Lenses and Imaging (Part II)

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Shannon Newton
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1 Lee ad Imagig (Part II) emider rom Part I Surace o poitive/egative power eal ad virtual image Imagig coditio Thick lee Pricipal plae 09/20/04 wk3-a-

2 The power o urace Poitive power : eitig ray coverge + >0 + >0 N + <0 + Simple pherical reractor (poitive) Plao-cove le Negative power : eitig ray diverge >0 Bi-cove le 09/20/04 wk3-a-2 <0 Simple pherical reractor (egative) Plao-cocave le <0 >0 <0 N Bi-cocave le

3 Thi le i P P i i i i thi le 0 P 09/20/04 wk3-a-3 ( ) + + P P P thi le Le-maker ormula

4 Thi le i i i P P 0 P thi le i i 09/20/04 wk3-a-4 i i P thi le i ay bedig i proportioal to the ditace rom the ai

5 Poitive thi le i object at ay bedig i proportioal to the ditace rom the ai 09/20/04 wk3-a-5

6 Poitive thi le i i, i 0 i, P thi le i P thi le > 0 thi le a a black bo i P thi le eal image 09/20/04 wk3-a-6 Focal poit image o a object at Focal legth ditace betwee le & ocal poit

7 Negative thi le i object at ay bedig i proportioal to the ditace rom the ai 09/20/04 wk3-a-7

8 Negative thi le i 09/20/04 wk3-a-8 object at P thi le Virtual image till applie, ow with P thi le < 0 < 0 (to the let )

9 Imagig coditio: ray-tracig object t FP chie ray 2 d FP image Image poit i located at the commo iterectio o all ray which emaate rom the correpodig object poit The two ray paig through the two ocal poit ad the chie ray ca be ray-traced directly 09/20/04 wk3-a-9

10 Imagig coditio: ray-tracig B M L F C A F N D 09/20/04 wk3-a-0 (ABF)~(FLN) ad (F CD)~(MLF ) are p o imilar triagle (AB) (AF) (LN) (FL) (LM) (LF) (CD) (F C) (AF) (F C) (FL) (LF) (AB) (ML) 2 (LN) (CD)

11 Imagig coditio: matri method object t FP chie ray 2 d FP image Locatio o image poit mut be idepedet o ray departure agle at the object 09/20/04 wk3-a-

12 Imagig coditio: matri method le object image + i i i i /20/04 wk3-a-2

13 Imagig coditio: matri method object le image Imagig coditio (aka Le Law) 09/20/04 wk3-a-3

14 Imagig coditio: matri method le object image M M magiicatio : Lateral T i T i i i 0 09/20/04 wk3-a-4

15 eal & virtual image object + + image object image t FP 2 d FP t FP 2 d FP image: real & iverted; M T <0 image: virtual & erect; M T > object image object image 2 d FP t FP 2 d FP t FP 09/20/04 wk3-a-5 image: virtual & erect; 0<M T < image: virtual & erect; 0<M T <

16 The thick le gla ay bed i two tep 09/20/04 wk3-a-6

17 The thick le gla 09/20/04 wk3-a-7 Equivalet to a thi le placed omewhere withi the thick elemet. The locatio o thi equivalet thi le i the Pricipal Plae o the thick elemet

18 The thick le 09/20/04 wk3-a-8 gla () i i i i d

19 The thick le 09/20/04 wk3-a-9 gla () i i ( ) ( ) + + i i 2 d d d d

20 The thick le: power gla i i ( ) ( ) + d d 0 2 i i i P Object at iiity Object at iiity 09/20/04 wk3-a-20

21 The thick le: power i i gla P 2 ( ) ( ) d ( ) + Power + ( ) 2 d : Eective Focal Legth 09/20/04 wk3-a-2

22 The very thick le gla 09/20/04 wk3-a-22 Fuy thig happeig: ray diverge upo eitig rom the elemet, i.e. too much poitive power leadig to a egative elemet!

23 The thick le: back ocal legth 09/20/04 wk3-a-23 gla i i z + i i 0 d d d z

24 The thick le: back ocal legth i i gla z 0 z d z: Back Focal Legth 09/20/04 wk3-a-24

25 Focal Legth & Pricipal Plae t PS 2 d PS geeralized optical ytem (e.g. thick le, multi-elemet ytem) FFL BFL 2 d FP t FP EFL EFL 09/20/04 wk3-a-25 EFL: Eective Focal Legth (or imply ocal legth ) FFL: Frot Focal Legth BFL: Back Focal Legth FP: Focal Poit/Plae PS: Pricipal Surace/Plae

26 PS ad FL or thi lee gla, ide P P2 D l 0 (EFL) P P + P 2 (BFL) (EFL) (FFL) The pricipal plae coicide with the (collocated) gla urace The ray bed preciely at the thi le plae (collocated gla urace & PP) 09/20/04 wk3-a-26

27 The igiicace o pricipal plae / t FP t PS 2 d FP geeralized optical ytem 2 d PS thi le o the ame power located at the 2 d PS or ray paig through 2 d FP 09/20/04 wk3-a-27

28 The igiicace o pricipal plae /2 t FP t PS 2 d FP geeralized optical ytem 2 d PS thi le o the ame power located at the t PP or ray paig through t FP 09/20/04 wk3-a-28

Section 7. Gaussian Reduction

Section 7. Gaussian Reduction 7- Sectio 7 Gaussia eductio Paraxial aytrace Equatios eractio occurs at a iterace betwee two optical spaces. The traser distace t' allows the ray height y' to be determied at ay plae withi a optical space