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 -∞ to +∞ 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, ΔZ ’ divided by the thickness in object plane, ΔZ.  For infinitesimal thickness, the longitudinal magnifications is obtained. K=1 for the optical system in air.

8 Angular magnification of nodal points/planes  Use the thickness magnification, the angular magnification, m N is 1 for the optical system in air (K=1).  This is the mechanism to set up the experiment finding the focal length of an optical system.

9 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.

10 Calculating the focal length  The focal length of the optical system can be determined by f=f’ R =BFD-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.