Cours d'Optique géométrique

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Université Pierre et Marie Curie - L1 - LP 103 - Année 2009-2010

Université Pierre et Marie Curie
erLicence 1 année
UE LP 103

Cours d’Optique géométrique

Reza.Samadi@obspm.fr

http://www.edu.upmc.fr/physique/lp103ElectOpt/


(illustration tirée du « Discours de la méthode » de Descartes , noter l’erreur …)
UE LP 103 - Cours d’optique géométrique -14/10/09 1/37

1 Bases de l’Optique géométrique......................................................................3
1.1 Faisceaux lumineux...................................................................................3
1.2 Lois de Snell-Descartes .............................................................................5
1.2.1 Loi de la réflexion ...............................................................................5
1.2.2 Loi de la réfraction..............................................................................5
1.3 Notion de stigmatisme ..............................................................................8
1.3.1 Stigmatisme parfait ............................................................................8
1.3.2 Stigmatisme approché ........................................................................9
1.4 L'approximation de Gauss.......................................................................10
1.5 Relation de conjugaison des dioptres sphériques ...................................11
2 Systèmes optiques de bases ..................................... ...
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            !       ""      Cours d’Optique géométrique  #$%&'(%)  *+,,,%%"%)*-.."/  
(Discours de la méthode » de Descartes , noter l’erreur …)illustration tirée du «
       14/10/09 
 

    0  ./ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 1"2 .2 %   &..3" %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 4 %%  4  . ).2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%   . )"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 4 %  65   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%  6& ) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% & "* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ! %7 82  9 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %4  #.  ":   * %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  &-;   ( %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3)   . %  * %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %% 1- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 7 %% #.  ": "   %%%%%%%%%%%%%%%%%%%%%%%%%%%% 4 %% #.  ":    "   )-   < %%7  #.  ":    "   "   %%4 #.   = >.*.$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 6 %  6.. " ?*@%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 1.  ":    "  2 )-  %% 1.  ":    "   "   %% .. "". %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %7 " -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %7%  .. " %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %7%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ..    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% A  % 9.  .   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  % B. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %  4 .%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %7  "" %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %4  6 .  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %<  ! ." %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 7 5  * %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  7%  .    " ".. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  7%%    "  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 7% . .%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  7%% A" %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  7%%  3) . %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 7%%  7. . .%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 7% &"  + ."  ". %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 7        14/10/09 
7%%  7"  -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 7%% ".%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% < 7%% "  ".   C   -;   <  1 Bases de l’Optique géométrique 1"2 .2 D .  &. D   5 D "32  9 D #.  ":   *%  1.1 Faisceaux lumineux
Ampoule
Lentille
objet diaphragme écran       . 1    .8(   )  .8"  **  .8(:" ;  . .;    )"2 ".%  8   .8  - .2   .2 %  "     . .; + . -      " .% &  - .2     C   0E   -  "(.  " " :  .   %  0  %   A"  - .2 +  . "  .    ."   " F . - .2 );   2 D  E  " "E . - .2  "  .   %  5  - . +  . 1  . - ..;.    . ... %  -  (.    " 1% G) .  1  1    ))"   .
       14/10/09  
 

.;% A.   - .  1 "  " ..%  
F’
A1
O A2
1    .8  + · )" + * C .  . ))" ?*;  . .;@%  *;  ..  . 1 % G  . *  ; .   . "" ? ; H . .   -@E . )"   . " . )"  .%  "* . .   " . "" . )"  .% · 8" "".  . .;+ . .; 2"  )"   ?)(.  .  *@  . ..   %  )    . .;  "  ".  . .. *%     2"   )"  .;   )"  . ( C  ).2  *  . )" ?. " . * "  $@%
LASER
Diaphragme ajustable
       14/10/09 
Écran
7
1  1.2 Lois de Snell-Descartes >+  .  . )" ) (. 2.  <  . *.. &..% . E  <E 3" (.  )2  I3"  . *  ( "    "*"* .   . ""E . . E .   . J% A. -  . .  . ).2   . )" ? "@ C .  . " D   ( "   "" "".  . .;% 1.2.1 Loi de la réflexion & .  ?)"  2 .2 "@ .  . 1 7% . 8""E .  ).28 ?1 7@% ·  )" )."*   . . 8"" ?. )  . .    . )" "@% ·  . )K  8%  . " + (..   :   %
 
  1.2.2 Loi de la réfraction ) ..  "" + ·  (: .  . + . (L  .8  M2. ( ?1 4@  .   (. . ;  . )" .   ?1 4@% · 82.   ?1 <@+    .8  " .  +   .8"% /     $+@ ? ΛK  FΛ .   .% 8" (.    . C .8 ?K@%  "  )) 2    . (.  +   A" ?ClK 46! @  E
       14/10/09 
4
N ", N ). 3 1.  
air
eau
E4 E< E7 E7
 
   )  . - )" ?1 7@ + ·  - )"   . . 8""% · . 8"" ?@   )" ?@  .  . .+ n1sini n2sinr?@ F   .8"  .     . %  
       14/10/09 
 
 
<
 .  ).2 .+ &  O E   . P.  . . %  ) "M  CϑE  ..ϑ   " .Ka ) .  + n n1sin1an2sin1n2sin1a2 2n1 /   .OaE ?@ O   . 2  . ) . . ?@% 2.  " ))" .O a  . .;  )."*%    " "   *; . 2.)D ..a  ..  ).2 .%  .  )" .+ &   OE .O .  . .  ... QEϑR% KϑE . .. .b )" .@   .  +? . n1nsinbsinb1n1 1 2  n2    S.+  E . .  3" ?% @  . )+ n i n r 1 2  /   .8" 8 .  . C+  K "   F .   . .;  . . " ""..  . %  "  1 +  .  . )"  .  "  1 ?<<<4@ + I . .; "* :E  ..   C  E . "* - .   " . J%  1  .. " "   .%
       14/10/09 
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(2)
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    .; " .  "* . : . . "+ . :  .  ?@  . .  . : ?@ "   ."    .   . (.T   . C . .;   ." . (.  . ?" U@% /   " "  (. . .  . )"  3"    . ). . ." . 2   . .;  " .   .  ?%%"K@% 1.3 Notion de stigmatisme 1.3.1 Stigmatisme parfait
   & .   . 1 6+ &+  -;  ."% + .(:% 8+ .   C  &%  /   8    ":   C &% 8  ..  . -   ))"  8 8  ..  . .  )"2           14/10/09 6
8 %                        !"   #         $%   &     ' "  3 .2.  . 1 6E   )  . "   2"%  2.   2+ .  .. (. ?  2 )-  ...E  1 !@E .  (. ?   .8(: ." C .8)@  .  . ? 2"   @% M
F F’   ( 1.3.2 Stigmatisme approché  "   2  E "    " (     "*%   -;     "*   -        8 ;   . -;  ?&@%  &-; "+ -;  - . -  .  8 2 . 2 %  5 8.+ . . .  ?ϑ@  ..;.  . (: ?ϑ@%  .   (:   ":%  
       14/10/09 
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 ) 1.4 L'approximation de Gauss   9+  -; "  .  .82  9 . . -  .  )  . )(. " .82   -; ? . I )(. J   )(.   C ..  ..   .  .@. "2"   .  .2  ?%% C  " "  ."*.. ""  -; @%  /  . .   ? 1 @+ · ":+  -; ) . "  9 #.      . "*% · 9 . + G ".   ": ?0E08@ ) . . ' ' A B1Cteº 9 AB F . "9 .  .%   .     . ** " . ":%   .   .   . ":%  · 9 . + . "   ) . +  ' u1Cteº l u  F . "l .  .%  E .  .     .   . ":%  ·A  >.*.$+   ) . .+  
       14/10/09 
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n AB u1n'A'B'u'    ; .+ n/n' l1 9  3 "      .8(.  "      ; 2."  "  G3   .  *   . "*   . "   *% 1.5 Relation de conjugaison des dioptres sphériques &   *  " E  -  "( #E   &    . "   . "  ? 1   . " F O@% & . - &E " -  . C . )"E .  .   H  ?"" ..@   .  . " %     - ." AE )  .Κ" .2 &E  .    A%  -  )" "  .    C . .     A% &  ."  . -   .2 &  % & ..   ? "9 @E   ? G3 @  .       ..Κ%   .(.  - A )  . )(.   C .2 &     % 3 " " .  *  " "* % /     .(:   .   .  ..  ": ? G3  V@ +  n2n1n2n1 % 1 SA'SA SC   ".   . +  . ? 1 @  .(. C  *; -  "( ) D %% &| υ" . "  ; C .% 3 "  . +        14/10/09 
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