Cardinal points

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  • notice that if f and f’ are equal (surrounded by the same media)
  • Cardinal points

    1. 1. Cardinal Points Gauri S Shrestha 1.2.1 light and optics
    2. 2. IntroductionThe analysis of an optical system using cardinalpoints is known as Gaussian optics, named afterC F GaussFor an optical lens system - characteristics aredefined by its "cardinal points”Knowing the location of the cardinal points – to finding out the image produced by an object passing through optical lens Gauri S. Shrestha, M.Optom, FIACLE
    3. 3. IntroductionEvery Optical systems has 6CARDINAL POINTS1. Focal Points- Primary & Secondary2. Principle Points- ‘’ ‘’ ‘’3. Nodal Points- ‘’ ‘’ ‘’ Gauri S. Shrestha, M.Optom, FIACLE
    4. 4. Focal Points:points at which light rays arrive parallelto the optic axis are brought to a common focus on theoptic axisPrimary focal point: F: Rays diverging from this point for a system with positive power, before refraction will emerge parallel to the optic axis after refraction Rays converging to this point for a system with negative power before refraction will emerge parallel to the optic axis after refractionSecondary focal point: F’: Rays parallel to theoptic axis before refraction will converge to {or appear todiverge from) this point after refraction Gauri S. Shrestha, M.Optom, FIACLE
    5. 5. Gauri S. Shrestha, M.Optom, FIACLE
    6. 6. Principle pointsThe principal points are the points at theintersection of two imaginary rays, created byextending the ray entering the lens, andextending the ray exiting from the lens.The principal planes are the planes normal tothe optic axis, intersecting the principal pointson the optical axisTwo Principle Planes (primary &Sec.) (1st = obj. = 2nd image) Gauri S. Shrestha, M.Optom, FIACLE
    7. 7. Focal points, Principal points and the Optical Axis Gauri S. Shrestha, M.Optom, FIACLE
    8. 8. Principle Planes & Points Gauri S. Shrestha, M.Optom, FIACLE
    9. 9. Nodal PointsThe nodal points are two axial points, suchthat a ray, directed at the first nodal point willseem to emerge from the second nodal pointparallel to its original directiona ray directed to a nodal point at a certainangle, will exit the lens at the same angle.Extending the exiting ray towards the insideof the lane will intersect the optic axis at thesecond nodal point. Vice versa Gauri S. Shrestha, M.Optom, FIACLE
    10. 10. Nodal Points Gauri S. Shrestha, M.Optom, FIACLE
    11. 11. •When an optical system is bounded on both sides by air(same refractive index both side), the nodal pointscoincide with the principal points. Gauri S. Shrestha, M.Optom, FIACLE
    12. 12. Significanceknown cardinal points of an opticalsystem - location and size of the imageformed by the optical system can befound by ray tracing Gauri S. Shrestha, M.Optom, FIACLE
    13. 13. Ray Tracing considering cardinal points Ray OB, parallel to the system axis will appear to refract at the second principal plane, it will then pass through the second focal point F2. The ray OF1C passing through the first focal point F1 will emerge from the system parallel to the axis, refracted at the first principal plane. A third ray may be constructed from O to the first nodal point. This ray appear to emerge from the second nodal point and would be parallel to the entering ray. ( as n1=n2, nodal points coincide principle points) Gauri S. Shrestha, M.Optom, FIACLE
    14. 14. Image formed by an optical system considering cardinal points) Gauri S. Shrestha, M.Optom, FIACLE
    15. 15. Ray Tracing considering cardinal points The intersection three rays at point O locates the image of point O. A similar construction for other points on the object would locate additional image points which would lie along the OA arrow Gauri S. Shrestha, M.Optom, FIACLE
    16. 16. Image formed by an optical system l l’ Gauri S. Shrestha, M.Optom, FIACLE
    17. 17. Steps to Calculate the Principal Points1. Calculate the F1 and F22. Calculate the Equivalent Power  Fe = F1 + F2 – cF1F23. Locate the primary principal point  Longitudinal distance from A1 (Front Apex) to H  A1H = (ncF2) / Fe4. Locate the secondary principal point  Longitudinal distance from A2 (Back Apex) to H’  A2H’ = -(ncF1) / Fe Gauri S. Shrestha, M.Optom, FIACLE
    18. 18. A1 H A2H’ Front Vertex Back Vertex Focal Length Focal Length fn fv im F A1 H H’ A 2 F’obj fe f e’ l l’ lH l’H’
    19. 19. Focal PointsFocal Lengths can be measured from a principalplane (fe and fe’) fe = - no / Fe fe ’ = ni / Fe no = ni = 1.00 in all cases where the lens is surrounded by AIR on both sidesFocal Lengths can be measured from theanterior or posterior lens surface (fn, fv) fn = - no / Fn fv = ni / Fv no = ni = 1.00 in Gauri S. Shrestha, M.Optom, FIACLE lens is surrounded all cases where the
    20. 20. A2A1 H H’ F’
    21. 21. fe’ A2H’A1 H H’ A2 F’
    22. 22. F A1 H H’ A2
    23. 23. fe A1HF A1 H H’ A2
    24. 24. Back Vertex Power Effective Power “Power” measure used in clinical applications• The power of the lens system referenced to theback vertex (A2)• Parallel light entering the lens from the left(normal direction) is focused to the secondary focalpoint by the back vertex power
    25. 25. fe’ A1H A2H’A1 H1 H’ A2 F’ fv
    26. 26. niFv = f where fv = fe’ + H’ A2 vFv F1 = + F2 1- tF 1 n Effective Power of the first surface stepped-along to the back surface + the back surface power
    27. 27. Front Vertex Power Neutralizing Power• The power of the lens system referenced to thefront vertex (A1)• Parallel light coming from the right (oppositedirection of normal) is focused to the primary focalpoint by the front vertex power• An entering vergence equal and opposite thefront vertex power will create an exiting vergenceout of the thick lens of zero (neutralizing power)
    28. 28. fe A1H A2H’F A1 H H’ A2 fn
    29. 29. -nFn = o where fn = f A H fn e + 1 F2Fn = F1 + 1 - t F n 2 The front surface power + effective power of the second surface stepped-along to the front surface (light traveling right to left)
    30. 30. Gauri S. Shrestha, M.Optom, FIACLE
    31. 31. What is the Back Vertex Power and Front Vertex Power of a lens (n=1.50) with a front surface radius of curvature of +8.00cm and a back surface radius of curvature of +3.3cm? Calipers measure the center thickness to be 20mm.F1 = (1.50-1.00)/0.080 F2 = (1.00-1.50)/0.033 = +6.25D = -15.15D Fv = F1 / [1 – (t/n)F1] + F2 = +6.25 / [1-(.02/1.5)(+6.25)]+(-15.15) r1 = +0.80cm = -8.33D C1 r2 = +0.33cm C2 Fn = (+6.25) + -15.15 / [1-(0.02/1.5)(-15.15)] = -6.35D Gauri S. Shrestha, M.Optom, FIACLE
    32. 32. Based on the lens described on the previous slide. What is the Fe and the positions of the primary principal plane and the secondary principal planeF1 = (1.50-1.00)/0.080 F2 = (1.00-1.50)/0.033 = +6.25D = -15.15D Fe = +6.25 + (-15.15) – (.02/1.5)(+6.25)(-15.15) = -7.64 D A1H = (1)(.02/1.5)(-15.15) / -7.64 A1 A2 = +2.6mm H’ A2H’ = - (1)(.02/1.5)(+6.25) / -7.64 = +1.1mm H Gauri S. Shrestha, M.Optom, FIACLE
    33. 33. Nodal Points and Optical Center
    34. 34. Nodal PointsIf the thick lens in not surrounded by thesame media on both sides then HN = H’N’ = fe + fe’ FN = fe’ F’N’ = fe HH’ = NN’ Nodal points are shifted towards the higher index medium for convergent systems and towards the lower index medium for divergent systems Gauri S. Shrestha, M.Optom, FIACLE
    35. 35. Optical Center (O)The position where the nodal raycrosses the optical axisWavelength independent.Index of refraction independent Gauri S. Shrestha, M.Optom, FIACLE
    36. 36. N’N OH H’
    37. 37. OH H’
    38. 38. or OOH H’ H H’
    39. 39. F2A1 O = t F1 +F2
    40. 40. r 1tA 1O = r1-r2 This form demonstrates that the optical center location is (n) independent Gauri S. Shrestha, M.Optom, FIACLE
    41. 41. r1 = +10cm r2=+20cm t = 3cm OA1O=(.10)(.03)/.1-.2 = -3.0cm H H’

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