Cardinal planes/points in paraxial optics Friday September 20, 2002

Find power of combined system 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

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

Summary

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’

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’

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

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

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

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

Huygen’s eyepiece ƒ1=2ƒ2 and d=1.5ƒ2 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’

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

Two separated lenses in air f1’=2f2’ H’ H H’ H F’ F’ F F f’ f’ d = f2’ d = 0.5 f2’

Two separated lenses in air f1’=2f2’ Principal points at  H’ H F’ F f’ d = 3f2’ d = 2f2’ e.g. Astronomical telescope

Two separated lenses in air f1’=2f2’ e.g. Compound microscope H H’ F’ F f’ d = 5f2’

Two separated lenses in air f1’=-2f2’ e.g. Galilean telescope d = -f2’ Principal points at 

Two separated lenses in air f1’=-2f2’ H H’ F F’ f’ e.g. Telephoto lens d = -1.5f2’