Lnss & Prism Considr light ntring a prism At th plan surac prpndicular light is unrractd Moving rom th glass to th slop sid light is bnt away rom th normal o th slop Using Snll's law n sin( ϕ ) = n sin( ϕ ) o sin( ϕ ) =. 75sin( 30 ) = 0. 875 ϕ = arcsin( 0. 875 ) = 6 o
Lns Lns is lik a sris o prisms Straight through at th cntr Sharpr wdg angls urthr out Mor ocusing urthr out Snll s law applid to gt th lns opration
Focal Points Two ocal points dpnding on surac & whr light coms rom Primary Focal Points ar Convx (a) whr divrg bam orms paralll light Concav surac (b) whr light appars to convrg whn it is convrtd into a paralll bam Scondary Focal Points Convx (c) whr paralll bam is ocusd Concav surac (d) whr paralll light coming in appars to divrg rom.
Typs o Lnss Convx (a) Biconvx or quiconvx (b) Planoconvx (c) positiv mniscus Concav (d) biconcav or quiconv () Planoconcav () ngativ mniscus Primary and scondary ocal points vry dpndnt on typ Planoconvx/Panloconcav asist to mak Two surac lnss about twic th pric
Frsnl Lns Lns with thicknss rmov Chapr, but can b lowr quality Rason: diraction cts at stp boundris
Lns Convntions From Jnkins & Whit: Fundamntals o Optics, pg 50 Incidnt rays travl lt to right Objct distanc s + i lt to vrtx, - i right to vrtx Imag distanc s' + i right to vrtx, - i lt to vrtx Focal lngth masurd rom ocal point to vrtx positiv or convrging, ngativ or divrging r positiv or convx suracs r ngativ or concav Objct and Imag dimnsion + i up, - i down rom axis
Gaussian Formula or a Sphrical Surac Th radius o curvatur r controls th ocus Gaussian Lns ormula n s n + s n n = r whr n indx on mdium o light origin n indx on mdium ntrd r = radius o curvatur o surac Clarly or s' ininit (paralll light output) thn s = (primary ocal lngth) n s + n = n = nr = n n n n r
Thin Lns Assum that thicknss is vry small compard to s, s' distancs This is otn tru or larg ocal lngth lnss Primary ocus on lt convx lns, right concav Scondary ocus on right convx, lt concav I sam mdium on both sids thn thin lns approximation is =
Basic Thin Lns ormula Basic Thin Lns ormula Lns Makr's ormula s + = s = r r ( n )
Magniication and Thin Lnss positiv or convx, ngativ or concav Magniication o a lns is givn by s m = = s = s s Magniication is ngativ or convx, positiv or concav
Thin Lns Principal Points Objct and imag distancs ar masurd rom th Principal Points Principal point H Location dpnds on th lns shap H also dpnds on a thin lns orintation Not i you rvrs a lns it otn dos not ocus at th sam point Nd to look at lns spciications or principal points Thick lnss hav sparat Principal points
Thick Lns Formula As lns gts thickr optical suracs may b not mt Lns thicknss t c (btwn vrtx at th optical axis i.. cntr) Now lns ormula much mor complicatd Distancs masurd rlativ to th principal points H or light coming rom th ront H or light coming rom th back o lns ( n ) tc = ( n ) + r r n r r Not simpl lns ormula assums t c = 0 which is nvr tru But i is larg thn r s larg and t c is small so good approximation Not plano-convx r = and thin = thick but principal point changs
Vry Thick Lnss Now primary and scondary principal points vry dirnt A = ront vrtx (optical axis intrcpt o ront surac) H = primary (ront) principal point A = back vrtx (optical axis intrcpt o back surac) H = scondary (back) principal point t c = cntr thicknss: sparation btwn vrtx at optic axis Rlativ to th ront surac th primary principal point is n A H = tc r Rlativ to th back surac th scondary principal point is n A H = tc r l ctiv ocal lngth (EFL): usually dirnt or ront and back
Numrical Aprtur (NA) NA is th sin o th angl th largst ray a paralll bam maks whn ocusd NA = ( ) sin θ = whr θ = angl o th ocusd bam φ = diamtr o th lns NA < ar common High NA lnss ar astr lnss NA is rlatd to th F# F# = NA φ
Combining Lnss Can combin lnss to giv Combination Ectiv Focal Lngth I many thin lnss in contact thn = + + Two lnss and sparatd by distanc d To compltly rplac two lns or all calculations Nw imag distanc or objct at ininity (g lasr bam) = + d or 3 L Distanc rom irst lns primary principal point to combind lns primary principal point d D = = + Distanc rom scond lns scondary principal point to combind lns scondary principal point d D = Combind "thick lns" xtnds rom D to D' d
Combining Two Lns Elmnts Combind objct distanc s s = s D Combind imag distanc s' s = s D NOTE: Combind objct/imag distanc may chang sign Th thick lns ollows th standard ormula s + s Combind magniication s m = s Scondary ocus distanc rlativ to nd lns vrtx is: == = + Not som dvics (.g. tlscops) cannot us ths ormulas D