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# Curved mirrors, thin thick lenses and cardinal points in paraxial optics - PowerPoint PPT Presentation

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

Hecht 5.2, 6.1

Monday September 16, 2002

General comments paraxial optics

• Welcome comments on structure of the course.

• Drop by in person

• Slip an anonymous note under my door

y paraxial optics

s’

s

Reflection at a curved mirror interface in paraxial approx.

φ

’

O

C

I

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)

• R > 0 (C to the right of V)

• R < 0 (C to the left of V)

Paraxial ray equation for reflection by curved mirrors paraxial optics

In previous example,

So we can write more generally,

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 paraxial optics

Calculate s’ for R=10 cm, s = 20 cm

Erect

Virtual

Reduced

ƒ

C

What if s < |f| ?

s

s’

Thin lens paraxial optics

First interface

Second interface

I paraxial optics

O

f

f ‘

s

s’

Bi-convex thin lens: Ray diagram

Erect

Virtual

Enlarged

n

n’

R1

R2

O paraxial optics

f

f ‘

I

s

s’

Bi-convex thin lens: Ray diagram

R1

R2

Inverted

Real

Enlarged

n

n’

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 paraxial optics

Why are the following lenses converging or diverging?

Converging lenses

Diverging lenses

O paraxial optics

x

f

f ‘

x’

I

s

s’

Newtonian equation for thin lens

R1

R2

n

n’

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: 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: 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 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: paraxial optics1. Nodal (N) points and planes

n

n’

N1

N2

nL

NP1

NP2

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 paraxial optics1. Spherical refracting surface

n

n’

Gaussian imaging formula obeyed, with all distances measured from V

V

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 …

n

H1

H1’

n2

H’

h’

n’

H2

H2’

1. Consider F’ and F1’

Find h’

y

Y

F’

F1’

d

ƒ’

ƒ1’

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 two thin lenses …

H

H’

H1’

H1

H2

H2’

F

F’

d

h

h’

ƒ

ƒ’

Summary two thin lenses …