Компьютерный практикум по оптике

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  • ..

    2003

  • 2 ..

    .. . . -

    , ( ).

    MATHCAD. -

    .. . . . MATHCAD.

    .. . . . 2003

  • 3..

    1. _____________________________________________ 4 1. _____________________________________________________________ 4

    _______________________________________________________________________ 4 1.1. _______________________________ 5 1.2. _________________________ 7 1.3. ____________________________ 10 ______________________________________________________ 13

    2. ____________________ 14 1. _____________________________________________________ 14

    ______________________________________________________________________ 14 2.1. ______________________________ 15 2.2. ____________________________ 16

    2. _____________________________________________________ 18 ______________________________________________________________________ 18 2.3. ______________________________ 19 2.4. ____________________________ 20 ______________________________________________________ 22

    3. ________________________________________________________ 23 ______________________________________________________________________ 23 3.1. ______________________________ 25 3.2. ____________________________ 26 ______________________________________________________ 28

    II. ______________________________________________________ 29 4. ___________________________________________ 29

    ______________________________________________________________________ 29 4.1. ___________________________ 31 4.2. _________________________ 32 4.3. N ________________________ 34 4.4. N ______________________ 35 4.5. N ________ 37 ______________________________________________________ 38

    5. _______________________________ 39 ______________________________________________________________________ 39 5.1. _________ 40 5.2. _______ 41 5.3. NM___ 42 5.4. NM_ 43 ______________________________________________________ 44

    III. ___________________________________________________ 45 6. _______________________ 45

    ______________________________________________________________________ 45 6.1. ___________________________________________________ 47 6.2. . ___________ 48 ______________________________________________________ 49

    IV. _______________________________ 50 7. _________________________________________ 50

    ______________________________________________________________________ 50 7.1. __________________________________ 52 7.2. __________________________________ 53 ______________________________________________________ 54

  • I

    4 ..

    1. 1.

    S1 S2 P

    ( ) ( ) 22

    22

    22

    21 2

    ,,2

    , zdyxyxrzdyxyxr +

    ++=+

    += .

    . 1

    ( ) ( ) ( )( ) ( )2

    ,,2

    , 010212

    = yxryxrkyx .

    ) :

    ( ) ( ) ( ) ( )( )yxIIIIyxI Plane ,coscos2, 02010201 ++= ;

    ) :

    ( ) ( ) ( ) ( ) ( ) ( )( ) ( )( )yx

    yxryxrII

    yxrI

    yxrIyxI Cyl ,coscos

    ,,2

    ,,,

    21

    0201

    2

    02

    1

    01

    ++= ;

    ) :

    ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( )yxyxryxrII

    yxrI

    yxrIyxI Spher ,coscos

    ,,2

    ,,,

    21

    02012

    2

    022

    1

    01

    ++= ;

    I01 I02 - S1 S2; 01 02 S1 S2.

    minmax

    minmax

    IIIIV

    +

    = .

  • I

    5..

    1.1.

    1.1.1. -, (. 1): ) ( )( )yLI Plane , , ) ( ) ( )yLI Cyl , , ) ( ) ( )yLI Spher , ,

    . 1

    . 2

    1.1.2. -, (. 1) : ) ( )( ) ( )( )yLIzyI PlanePlane ,, = , ) ( )( ) ( )( )yLIzyI CylCyl ,, = , ) ( )( ) ( )( )yLIzyI SpherSpher ,, = .

  • I

    6 ..

    1.1.3. I(x, y) (x, y): a) ( ) ( ) ( ) ( ) ( )( ) ( )[ ]010221122102010201 ,,coscos2, ++= yxryxrkIIIIyxI Plane ,

    ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )[ ]010221

    1221

    21

    0201

    2

    02

    1

    01 ,,coscos,,

    2,,

    ,

    ++= yxryxrk

    yxryxrII

    yxrI

    yxrI

    yxI Cyl ,

    ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )[ ]010221

    1221

    21

    02012

    2

    022

    1

    01 ,,coscos,,

    2,,

    ,

    ++= yxryxrkyxryxr

    IIyxr

    Iyxr

    IyxI Spher .

  • I

    7..

    1.2.

    A S1 (S2) - (. 3) S1 S1 (S2 S2), d:

    ( ) ( ) ( )[ ]

    ++

    =+=

    2,,

    2,,

    21,,

    21, 21

    ddyxIddyxIyxIyxIyxI A .

    . 3

    B S1 (S2) d (y d/2 < y < y + d /2) (. 4):

    ( ) ( ) ( )

    = '',',,, dyyywyyxIyxI B , ( )

    +>

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