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Class7

# Class7 - Read Hecht from Chapter 5 5.3 and 5.7 from Chapter...

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Matrix method: summary = 1 1 2 2 1 0 1 Y n n d Y n α α Translation: (1) = Τ 1 0 1 n d = 1 1 1 1 2 2 2 2 1 0 1 Y n R n n Y n θ θ = 1 0 1 D R R n n D ) ( 1 2 = Refraction: (2) = 1 1 1 2 2 2 1 0 2 1 Y n R n Y n θ θ = 1 0 1 D M R n D 2 = Reflection: (3) (n=n 1 =-n 2 ) Note : “–” sign OK See next lecture Note : det(T)=det(R)=det(M)=1
Matrix method: summary α 2 α 1 Y 1 Y 2 d n 1 n 2 Surface 1, R 1 n 3 Single thick lens: Surface 2, R 2 + = 2 1 2 2 2 1 2 1 2 2 1 1 n d D n d n d D D D D n d D A ( ) 2 1 2 1 R n n D = ( ) 2 2 3 2 R n n D = (4)

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( ) ( ) + = = 2 1 2 1 12 1 1 1 1 1 R R n d n R R n f a l l l Focal length for a thick lens in air Matrix method: summary
Matrix method summary Single thin lens in air: For a thin lens d 0 , T becomes the identity matrix (see eq. 4, also for a thin lens there is no translation!). For n 1 =n 3 =1 (thin lens in air): = + = 1 0 1 1 1 0 ) ( 1 2 1 f D D A (5) Where: compare to eq. 13, class 3 ( ) = 2 1 2 1 1 1 1 R R n f

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Matrix method summary Thin lens combination in air: d f 1 f 2 For two thin lenses separated by a distance d in air , the system matrix is: + + = = 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 2 1 2 1 2 1 2 f d d f f d f f f d f d f A Lens 2 Translation Lens 1 2 1 2 1 12 1 1 1 f f d f f f a + = = 2 1 1 1 1 f f f + = d 0 , leads to the well-known: And:
Thick Lenses Thick lens: thin lens condition is not satisfied, d 0 . Principal planes: The extensions of incoming rays from first focal point and outgoing parallel rays will intersect. These intersection points will form a curved surface. This surface can be approximated as plane, in the paraxial ray condition. This plane is called the first (primary) principal plane . Similarly, we can define secondary principal plane . The points where the primary and secondary principal planes intersect the optical axis are known as first and second principal points : H 1 and H 2 .

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