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/ /20/04 wk3-a-1
MIT 2.71/ /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/ /20/04 wk3-a-3 Thin lens in air in out in thin lens Lens-makers formula
MIT 2.71/ /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/ /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/ /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/ /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/ /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/ /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/ /20/04 wk3-a-10 Imaging condition: ray-tracing (ABF)~(FLN) and (FCD)~(MLF) are pairs of similar triangles
MIT 2.71/ /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/ /20/04 wk3-a-12 Imaging condition: matrix method objectimage lens in out in out
MIT 2.71/ /20/04 wk3-a-13 Imaging condition: matrix method objectimage lens Imaging condition (aka Lens Law)
MIT 2.71/ /20/04 wk3-a-14 Imaging condition: matrix method objectimage lens in out in out Lateral magnification : in out
MIT 2.71/ /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/ /20/04 wk3-a-16 The thick lens Rays bend in two steps air glass
MIT 2.71/ /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/ /20/04 wk3-a-18 The thick lens air glass in out in
MIT 2.71/ /20/04 wk3-a-19 The thick lens air glass in out in
MIT 2.71/ /20/04 wk3-a-20 The thick lens: power air glass in out Object at infinity out in outin
MIT 2.71/ /20/04 wk3-a-21 The thick lens: power air glass in out Powerf: Effective Focal Length
MIT 2.71/ /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/ /20/04 wk3-a-23 The thick lens: back focal length air glass in out in
MIT 2.71/ /20/04 wk3-a-24 The thick lens: back focal length air glass in out z: Back Focal Length
MIT 2.71/ /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/ /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/ /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/ /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