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Curved mirrors, thin & thick lenses and cardinal points in paraxial optics. Hecht 5.2, 6.1 Monday September 16, 2002. General comments. Welcome comments on structure of the course. Drop by in person Slip an anonymous note under my door …. y. s’. s.

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Curved mirrors thin thick lenses and cardinal points in paraxial optics l.jpg

Curved mirrors, thin & thick lenses and cardinal points in paraxial optics

Hecht 5.2, 6.1

Monday September 16, 2002


General comments l.jpg
General comments paraxial optics

  • Welcome comments on structure of the course.

  • Drop by in person

  • Slip an anonymous note under my door


Reflection at a curved mirror interface in paraxial approx l.jpg

y paraxial optics

s’

s

Reflection at a curved mirror interface in paraxial approx.

φ

’

O

C

I


Sign convention mirrors l.jpg
Sign convention: Mirrors paraxial optics

  • 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 l.jpg
Paraxial ray equation for reflection by curved mirrors paraxial optics

In previous example,

So we can write more generally,


Ray diagrams concave mirrors l.jpg
Ray diagrams: concave mirrors paraxial optics

Erect

Virtual

Enlarged

C

ƒ

e.g. shaving mirror

What if s > f ?

s

s’


Ray diagrams convex mirrors l.jpg
Ray diagrams: convex mirrors paraxial optics

Calculate s’ for R=10 cm, s = 20 cm

Erect

Virtual

Reduced

ƒ

C

What if s < |f| ?

s

s’


Thin lens l.jpg
Thin lens paraxial optics

First interface

Second interface


Bi convex thin lens ray diagram l.jpg

I paraxial optics

O

f

f ‘

s

s’

Bi-convex thin lens: Ray diagram

Erect

Virtual

Enlarged

n

n’

R1

R2


Bi convex thin lens ray diagram10 l.jpg

O paraxial optics

f

f ‘

I

s

s’

Bi-convex thin lens: Ray diagram

R1

R2

Inverted

Real

Enlarged

n

n’


Bi concave thin lens ray diagram l.jpg

O paraxial optics

I

f

f ‘

s

s’

Bi-concave thin lens: Ray diagram

n’

n

R1

R2

Erect

Virtual

Reduced


Converging and diverging lenses l.jpg
Converging and diverging lenses paraxial optics

Why are the following lenses converging or diverging?

Converging lenses

Diverging lenses


Newtonian equation for thin lens l.jpg

O paraxial optics

x

f

f ‘

x’

I

s

s’

Newtonian equation for thin lens

R1

R2

n

n’


Complex optical systems l.jpg
Complex optical systems paraxial optics

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 focal f points principal planes pp and points l.jpg
Cardinal points and planes: paraxial optics1. Focal (F) points & Principal planes (PP) and points

n

nL

n’

F2

H2

ƒ’

PP2

Keep definition of focal pointƒ’


Cardinal points and planes 1 focal f points principal planes pp and points16 l.jpg
Cardinal points and planes: paraxial optics1. Focal (F) points & Principal planes (PP) and points

n

nL

n’

F1

H1

ƒ

PP1

Keep definition of focal pointƒ


Utility of principal planes l.jpg
Utility of principal planes paraxial optics

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 l.jpg
Cardinal points and planes: paraxial optics1. Nodal (N) points and planes

n

n’

N1

N2

nL

NP1

NP2


Cardinal planes of simple systems 1 thin lens l.jpg
Cardinal planes of simple systems paraxial optics1. 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 l.jpg
Cardinal planes of simple systems paraxial optics1. Spherical refracting surface

n

n’

Gaussian imaging formula obeyed, with all distances measured from V

V


Conjugate planes where y y l.jpg
Conjugate Planes – where y’=y paraxial optics

n

nL

n’

y

F1

F2

H1

H2

y’

ƒ’

ƒ

s

s’

PP1

PP2


Combination of two systems e g two spherical interfaces two thin lenses l.jpg
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 l.jpg

d two thin lenses …

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’


Summary l.jpg
Summary two thin lenses …

H

H’

H1’

H1

H2

H2’

F

F’

d

h

h’

ƒ

ƒ’


Summary25 l.jpg
Summary two thin lenses …


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