Formulas Optica Geometrica (by Carrascal)

7/23/2019 Formulas Optica Geometrica (by Carrascal)

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}wdnj ek`hwsdnjYFktk~ gk fj }wdnj ek`hwsdnjX YGd`}wsd`~X YK~}ko`~X YFklwk~X Y]sd~hj, Gd~}ks~dlX Y^d~wkhj~ nklwsjg`~

skjfk~X YDl~ws{hklw`~ }wdn`~X YKf `o` a{hjl`X

lgdnk gk skbsjnndl l 8 n / r

Gd~}ks~dl ns`hwdnj l 8 l !$

Njhdl` }wdn`!F$ 8 l ~ ld ~dJ

l g~

8 n w

]sdlnd}d` gk Bkshjw, Kf njhdl` }wdn` j f` fjse` gk {lj wsjtknw`sdj skjf gk fjf{z k~ k~wjnd`ljsd`,

!F$ 8 Jl g~ 8 =

Fktk~ gk fj }wdnj ek`hwsdnjD, Fj~ wsjtknw`sdj~ kl f`~ hkgd`~ a`h`elk`~ ~`l sknwdflkj~

DD, Kf sjt` dlndgklwk& kf skbsjnwjg` t fj l`shjf k~wl kl {l hd~h` }fjl`

DDD, Fkt gk fj skbsjnndl gk ^lkfd{~ !^lkff$ l ~kl 8 l% ~kl %

^d l% < lkf sjt` ~k jnksnj j fjl`shjf

^d l% 6 lkf sjt` ~k jfkoj gk fj l`shjf

Skbfkqdl w`wjf, le{f` fhdwk~kl F 8 l% / l 6 :

DR, Fkt gk fj skbfkqdl 8 %

R, Fj~ wsjtknw`sdj~ gk fj f{z j wsjr~ gk gd~wdlw`~ hkgd`~ ~`l skrks~dcfk~

Kn{jndl gk fj~ wsjtknw`sdj~? l 8 g !l W$ / g~ l / q ( g !l gq/g~$ / g~ 8=

l / t ( g !l gt/g~$ / g~ 8=

l / z ( g !l gz/g~$ / g~ 8=

Skfjnd`lk~ gk C`{tks

K~wsjwdbdnjndl k~bsdnj l S ~kl 8 nwk 8 l= S= ~kl


2/6

=

K~wsjwdbdnjndl }fjljl ~kl 8 nwk 8 l= ~kl =

Gd`}wsd` k~bsdn`

Dlrjsdjlwk gk Jcck l ! : / s ( : / ~ $ 8 l% ! : / s ( : / ~% $

l% / ~% ( l / ~ 8 !l% ( l$ / s

K~bksj kl z`lj }jsjqdjf, Dlrjsdjlwk gk Akfh`fwz? l t 8 l% t% %

J{hklw` fjwksjf?8 t% / t 8 ( !~% b $ / !~ b % $ 8 !~% l $ / !~ l% $

J{hklw` jle{fjs?8 % / 8 ~ / ~% 8 ( b / ! b %$ 8 l / ! l %$

B`njf `cokw` !~% 8 $ b 8 ( s l / !l% ( l$

B 8 l / b 8 ( !l% ( l$ / s

B`njf dhjekl !~ 8 $ b % 8 s l% / !l% ( l$

B % 8 l% / b % 8 !l% ( l$ / s

b / b % 8 ( l / l% b / ~ ) b % / ~% 8 :

B`shj gk fj dhjekl

^d ~ % < = 88< dhjekl skjf^d ~ % 6 = 88< dhjekl rdsw{jf

^d < : 88< dhjekl hjt`s^d 6 : 88< dhjekl hkl`s

^d < = 88< dhjekl gksknaj

^d 6 = 88< dhjekl dlrkswdgj

Gd`}wsd` }fjl`

^{}ksbdndk }fjlj skbsjnwjlwk !s 8 $ ~% 8 l% ~ / l

K~}ko` k~bsdn`

K~}ko` k~bsdn` l% 8 ( l

Kn{jndl gkf k~}ko`: / ~ ) : / ~% 8 3 / s 8 : / b

Gd~wjlndj b`njfb % 8 b 8 s / 3

nlnjr` b`n` skjf& b`njf 6 =


3/6

n`lrkqjb`njf B% rdsw{jf& b % < =

J{hklw` fjwksjf 8 t% / t 8 ( ~% / ~

Dhjekl^d ~ % < = 88< dhjekl rdsw{jf^d ~ % 6 = 88< dhjekl skjf

Fklwk~

Fklwk~ Kl kf jdsk l% 8 l 8 : 9 b % 8 ( b

Fklwk es{k~j?% 8 !l ( :$ !: / s: ( : / s3$ ) !l ( :$

3 g / !l s: s3$

Fklwk gkfejgj?

% 8 !l ( :$ !: / s: ( : / s3$

N`lrkseklwk?b`n` dhjekl skjf& b % < =

Gdrkseklwk?b`n` dhjekl rdsw{jf& b % 6 =

: / b % 8 : / ~% ( : / ~

J{hklw` 8 t % / t 8 ~ % / ~

Dhjekl^d ~ % < = 88< dhjekl skjf^d ~ % 6 = 88< dhjekl rdsw{jf

N`lrkseklndj gk {l g`cfkwk]kejg`? % 8 %: ) %3

Gk~}kejg`? % 8 %: ) %3 ( g %: %3

]sd~hj

N`lgdndl gk khkseklndjL` khksek ~d < 3

fdg`lgk

fdk~ kf le{f` fhdwk t k~ kf le{f` gkf

}sd~hj

Gk~rdjndl !$ 8 : ( 3%( g`lgk : k~ kf le{f` n`l kf {k dlndgk 9 3% kf le{f` n`l kf{k khksek gkf }sd~hj

]sd~hj gkfejg` 8 !l (:$

Gk~rdjndl hldhj h

h 8 3 : (

: 8 3%


4/6

@cwklndl gkf lgdnk gkskbsjnndl

l 8 y ~kl Y!h) $ / 3X x / ~kl !/3$

Gd~}ks~dl

l 8 l !$ 8 J ) C / 3 ) N/ 7 ) ,,,

Gd~}ks~dl ns`hwdnj g l / g

Lhks` gk Jcck g 8 !lg ( :$ / !lB ( lN$

g< ;15,2 lh !Ak$ jhjsdff`B< ;72,: lh !Ae$ rksgkN< 2;2,> lh !A$ s`o`

Kl rdgsd`~ }wdn`~ 3= 6g 6 5;

NS@ULg < ;=

BFDLWg 6 ;=

Gd~}ks~dl kl }sd~hj~ g8 ~kl gl / !n`~ :% n`~ 3%$

^d~wkhj~ nklwsjg`~ skjfk~

Fdhdwjndl gk sjt`~

Gdjbsjehj gk j}ksw{sj !GJ$@sdbdnd` {k fdhdwj fj kqwkl~dl gkf ajz {k }klkwsj kl f }s`nkgklwk gkf

}{lw` gkf `cokw` ~dw{jg` kl kf kok gkf ~d~wkhj

]{}dfj gk klwsjgj !]K$ Dhjekl gkf gdjbsjehj gk j}ksw{sj kl kf k~}jnd` cokw`

J}ksw{sj !J$J 8 / b %g`lgk k~ kf gdhkws` gk fj ]K t b fj b`njf

Jcksw{sj skfjwdrj?N{jlg` kf `cokw` k~w kl kf

Lhks` gk jcksw{sj !L$ L 8 b % /

J}ksw{sj l{hsdnj !JL$!n{jlg` kf `cokw` k~w jgd~wjlndj bdldwj$

JL 8 l ~kl g`lgk l k~ kf lgdnk kl kf k~}jnd` `cokw`

Jckssjnd`lk~ kl f`~ ~d~wkhj~ nklwsjg`~

Jckssjndl k~bsdnj

N`hj ]s`}dj gk }{lw`~ kqwsjqdjfk~ n{jlg` fj~ jcksw{sj~ ~`l esjlgk~, N{jlg` fjdhjekl gk {l }{lw` ~k}jsjg` gkf kok l` k~ fj {k ~k `cwklgsj


5/6

#}jsjqdjfhklwk# ~dl` {k k~w gk~}fjzjgj,

J~wdehjwd~h`

N{srjw{sj gk dhjeklN{jlg` fj~ dheklk~ gk f`~ }{lw`~ gkf }fjl` `cokw` l` k~wl w`gj~ kl kf

}fjl` dhjekl }jsjqdjf

Gd~w`s~dl ^k gkck j {lj bjfwj gk n`l~wjlndj gkf j{hklw` fjwksjf

Gd~w`s~dl gk n`s~?J{hklw` hjt`s {k kf }jsjqdjf

Gd~w`s~dl gk cjssdf

^d~wkhj sw`~n}dn`?N{jlg` kf ~d~wkhj k~w kqklw` gk gd~w`s~dl

Dl~ws{hklw`~ }wdn`~

L gdjbsjehjB 8 b / g !jgdhkl~d`ljf$g`lgk b k~ fj gd~wjlndj b`njf t g kfgdhkws` gk fj j}ksw{sj

Gdjbsjehj ndsn{fjs ~kl 8 :,33 /g

L gd`}wsj~] 8 : / b!n{jlg` b ~k kq}sk~j kl hkws`~& ] ~khdgk kl gd`}wsj~$

Fhdwk gk sk~`f{ndl? ~k}jsjndl hldhj j fj {k }{kgkl k~wjs g`~ }{lw`~ n`lwde{`~ gkf `cokw``c~ksrjg` gk b`shj {k ~k }{kgkl gd~wdle{ds n`h` }{lw`~ gdbksklndjg`~,

~kl 8 :,33 / !3s$g`lgk s k~ kf sjgd` gkf `sdbdnd` ndsn{fjs t k~ fj f`ledw{g gk`lgj kl kf hkgd` l

l 8 = / l

~kl :,33 = / !3 s l$

Fhdwk gk sk~`f{ndl FS s :,33 = / !3 l$

( Hdns`~n`}d`

FS 8 :,33 = / !3 L$g`lgk L k~ fj j}ksw{sj l{hsdnj gkfhdns`~n`}d`

L 8 l ~kl !g`lgk l k~ kf lgdnk gkskbsjnndl$Kl {l hdns`~n`}d` kfknwsldn` L :=(3 8 jsn we !sjgd` gkf `cokwdr` / gd~wjlndjb`njf$

( Kl kf nj~` gk {l wkfk~n`}d` kl {k f`~ `cokw`~ ~k kln{klwsjlj {lj gd~wjlndj dlbdldwj& kf fhdwk gk sk~`f{ndl ~k skbdksk j fj~k}jsjndl jle{fjs hldhj sk~`f{cfk {k rdklk gjgj }`s

~kl 8 :,33 / !3 S$


6/6

Kf }`gks gk sk~`f{ndl gk}klgkklwksjhklwk gkf sjgd` gkf `cokwdr` t ~kgkbdlk l`shjfhklwk n`h` n`~kn

]`gks gk sk~`f{ndl gkf wkfk~n`}d`n`~kn 8 !3 S$ / !:,33 $

( ^d ~k `c~ksrj {l `cokw` j fj hldhj gd~wjlndj gk rd~dl

gd~wdlwj g= 8 3; nh& kl df{hdljndl hkgdj n`l S 8 :,3; hh&fj ~k}jsjndl hldhj gk gkwjffk~ {k kf ò` }{kgk sk~`frks k~

t=8 :,33 g= / !3 S$

Kf ò` a{hjl`

( Kf ò` ~k }{kgk n`l~dgksjs n`h` {l ~d~wkhj }wdn` b`shjg` }`s {l gd~}`~dwdr`& fj nslkj t kf nsd~wjfdl`,

( [l ò` l`shjf }{kgk jn`h`gjs ~dl bjwdej `cokw`~ ~dw{jg`~ aj~wj {lj gd~wjlndj hldhj gk 3; nh&}`~dndl {k ~k ffjhj }{lw` }sqdh`,( Kf }{lw` skh`w` k~ j{kf {k ~k ajffj j {lj gd~wjlndj }jsj fj n{jf kf ò` aj ffkejg` jf fhdwk gk

jn`h`gjndl !}jsj {l ò` l`shjf k~w kl kf dlbdldw`$,

Gkbknw`~ gk fj rd~dl h~ dh}`swjlwk~

HD@]J

Kl {l ò` hd`}k& fj dhjekl ~k b`shj gkfjlwk gk fj skwdlj,^{ }{lw` skh`w` l` k~w kl kf dlbdldw`,

L` klb`nj n`ssknwjhklwk f`~ `cokw`~ fkojl`~,^k n`ssdek n`l fklwk~ gdrkseklwk~,

AD]KSHKWS@]

J

Kf ò` ad}kshws`}k l` klb`nj n`ssknwjhklwk f`~ `cokw`~ nksnjl`~,Fj~ dheklk~ ~k b`shjl gkws~ gk fj skwdlj,^k n`ssdek n`l fklwk~ n`lrkseklwk~,

]SK^CDNDJKf ò` jf klrkoknks }dksgk bfkqdcdfdgjg ` }`gks gk jn`h`gjndl !jfkojhdklw` gkf

}{lw` }sqdh` n`l fj kgjg$& }`s f` {k rk hjf f`~ `cokw`~ nksnjl`~,^k n`ssdek n`l fklwk~ n`lrkseklwk~,

J^WDEHJWD^H@K~ {l gkbknw` gk fj k~bksdndgjg gk fj nslkj ` gkf nsd~wjfdl`& f` {k ~k wsjg{nk kl fjdhjekl gk {l }{lw` kl {l wsjz`,^k n`ssdek n`l fklwk~ ndflgsdnj~,

]edlj dldndjf !jlwk~ kl aww}?//k~,ek`ndwdk~,n`h/bd~dnj~$? aww}?//uuu,njssj~njf,lkw72,lkw/bd~dnj~/K~wj ~knndl !gk~gk fj }edlj dldndjf$? BSH[FJ^ / B^DNJ / ]WDNJ EK@HWSDNJ

F`~ j{w`sk~? Hjsd ]jz A`swkfjl` Ehkz k Djid Njssj~njf H`z` Nj~wsdff` gk G`l O{jl, ]jfklndj, !K~}jj$

N`ssk` kfknwsldn`? bd~dnj~Mtja``,k~

Kl fj skg gk~gk kf :;/=>/:441 ( fwdhj~ h`gdbdnjnd`lk~? 3>/=2/3==3( 33/=2/3==>
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Formulas Optica Geometrica (by Carrascal)