Lenses, mirrors and refractive surfaces

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Lenses, mirrors and refractive surfaces

• Friday Sept. 13, 2002

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Refraction at a spherical interface Paraxial ray
approximation

• Snells law
• ____________________________
• Leads to

All rays from O pass through I, i.e. I image of
O For a given object distance s, can find a
conjugate distance s
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Definitions Focal points of a curved interface

• Focal Points
• Suppose object at s ?
• All rays arriving at lens will travel parallel to
  optic axis and,

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Definition Focal points of a curved interface
f
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Definitions Focal points of a curved interface

• Focal Points
• Suppose image at s ?
• All rays leaving lens will travel parallel to
  optic axis and,

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Focal points for curved interface
Show
Definition Focal points, f, f are conjugate
with s, s ?
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Definitions Power
ngtn
Rgt0
P gt 0 for converging surface
C
n
n
P lt 0 for diverging surface
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Definitions Power

• Thus if n gt n and Rlt 0

? f, f, and P are all negative
In general,
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Refraction at a spherical interface
f
f
h
h
R
C
h
h
n
n
s
s
In paraxial ray approximation Imaging occurs
according to
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Object-image height relationship
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Lateral Magnification
Since h is negative
True for all imaging according to
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Lateral magnification
f
f
h
R
C
h
n
n
s
s
In above, since s, s gt 0 ? m lt 0 ?
inverted image

• New image shown in figure is
• real (light actually passes through)
• inverted
• demagnified or reduced

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Thin lenses
Treat as two spherical interfaces Assume that
the lens thickness t is negligible
n
n
O
I
C1
C2
nL
R1
R2
s
s
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Thin lens First surface
n
nL
P
P
V
R1
s, R1 gt 0
s
s
s lt 0 since to the left of V
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Thin lens Second surface
n
n
R2
P
t
nL
s
s
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Thin lens second interface
Second interface
First interface
Object distance t s t - s
Thin lens ? t ? 0, so object distance - s
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Thin lens
First interface
Second interface
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Thin lens
In a single medium (nn)
In air (n 1)
Lens makers formula
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Thin lens (nL1.5) Examples

• Double convex lens
• R1 R2 20 cm
• f ____ P _____
• Double concave lens
• R1 R2 20 cm
• f ____ P _____
• Plano-convex
• R1 R2 20 cm
• f ____ P _____

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Thin lens Power

• Thicker in middle
• P gt 0
• Thinner in middle
• P lt 0

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Thin lens Ray diagrams
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Reflection at a curved mirror interface in
paraxial approx.
?
?
f
?
?
C
O
I
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Reflection at a curved mirror interface
Show that