The calculation of focal length using the nodal slide

1
The calculation of focal length using the nodal
slide

• University of Arizona
• Yen-Te Lee
• OPTI 521, Fall 2008

2
Optical Spaces

• ?Each space (object or image) extends from -8 to
  8 for each optical surface being encountered.
• ?Gaussian Imagery is a collinear transformation
  mapping the object plane to the image plane. And
  Cardinal points result.
• ?Use paraxial analysis for the Gaussian
  properties of optical system.

3
Cardinal points and planes

• ?Completely describe the focal mapping and
  defined by specific magnifications.
• ?Focal length is the direct
• distance from principal
• plane to focal point.

4
Cardinal points and planes-continue

• ?Nodal planes have the characteristic of identity
  angular magnification.
• ?When the optical system is in air, nodal
  points/planes coincide with the principal
  points/planes.
• ?Principal points/planes can be described using
  Newtonian equations or Gaussian equations which
  measure the distances from focal planes or
  principal planes respectively. (Here the Gaussian
  equations are used)

5
Gaussian equations

• ?Describe the focal mapping with respect to
  principal planes.
• ?Use similar triangles to analysis the properties
  of the optical system.

6
Locations of nodal points/planes

• ?Ray 1 and 2 must be parallel in image space,
  since their conjugate rays cross in the front
  focal plane.
• ?The distances from principal planes to respect
  nodal planes are equal due to similar and
  identical triangles.

7
Longitudinal magnification

• ?The thickness magnification of pairs of
  conjugate planes is the thickness in image plane,
  ?Z divided by the thickness in object plane, ?Z.
• ?For infinitesimal thickness, the longitudinal
  magnifications is obtained. K1 for the optical
  system in air.

8
Angular magnification of nodal points/planes

• ?Use the thickness magnification, the angular
  magnification, mN is 1 for the optical system in
  air (K1).
• ?This is the mechanism to set up the experiment
  finding the focal length of an optical system.

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Nodal slide

• ?Allows the principal planes and the focal length
  to be experimentally determined.
• ?When the system rotates about its rear nodal
  point, N, the rays will converge to the same
  point. Thus, the image will not move.

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Calculating the focal length

• ?The focal length of the optical system can be
  determined by
• ffRBFD-d
• where BFD is the back focal distance of
  the system
• d is the distance from rear
  vertex of the system
• to the rear nodal point (rear
  principal point) of
• the system.