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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

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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

### 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)

• 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’

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

### Converging and diverging lenses

Why are the following lenses converging or diverging?

Converging lenses

Diverging lenses

O

x

f

f ‘

x’

I

s

s’

R1

R2

n

n’

### 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. 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 points

n

nL

n’

F1

H1

ƒ

PP1

Keep definition of focal pointƒ

### 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…

n

n’

N1

N2

nL

NP1

NP2

### Cardinal planes of simple systems1. Thin lens

V’ and V coincide and

V’

V

H, H’

is obeyed.

Principal planes, nodal planes,

coincide at center

### Cardinal planes of simple systems1. Spherical refracting surface

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

### 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

### 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’

H

H’

H1’

H1

H2

H2’

F

F’

d

h

h’

ƒ

ƒ’