or a 800mm+ or if the #amera is from 9B8 or from last Iuly% (ot it% ) think$ *hat about other f/stop terms'  *hen people talk about a fast lens% +hat does that mean' -eses are referred to by their maximum aperture 'that,s the biggest hole+ the smaller umber*% Thus+ 6i1o made 'at least* four 27mm leses at oe poit+ a 27 f$9%8+ a 27 f$2%0+ a 27 f$2%7 ad a 27 f$;%% All four of these leses had f$8+ f$%<+ ad so o up to f$9<4 they were distiguished by the maximum amout of light they #ould let i% The 27mm f$;%+ oe of whi#h ( ow+ whe set to its maximum aperture of f$;%+ lets i oe third less light that the 27 f$2%7% The 27 f$2%7+ i tur+ at its maximum aperture+ lets i oly half the light of the 27 f$2%0 at its maximum aperture% The 27 f$2%0 lets i oly half the light of the 27 f$9%8 at its maximum aperture% -eses whi#h ha&e wide maximum apertures ad let i lots of light are #alled fast leses% -eses whi#h let i #omparati&ely less light at their maximum apertures are #alled slow leses% The 27 f$9%8 is a &ery fast 27mm4 27 f$2%0 would be a fast les4 the 27 f$2%7 would be sort of regular+ for whi#h there is,t really a ame4 the 27 f$;% would be 1id of slow% That 27 f$9%8 sold for eough ew that  6i1o did,t ma1e may4 o#e dis#otiued+ their pri#e i the used mar1et wet upF Gou #a fid them o e3ay from time to time goig for J2+00 or more% 6i1o i 2090 itrodu#ed a 28 f$9%8 les+ ust a bit wider+ so you do,t ha&e to buy used but you still ha&e to pay aroud J2+00% *h, +ouldn-t ,ou al+a,s use a fast lens' /eight ad expese% To get those larger diameter apertures meas you eed larger pie#es of glass mouted i #orrespodigly larger les barrels% They,re harder to maufa#ture+ the les  barrel 1eeps gettig hea&ier to hold all that glass i aligmet so it all gets weighty i a hurry+ they,re harder to autofo#us ad they,re more #hallegig opti#al desigs% ( the ragefider world there start to be #o#ers about the a##ura#y of the fo#usig si#e depth of field gets to be &ery limited at large apertures% Also+ there ha&e bee &ery fast leses made whi#h ha&e the reputatio of beig really i#e wide ope but 1id of doggy stopped dow% (f you ormally do ot use the fast les at its widest settigs+ if you are mostly at+ say+ f$7+ the you are #arryig aroud a hea&y ad expesi&e opti# whi#h may be uderperformig its #heaper brether stopped dow% The si.e pealty is really ob&ious i the log leses% The weight balloos ad the #ost s1yro#1ets% or ista#e+ ( used to ow a 6i1o ;00mm f$8% E!( les% The ( is iteral fo#us+ the E! had to do with the Extralow !ispersio glass used% (t was a sweet les+ ;00mm i legth+ with sil1y smooth 'maual* fo#usig ad weighed i at 2 lbs% 2%B o.% 'B7Bg*% (f ( stepped up to the ;00 f$2%7 les the weight wet to  lbs% 7 o. '200g*% 6ot fast eough? How about  6i1o,s ;00 f$2? (t weighed i at 9 lbs% <%B o.% 'D000g*% The ;00 f$2 pi#1s up 2 9$; stops o&er the ;00 f$8% ( owed+ but it ta1es a emietly hadholdable telephoto that fits i the #amera  bag ad ma1es it ito a uwieldly uit eedig a tripod+ re5uirig its ow suit#ase ad weighig se&e times as mu#h% The f$2s still sell used i the J20+000K rage% Gou also see the si.e i the .oom leses% Most moder #osumer .ooms are hady+ light ad slow% They are also ha&e a &ariable maximum f$stop a#ross their .oom rage% The professioal le&el leses ted to be fixed f$stop 'the 6i1o D0200 f$2%7+ for ista#e+ is f$2%7 a#ross the whole rage+ is a stadard pro les+ but it weighs a lot ad #osts J2+00*% ( e&erythig there are tradeoffs%
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