Lenses and Imaging (Part II)
• Reminders from Part I• Surfaces of positive/negative power• Real and virtual images• Imaging condition• Thick lenses• Principal planes
MIT 2.71/2.710 09/20/04 wk3-a-1
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The power of surfaces• Positive power : exiting rays converge
• Negative power : exiting rays diverge
Simple sphericalrefractor (positive)
Plano-convexlens
Bi-convexlens
Simple sphericalrefractor negative)
Plano-convexlens
Bi-convexlens
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Thin lens in air
in
in
out
out
out
out
in
in
thin lens
thin lens
Lens-maker’sformula
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Thin lens in air
in
in
out
out
out
out
in
in
thin lens
out
out
in
in
thin lens in Ray bending is proportional proportional to the distance to the distance from the axis
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Positive thin lens in air
object at ∞Ray bending is proportional proportional to the distance to the distance from the axis
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Positive thin lens in air
in in
out
out
in
inthin lens
thin lens
thin lens as a “black box”
Real image
in
out thin lens
Focal point = image of an object at ∞
Focal length = distance between lens & focal point
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Negative thin lens in air
object at ∞
Ray bending is proportional proportional to the distance to the distance from the axis
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Negative thin lens in air
object at ∞Virtual image
still applies, now with thin lens
thin lens(to the “left”)
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Imaging condition: ray-tracing
objectimage
chief ray
• Image point is located at the common intersection of all rays which emanate from the corresponding object point• The two rays passing through the two focal points and the chief ray can be ray-traced directly
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Imaging condition: ray-tracing
• (ABF)~(FLN) and (F’CD)~(MLF’) are pairs of similar triangles
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Imaging condition: matrix method
object
chief ray
• Location of image point must be independent of ray departure angle at the object
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Imaging condition: matrix method
object image
lens
in
inout
in
in
out
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Imaging condition: matrix method
object image
lens
Imaging condition(aka Lens Law)
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Imaging condition: matrix method
object image
lens
inout
in
in
out
out
Lateral magnification :
in
out
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Real & virtual imagesobject
imageobject
image
image: real & inverted; MT<0 image: virtual & erect; MT>1
object
image
object
image
image: virtual & erect; 0<MT<1 image: virtual & erect; 0<MT<1
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The thick lens
Rays bend in “two steps”
air air
glass
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The thick lens
air airglass
Equivalent to a thin lens placed “somewhere” within the thick element.
The location of this “equivalent thin lens” is
the Principal Plane of the thick element
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The thick lens
air airglass
in
in
out
out
out
out
in
in
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The thick lens
air airglass
in
in
out
out
out
out
in
in
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The thick lens: power
air air
glassin
in out
out
Object at infinity
out
out
in
in
out in
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The thick lens: power
air air
glassin
in out
out
Power f: Effective Focal Length
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The very thick lens
air air
glass
Funny things happening:rays diverge upon exiting from the element, i.e.
too much positive power leading to a negative element!
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The thick lens: back focal length
air air
glassin
in
out
out
out
out
in
in
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The thick lens: back focal length
air air
glassin
in
out
out
out
z: Back Focal Length
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Focal Lengths & Principal Planes
generalized optical system(e.g. thick lens,
multi-element system)
EFL: Effective Focal Length (or simply “focal length”)FFL: Front Focal LengthBFL: Back Focal LengthFP: Focal Point/Plane PS: Principal Surface/Plane
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PSs and FLs for thin lenses
glass, index n
• The principal planes coincide with the (collocated) glass surfaces• The rays bend precisely at the thin lens plane (=collocated glass surfaces & PP)
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The significance of principal planes /1
thin lensof the same power
located at the 2nd PS for rays passing through 2nd FP
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The significance of principal planes /2
thin lensof the same power
located at the 1st PS for rays passing through 1st FP