cours - profdephysique

  !"#$%&'( )*%+",
-.)/ "-#$%+0$-+12
$3+ , $%04 536,, $)%+ (,-+ $*"7%(#53 $3
*(-"%)53$%0$%$ 4$%08,"3 ."-0,6"34
'3!%+3) ,'9(%$*:%00)/ "-#$%
6+3%-" "-+( )#530'9(%$*:%$%03,"+$) 
$ 5363% .")-"3 ,"  %-$%+  3% $+"-,
0 '#+ +"),,4 ), %  ' $'"7 ',3 % ,)7%
0 $)+,.")-"3+(," 7)0"%,"0) -#$%0
'#+ 0)*%)$% 0 ,6$+"-, " ('" ##$%
06)%+%)+( ,3*)%3 3  ,6(- "% ' (%+ ",$ 
0*"&)*"+0*)%)*"
 (;%)#$%
*" 53
✔6$%0-$% !". (53%-"3'""70,6$+"-,
✔),*),)30' $'"7"#$%+,*<*0'" ++06"3+ 0,6$+"-,4,"-(,( )+(
0,6$%0+)%-9"%7()%)4,",$%733 06$%0%!" )'"
= %>3%-0,"+"),,0,6$+"-,
$3 +$3+,$%04,".$ *0,6$%0"' :,'""70,6$+"-,0('%00,"
+"),,0-+$+"-,
?@"AAB ?@"CCB ?@"' $-90
6$%0+ "!  6$%0%+ "!  6$%0+ "! 
,6$+"-,"% '",6$+"-, %(+"%+0)/ "-+(
*$0);-"#$% ?$ #D?%+ (
"% , -" 0 $%0 ,3*)%34 , - )+:  + *$)% + )-#. , '9(%$*:% +
%-$  )% "''" %+ "!- 0 $3! +3  $3 0 $+"-, 0 0)*%)$% E35368
FF.$)',37 "%053,",$%733 06$%0%$ 0 07 "%03 
'',)-"#$%
 %$%0$%$ 0. (53%-GDFFH+0-(,( )+(0"%,6") vD=IF*J+J
,,0)/ "-+('" 3%$3! +3 0'$ +0," 73 aD4F*K
 %$%0,3*)%30,$%733 06$%0 ?D2==%*+J,,0)/ "-+('" 3%+ $3
00)"*:+ aDFL*K
$,3#$%
λ= -
ν
λ==IF
FF ==4I*
"," 73 a0,6$3! +3 +03*<*$ 0 07 "%03 53
,",$%733 06$%00,6$%0$%$ ,6$%0+0)/ "-+(
λ
"=2==F−M
FF−2=24==F−
$)+
"
λ=2
"0)/ "-#$%+!)),
I -" +"%73,") 00)/ "-#$%
6(+",*%+0,";73 00)/ "-#$%+*3 ('" 
"3) "'',( demi-ouverture4-6+80) ,6"%7,$3 ,53,+!3 ,"*$)#( 0,"
+"-9-%+ ", 0'3),6$+"-,)%)4-6+,6"%7,%+ ," 0) -#$%0' $'"7"#$%
"!"%+0)/ "-#$%+,"0) -#$%0(;%)'" ,*),)30,"' *): &#%-#$%
+(-" +"%73,") 4%$+(N% "0)"%4"%0)*%)$%40('%00,",$%733 06$%0
?+0,"+"),,0,6$+"-,a
 !a
*" 53'$3 3%$+"-,0+O';,;%$3.%+;%4
θ= λ
"
4",$ 53'$3 3%
$3! +3 -) -3,") 4
θ=4×λ
"
4"!-?+a%*:+ +N% "0)"%
 "     #        
9"')+ P $' )(+(0$%0 "7@I
L
O
M
D
θ
obstacle

1 )/ "-#$%'" ,",3*): ,"%-9
",3*): ,"%-9+3%,3*): '$,O-9 $*"#534
- $ * ' $  (  0 6 3 %  ) % ; % ) + ( 0  " 0 ) " # $ % 
*$%$-9 $*"#53
9"53 "0)"#$%*$%$-9 $*"#530$%%"' $' 
;73 00)/ "-#$%4+$3+,;73 3' '$"%+
3 ,6(- "%
"% ," 0) -#$% 0 ' $'"7"#$% )%)#",4 +$3+ ,
;73  ' (%+%+ 3% *"&)*3* 06"*',)+30 ,
-$3,3   3' '$%+4 $% $#%+ 3% "
"
9"53 ;73  0 0)/ "-#$% '$:0 " ' $' 
0*)J$3! +3  ' $'$ #$%%,, 8 ," ,$%733
06$%00," "0)"#$%)%)4,&#%-#$%%
' $03)%+ '" "3 *<* %0 $)+ '$3  +$3+ ,
-$3,3  $% $ ! 0  0 '" + +
06"3+ 0,"+"-9-%+ ",
$%&'&()*'&&
-.%+ .( %-
 3' '$)#$%003&$%0
$%+  ,6"%)*"#$%- $)*%+Q0Q03&Q$%0R.
% '$)%+  '3+ <+  "/-+( )*3,+"%(*%+ '"
',3)3  $%0 ,  0(',"- ",$  $3 ,6/+ 0
03& ' +3 "#$%4 , 0(',"-*%+ (3,+"%+
-$ '$%0"%+8,"S$**T003&' +3 "#$%
' : 6<+  - $)(4 , 03& $%0 -$%#%3%+ ,3
' $7 )$%"%<+ *$0);(
$ 53 , 03& ' +3 "#$% $%+ )%3$U0",4 0
*<*. (53%-4-,,J-))%+ .: %+
+   ,        - #   .
#
!- 0 $%0 ,3*)%3 ,"  $3 ,3*):  ,"%-94 $% $#%+ - ('" ##$%
,3*)%33 ,6(- "%
)%)4,"$**003&$%0,3*)%3'3+0$%% 0,6$-3 )+(V
lumière + lumière = parfois ombre !
 $9( %-0$3 -
$%+  "!-"." ),6"%)*"#$%3!8$%0)'',"%W.",+"04 -@. 5'3)
 -@. 5)%0)#%-+
6&'( )%- *$%+  53 0 )%+ .( %- % $%+ +",4 0$%- !)),4 53 ) ,
#"4-6+80)  .
#/0déphasage1
X$-"3,")  
•3& )7%"3& $%+ 0)+  ",$ 53, "*',)+30*"&)*",003&
)7%"3&$%+"Y)%+"3&*<*)%+"%+0('9""7%3,$3*3,#',%#
0,"'( )$0B
•3&)7%"3&$%+0)+ ",$ 53,6"*',)+30*"&)*",
063%)7%", +"Y)%+ %*<* +*'53,6"*',)+30*)%)*",0,6"3+ 
0('9""7063%0*)J'( )$0'" &*',B
•$3 3%0('9""753,-$%534,03&)7%"3&$%+0)+"
$3  $+%)  03& $3 - -$9( %+4 $% ' $03)+ 03& $3 - -$%0")  8 '" #
063%*<*$3 -' )*") " &*',4,.%+06$3%7' *Y%+0-$3'
3%*<*.")-"3' )*") %03&.")-"3&-$%0") -$9( %+
= %+ .( %--$%+ 3-#!+0+ 3-#!
$ 5303&$%0)%+ .: %+4,3 03&)7%"3&6"00)#$%%%+
)4%3%'$)%+4,03&)7%"3&$%+%'9"4,"$**003&+ #
$% $ ! 3% *"&)*3* 06)%+%)+( 3  ,6(- "% % '" , 06
)4%3%'$)%+4,03&)7%"3&$%+%$''$)#$%0'9"4,"$**003&
0!)%+ $%$ !3%*)%)*3*06)%+%)+(3 ,6(- "%!$) 3%$-3 )+(
-$*',:+ ) , 03& )7%"3& $%+ ," *<* "*',)+30 % '" , 06
9"')+ P $' )(+(0$%0 "7@I

*" 53  ) , 03& )7%"3& % $%+ '" 0 *<* . (53%-4 ), )%+ .( %+
(7",*%+ *") , )%+ .( %- % $%+ '" !)), , 03& )7%"3& % $%+ '"
-$9( %+4 -"  , 0('9""7 % 3% '$)%+  %+  - 03& )7%"3& !" ) %
' *"%%-
I +" 0%+ ,03&)7%"3&
%-$%)0: 03&$3 -+-$9( %+4
3''$( % '9" % '$)%+  03 *),)3
Z$)+ , )7%"3& (*) '"  , 03& $3 -4
"!- 3% +" 0 -$ '$%0"%+ 8 ,3  +*' 0
'" -$3  '-#.
$**,6$%0' $'"78,"!)+v4$%"
τ=0
!
+
τ=0
!
) , 03& 0)+"%- $%+ (7",4 , )7%"3& '" # % '9" " )!%+ (7",*%+ 
""3'$)%+)%+ .( %-O$%+0$%-
 )%+ .( %- $%+ (7",*%+ -$%+ 3-#! '$3  +$3 ,'$)%+ '$3 ,53, ,"
0)/( %-0 +" 0+3%
% !"%-94 ) ," 0)/( %- 0 +" 0 -$ '$%0 8 3% 0*)J'( )$04 , 03&
)7%"3&'" #%'9"" )!%+% ""3'$)%+,)%+ .( %-
$%+",$ %-'$)%+
)%",*%+
2343563)4789
W∈ℤ
2343563)4789:9!54057:)189!5
W∈ℤ
1 )/( %-0*" -9
$3!%$%0!$) 53,6)%+%)+(,3*)%3"3'$)%+0('%00,"0)/( %-0
+" 0%+ ,03&)7%"3&)30+0Y0)/( %-0 +" 0[\+,)(
8,"0)/( %-0,$%733  %+ ,+ "E+'" -$3 3 '" ,03&)7%"3&4"'',(
"7 "%03 %$+(]+&' )*(%*:+ ]D0P0
)%)4
δ=!×τ−!×τ=!×Δ τ
•%+ .( %--$%+ 3-#!
δ=!×Δ τ=!×W×=W×λ
4"!-
W∈ℤ
•%+ .( %-0+ 3-#!
δ=!×Δ τ= !×
( W+ ) ×
=W+ ×λ
4
W∈ℤ
;456)478 
W∈ℤ
;456)4057:)18 !5
W∈ℤ
% (3*(
O'06)%+ .( %- -$%+ 3-#! 0+ 3-#!
%+%)+( *"&)*", *)%)*",
 "%7 ,3*)%3 $* 
)/( %-0 +" 0%+ 
,03&.")-"3& W^
( W+ ) ×
)/( %-0*" -9%+ 
,03&.")-"3& W^?
( W+ ) ×λ
2 $#$%06)%+ . "%7
&'( )*%+",*%+4$%$ !0( )0. "%7,3*)%3+$* 
$3 -" "-+( ) 3%;73 06)%+ .( %-4$%*3 ,"0)+"%-%+ 03&. "%7
,3*)%3$303&. "%7$* -$%(-3#!
Y0)+"%-+"'',(
)=λ×
"
4$_
•)+,6)%+ . "%70,";73 06)%+ .( %-%*:+ B
•?+,",$%733 06$%00,"$3 -,3*)%3%*:+ B
•+,"0)+"%-%+ ,$3 --$%0") +,6(- "%%*:+ B
•"+,"0)+"%-%+ ,03&$3 --$%0") %*:+ 
 $3,3 )%+ .( %#,,
6)%+ . "%7 0('%0 0 ," ,$%733  06$%0 ',3
,,+(,!(4',3,6)%+ . "%7+7 "%0)%)4%
,3*): '$,O-9 $*"#534,;73 06)%+ .( %-
- (( '"  -9"53 -$3,3   3' '$%+ %
$#%+0) )"#$%
9"')+ P $' )(+(0$%0 "7=@I
)7%"3&%$''$)#$%0'9"
S1
S2
M
d1
d2
)7%"3&%'9"

"%,"!)-$3 "%+4)," )!53- +")%$E+' (%+%+0-$3,3 !)!!" )"%+
,$% ,6"%7, $3 ,53, $% , 7" 0 "), 0 '"'),,$%4 +"-9 0693), 3  3% $,
*$3),,(4-$3,3 $%+0380)%+ .( %-0+ 3-#!
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