# Граници приминимости методов геометрической оптики

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1980 .

132, , 3

535,310

*) . . , . . , 7. . . . . 8. 9. - 10. . . 1. 2. 3. 4. 5. 6. 475 477 480 481 484 486 488 490 492 494 495

1.

)

- - . , , . , , **). , - . (. . 4 ).*) *, V {, 1979). **) , . ., , , . : (/) < , = /, 0 = 2JW/ . 2. , [ - '-^-2 > (. 2). , (, ) F (') = 0 . ) . (2.2) (2.3) ' . r s ' (. . 1 2), ' 3

F(T')

4 | ( r ' - r , , V3)2H>(r,,

3

, r2)] | ^ = 0 ,

(2.4)

V 3 3 . . , (2.3)

, 2 )! I2^ =

(2.5)

(2.4) (2.5) , , . .

)

(, ) ~ \ \ (2.2) (2.5) . rt 2 2, ' = y V a -|- '2, (2.4) (2.6)

480

. , , , ,

Lx ' zlt L2 = z a '. ' = const a

f=Vntp

L

'l+nL-i

(2-7)/ \' ^'

, , (2.5) F(r'\~

'> 2

- -2 ""

'

2 \ '\

(2.9)3. - , : I. , ( ) . at \VXAO I < 0 , at \ Vp} \ < , O | Vn | J < n , f (3.1) Vx , 3 = dtyfdxj, a at * ) . (3.1) , , (3.1) i?j 2 : at < I , 2 |. . (3.2) , , , . , , (3.1) - . , (3.1) . , , I, : I I . 0 ( ), , : & > (3.3) ( | 2 I /2). , , , . II *) , I , . , (3.1) at , , .

481

( , ) *). , . . , ( ) 8 . - (. . , ,, ) , (3.1) - , II - . - , . , 32> 3 3 . , , I II , , . I II . , , . I II , I II : , , . . 59. . 3 . , I II . , . 4. , )

, , , . *) . . : , , , , , . , I, - .

482

. . , . .

. , (3.1), (3.2) (1.6):

(4.1) , , , . , , . 1. ) , , , : > X , . )

, , . - ,

484

, . , . .

, , (. . )). , , , . , , , . , , . 5. )

; () (. 5)^ ( . ), . at = at (z) (2.7), Lx == z 0 , L% = :

at =

/

020

(5.1)

(. . 5)

,(*) =. 5.

^ = / () . = [(z -J- ( /2)]|/ / . , , . , , . (->- ) (5.2) = ~. ; . , (5.1) , 0 , . ) ,

, , . 2 (-

485

) , . , , I, at = , . . F) , at . =s = F . , at 1\ ( , Z), (5.6> | " I

(5.6>

: ** | = I , 0 | = 2 | | "J/ (5.7)

, (5.6) .6.

)

. 0 S , (6.1) D , , (. 7). (6.1) , . (3.1) , D &*;. bt = af/cos , .

487

, (3.2) , aelt 2 bt : aBlt 2 ~> h as (2.7) , Lx R\$ () (), L% (). > 1 2 . , D . ) ,

= (. 8), . cos 0 m l n ?COS I

* 8 9 . > cos 0 m l n = (2/0 | 8 )1/3, . . 12 , ) = , , , = arg , | VF | = . , . . 9 , . ( . 9 ) 1 3 , . . (. * ). , , 1 3 .

488

. . , . .

, . . , > . ( ), , (. . , ) 0 , , . , , : . 9. | .- , t|) m +i " ^ /2. I I : (. + 1)- m- .7.

. " , I I : , , [ (. 10), : (. . ) , , . . 10. | 2 I < (7.1) 1 5 , () | |* 1/2

)

! ,

2

= 20,

(7.2)

489

/ , , v 0TH = | vKayCT Vy cos | , , , ^4 , ( ). (7.2) (7.1), | lN | (17. (7.4) , 1 8 , 59 = 1, = (/2^) 1 / 3 , = viiycr . )

0 , 1 ~ (. . 10), , (4.5) AS0 /0 ASu ,

14> 1 ? . * , ( 1 = 1,02 ) 1,34 (7.5). , , , 1 6

() = , I W - W [ ( - | ) " 1 / 4 (iAl + 2) () + ( - 11/4 (lAt-

V ()], (7.6)

() ,

yplt 2 Alt 2 , , '1 2 Alt 2 , . , , . . , , 1 9 2 0 . ) 2 = 0 : 0 = exp (ikopV2F). *= F . . 3 = 0: (7.7) , . 132, . 3

490

. . , . .

1 (5.5), *, at. l ~ (FI4)lt*. (4.5) = }, 50 = \, W-

(7.8)

/"|^2 = 2,2 . )

, . = ilkQLn, * I " 1 ~ lit" " * , (7.9) . , . , = 1/6, = 1/4, = 1/4, , = 3/10. = 1 ^ ( 0) . , , , , ^ 31 22 8 5 . , . 8,

)

== (), ?

a)

VvSn

(8.1)

491

, s = sin , , & = (. 11, ). (sQ = 0)

(8 2)

(8.2) () , = const =s = (), () : at (') > ]/ 0 ( ')/ ().

) , , . Vt F 2 (. 11, ), Vx (. . 11, ), V2 , ( . ) . : ^ ( /2) , , [ = sin 2 , ,' ~ /2 . at (2.7) ~ 1: af,max ~ 01//2 (L ). I , () 2at ~ 1^XOL : )

4!-2, 2 5 .9. -

)

(, ) , 9~, , (, f) (, t) . ) (9.1) - | | ~ ~ , , . Oft

-, -f, ^}

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