# Lenses and Imaging (Part II) Reminders from Part I Surfaces of positive/negative power Real and virtual images Imaging condition Thick lenses Principal.

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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

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 spherical refractor (positive) Plano-convex lens Bi-convex lens Simple spherical refractor negative) Plano-convex lens Bi-convex lens

MIT 2.71/2.710 09/20/04 wk3-a-3 Thin lens in air in out in thin lens Lens-makers formula

MIT 2.71/2.710 09/20/04 wk3-a-4 Thin lens in air in out in thin lens out 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 out in 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 (to the left)

MIT 2.71/2.710 09/20/04 wk3-a-9 Imaging condition: ray-tracing object image 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 (FCD)~(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 objectimage lens in out in out

MIT 2.71/2.710 09/20/04 wk3-a-13 Imaging condition: matrix method objectimage lens Imaging condition (aka Lens Law)

MIT 2.71/2.710 09/20/04 wk3-a-14 Imaging condition: matrix method objectimage lens in out in out Lateral magnification : in out

MIT 2.71/2.710 09/20/04 wk3-a-15 Real & virtual images object image object image image: real & inverted; M T <0image: virtual & erect; M T >1 object image object image image: virtual & erect; 0<M T <1

MIT 2.71/2.710 09/20/04 wk3-a-16 The thick lens Rays bend in two steps air glass

MIT 2.71/2.710 09/20/04 wk3-a-17 The thick lens air glass 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 glass in out in

MIT 2.71/2.710 09/20/04 wk3-a-19 The thick lens air glass in out in

MIT 2.71/2.710 09/20/04 wk3-a-20 The thick lens: power air glass in out Object at infinity out in outin

MIT 2.71/2.710 09/20/04 wk3-a-21 The thick lens: power air glass in out Powerf: Effective Focal Length

MIT 2.71/2.710 09/20/04 wk3-a-22 The very thick lens 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 glass in out in

MIT 2.71/2.710 09/20/04 wk3-a-24 The thick lens: back focal length air glass in 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 Length BFL: Back Focal Length FP: 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 lens of the same power located at the 2 nd PS for rays passing through 2 nd FP

MIT 2.71/2.710 09/20/04 wk3-a-28 The significance of principal planes /2 thin lens of the same power located at the 1 st PS for rays passing through 1 st FP

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