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

2. 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

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

4. Summary

5. 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’

6. 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’

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

8. 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

9. Examples: Two thin lenses in airƒ1 ƒ2
n = n2 = n’ = 1
Want to replace Hi, Hi’ with H, H’ d h h’ H1
H1’ H2
H2’

10. Examples: Two thin lenses in airƒ1 ƒ2
n = n2 = n’ = 1 F F’ d ƒ’ ƒ s s’

11. 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’

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

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

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

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

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

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