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

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

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

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

Hecht 5.2, 6.1

Monday September 16, 2002

- Welcome comments on structure of the course.
- Drop by in person
- Slip an anonymous note under my door
- …

y

s’

s

φ

’

O

C

I

- 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)

In previous example,

So we can write more generally,

Erect

Virtual

Enlarged

C

ƒ

e.g. shaving mirror

What if s > f ?

s

s’

Calculate s’ for R=10 cm, s = 20 cm

Erect

Virtual

Reduced

ƒ

C

What if s < |f| ?

s

s’

First interface

Second interface

I

O

f

f ‘

s

s’

Erect

Virtual

Enlarged

n

n’

R1

R2

O

f

f ‘

I

s

s’

R1

R2

Inverted

Real

Enlarged

n

n’

O

I

f

f ‘

s

s’

n’

n

R1

R2

Erect

Virtual

Reduced

Why are the following lenses converging or diverging?

Converging lenses

Diverging lenses

O

x

f

f ‘

x’

I

s

s’

R1

R2

n

n’

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!!

n

nL

n’

F2

H2

ƒ’

PP2

Keep definition of focal pointƒ’

n

nL

n’

F1

H1

ƒ

PP1

Keep definition of focal pointƒ

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…

n

n’

N1

N2

nL

NP1

NP2

V’ and V coincide and

V’

V

H, H’

is obeyed.

Principal planes, nodal planes,

coincide at center

n

n’

Gaussian imaging formula obeyed, with all distances measured from V

V

n

nL

n’

y

F1

F2

H1

H2

y’

ƒ’

ƒ

s

s’

PP1

PP2

n

H1

H1’

n2

H’

h’

n’

H2

H2’

1. Consider F’ and F1’

Find h’

y

Y

F’

F1’

d

ƒ’

ƒ1’

d

H2

H2’

h

H

H1’

Find h

H1

y

Y

F2

F

ƒ

ƒ2

1. Consider F and F2

n

n2

n’

H

H’

H1’

H1

H2

H2’

F

F’

d

h

h’

ƒ

ƒ’