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 -∞ 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, mN 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.