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Lenses and Imaging (Part II) Reminders from Part I Surfaces of positive/negative power Real and...
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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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Transcript of Lenses and Imaging (Part II) Reminders from Part I Surfaces of positive/negative power Real and...
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
MIT 2.71/2.710 09/20/04 wk3-a-2
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
MIT 2.71/2.710 09/20/04 wk3-a-3
Thin lens in air
in
in
out
out
out
out
in
in
thin lens
thin lens
Lens-maker’sformula
MIT 2.71/2.710 09/20/04 wk3-a-4
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
MIT 2.71/2.710 09/20/04 wk3-a-5
Positive thin lens in air
object at ∞Ray bending is proportional proportional to the distance to the distance from the axis
MIT 2.71/2.710 09/20/04 wk3-a-6
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
MIT 2.71/2.710 09/20/04 wk3-a-7
Negative thin lens in air
object at ∞
Ray bending is proportional proportional to the distance to the distance from the axis
MIT 2.71/2.710 09/20/04 wk3-a-8
Negative thin lens in air
object at ∞Virtual image
still applies, now with thin lens
thin lens(to the “left”)
MIT 2.71/2.710 09/20/04 wk3-a-9
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
MIT 2.71/2.710 09/20/04 wk3-a-10
Imaging condition: ray-tracing
• (ABF)~(FLN) and (F’CD)~(MLF’) are pairs of similar triangles
MIT 2.71/2.710 09/20/04 wk3-a-11
Imaging condition: matrix method
object
chief ray
• Location of image point must be independent of ray departure angle at the object
MIT 2.71/2.710 09/20/04 wk3-a-12
Imaging condition: matrix method
object image
lens
in
inout
in
in
out
MIT 2.71/2.710 09/20/04 wk3-a-13
Imaging condition: matrix method
object image
lens
Imaging condition(aka Lens Law)
MIT 2.71/2.710 09/20/04 wk3-a-14
Imaging condition: matrix method
object image
lens
inout
in
in
out
out
Lateral magnification :
in
out
MIT 2.71/2.710 09/20/04 wk3-a-15
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
MIT 2.71/2.710 09/20/04 wk3-a-16
The thick lens
Rays bend in “two steps”
air air
glass
MIT 2.71/2.710 09/20/04 wk3-a-17
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
MIT 2.71/2.710 09/20/04 wk3-a-18
The thick lens
air airglass
in
in
out
out
out
out
in
in
MIT 2.71/2.710 09/20/04 wk3-a-19
The thick lens
air airglass
in
in
out
out
out
out
in
in
MIT 2.71/2.710 09/20/04 wk3-a-20
The thick lens: power
air air
glassin
in out
out
Object at infinity
out
out
in
in
out in
MIT 2.71/2.710 09/20/04 wk3-a-21
The thick lens: power
air air
glassin
in out
out
Power f: Effective Focal Length
MIT 2.71/2.710 09/20/04 wk3-a-22
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!
MIT 2.71/2.710 09/20/04 wk3-a-23
The thick lens: back focal length
air air
glassin
in
out
out
out
out
in
in
MIT 2.71/2.710 09/20/04 wk3-a-24
The thick lens: back focal length
air air
glassin
in
out
out
out
z: Back Focal Length
MIT 2.71/2.710 09/20/04 wk3-a-25
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
MIT 2.71/2.710 09/20/04 wk3-a-26
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)
MIT 2.71/2.710 09/20/04 wk3-a-27
The significance of principal planes /1
thin lensof the same power
located at the 2nd PS for rays passing through 2nd FP
MIT 2.71/2.710 09/20/04 wk3-a-28
The significance of principal planes /2
thin lensof the same power
located at the 1st PS for rays passing through 1st FP
