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Lenses and Imaging (Part II)

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. The power of surfaces. • Positive power : exiting rays converge.

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Lenses and Imaging (Part II)

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  1. 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

  2. The power of surfaces • Positive power : exiting rays converge Simple spherical refractor (positive) • Plano-convex • lens • Bi-convex • lens • Negative power : exiting rays diverge Simple spherical refractor negative) • Plano-convex • lens • Bi-convex • lens MIT 2.71/2.710 09/20/04 wk3-a-2

  3. Thin lens in air in out in out thin lens in out out in • Lens-maker’s • formula thin lens MIT 2.71/2.710 09/20/04 wk3-a-3

  4. Thin lens in air in out in out thin lens in out out in Ray bending is proportional proportional to the distance to the distance from the axis thin lens out in in out in MIT 2.71/2.710 09/20/04 wk3-a-4

  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-5

  6. Positive thin lens in air in out thin lens in in thin lens in out • 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-6

  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-7

  8. Negative thin lens in air object at ∞ Virtual image thin lens still applies, now with (to the “left”) thin lens MIT 2.71/2.710 09/20/04 wk3-a-8

  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-9

  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-10

  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-11

  12. Imaging condition: matrix method lens object image in in out out in in MIT 2.71/2.710 09/20/04 wk3-a-12

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

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

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

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

  17. The thick lens air air glass • Equivalent to a thin lens placed “somewhere” • within the thick element. • The location of this “equivalent thin lens” is • the Principal Planeof the thick element MIT 2.71/2.710 09/20/04 wk3-a-17

  18. The thick lens air air glass out in in out out in out in MIT 2.71/2.710 09/20/04 wk3-a-18

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

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

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

  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-22

  23. The thick lens: back focal length air air glass in in out out out in out in MIT 2.71/2.710 09/20/04 wk3-a-23

  24. The thick lens: back focal length air air glass in in out out out z: Back Focal Length MIT 2.71/2.710 09/20/04 wk3-a-24

  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-25

  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-26

  27. The significance of principal planes /1 located at the 2nd PS for rays passing through 2nd FP thin lens of the same power MIT 2.71/2.710 09/20/04 wk3-a-27

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

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