Hecht 5.2, 6.1 Monday September 16, 2002

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Hecht 5.2, 6.1 Monday September 16, 2002
Curved mirrors, thin & thick lenses and cardinal points in paraxial optics Hecht 5.2, 6.1 Monday September 16, 2002

Drop by in person Slip an anonymous note under my door

Reflection at a curved mirror interface in paraxial approx.
y φ ’ O C I s’ s

Sign convention: Mirrors
Object distance S >0 for real object (to the left of V) S<0 for virtual object Image distance S’ > 0 for real image (to left of V) S’ < 0 for virtual image (to right of V) Radius R > 0 (C to the right of V) R < 0 (C to the left of V)

Paraxial ray equation for reflection by curved mirrors
In previous example, So we can write more generally,

Ray diagrams: concave mirrors
Erect Virtual Enlarged C ƒ e.g. shaving mirror What if s > f ? s s’

Ray diagrams: convex mirrors
Calculate s’ for R=10 cm, s = 20 cm Erect Virtual Reduced ƒ C What if s < |f| ? s s’

Thin lens First interface Second interface

Bi-convex thin lens: Ray diagram
Erect Virtual Enlarged O f f ‘ n n’ R1 R2 s s’

Bi-convex thin lens: Ray diagram
Inverted Real Enlarged O I f f ‘ n n’ s s’

Bi-concave thin lens: Ray diagram
f f ‘ n’ n R1 R2 s’ s Erect Virtual Reduced

Converging and diverging lenses
Why are the following lenses converging or diverging? Converging lenses Diverging lenses

Newtonian equation for thin lens
x I f f ‘ x’ n n’ s s’

Complex optical systems
Thick lenses, combinations of lenses etc.. Consider case where t is not negligible. We would like to maintain our Gaussian imaging relation n n’ t nL But where do we measure s, s’ ; f, f’ from? How do we determine P? We try to develop a formalism that can be used with any system!!

Cardinal points and planes: 1
Cardinal points and planes: 1. Focal (F) points & Principal planes (PP) and points n nL n’ F2 H2 ƒ’ PP2 Keep definition of focal point ƒ’

Cardinal points and planes: 1
Cardinal points and planes: 1. Focal (F) points & Principal planes (PP) and points n nL n’ F1 H1 ƒ PP1 Keep definition of focal point ƒ

Utility of principal planes
Suppose s, s’, f, f’ all measured from H1 and H2 … n nL n’ h F1 F2 H1 H2 h’ ƒ’ ƒ s s’ PP1 PP2 Show that we recover the Gaussian Imaging relation…

Cardinal points and planes: 1. Nodal (N) points and planes
nL NP1 NP2

Cardinal planes of simple systems 1. Thin lens
V’ and V coincide and V’ V H, H’ is obeyed. Principal planes, nodal planes, coincide at center

Cardinal planes of simple systems 1. Spherical refracting surface
Gaussian imaging formula obeyed, with all distances measured from V V

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

Combination of two systems: e. g
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’

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

Summary H H’ H1 H1’ H2 H2’ F F’ d h h’ ƒ ƒ’

Summary