Cardinal planes/points in paraxial optics

1. Cardinal planes/points in paraxial optics Wednesday September 18, 2002

2. Thick Lens: Position of Cardinal Planes Consider as combination of two simple systems e.g. two refracting surfaces Where are H, H’ for thick lens? H1, H1’ H2, H2’ H H’

3. Cardinal planes of simple systems1. Thin lens V’ and V coincide and V’ V H, H’ is obeyed. Principal planes, nodal planes, coincide at center

4. Cardinal planes of simple systems1. Spherical refracting surface n n’ Gaussian imaging formula obeyed, with all distances measured from V V

5. Conjugate Planes – where y’=y n nL n’ y F1 F2 H1 H2 y’ ƒ’ ƒ s s’ PP1 PP2

6. Combination of two systems: e.g. two spherical interfaces, two thin lenses … n H1 H1’ n2 H’ h’ n’ H2 H2’ 1. Consider F’ and F1’ Find h’ y Y F’ F1’ d ƒ’ ƒ1’

7. d Combination of two systems: H2 H2’ h H H1’ Find h H1 y Y F2 F ƒ ƒ2 1. Consider F and F2 n n2 n’

8. Combination of two systems: e.g. two spherical interfaces, two thin lenses … n H1 H1’ n2 H’ h’ n’ 1. Consider F’ and F2’ H2 H2’ y’ y Y θ θ F2 F’ F2’ d ƒ2’ ƒ2 ƒ’ Find power of combined system

9. Summary I II H H’ H1’ H1 H2 H2’ F’ F n2 n’ n d h h’ ƒ ƒ’

10. Summary

11. Thick Lens In air n = n’ =1 Lens, n2 = 1.5 n n2 n’ R1 = - R2 = 10 cm d = 3 cm Find ƒ1,ƒ2,ƒ, h and h’ Construct the principal planes, H, H’ of the entire system R1 R2 H1,H1’ H2,H2’

12. Principal planes for thick lens (n2=1.5) in air Equi-convex or equi-concave and moderately thick  P1 = P2≈ P/2 H H’ H H’

13. Principal planes for thick lens (n2=1.5) in air Plano-convex or plano-concave lens with R2 =   P2= 0 H H’ H H’

14. Principal planes for thick lens (n=1.5) in air For meniscus lenses, the principal planes move outside the lens R2 = 3R1 (H’ reaches the first surface) H H’ H H’ H H’ H H’ Same for all lenses

15. Examples: Two thin lenses in air H H’ ƒ1 ƒ2 n = n2 = n’ = 1 Want to replace Hi, Hi’ with H, H’ d h h’ H1 H1’ H2 H2’

16. Examples: Two thin lenses in air H H’ ƒ1 ƒ2 n = n2 = n’ = 1 F F’ d ƒ’ ƒ s s’

17. Huygen’s eyepiece In order for a combination of two lenses to be independent of the index of refraction (i.e. free of chromatic aberration) Example, Huygen’s Eyepiece ƒ1=2ƒ2 and d=1.5ƒ2 Determine ƒ, h and h’

18. Huygen’s eyepiece H1 H’ H2 H h’ = -ƒ2 h=2ƒ2 d=1.5ƒ2