<P> In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system . These are the focal points, the principal points, and the nodal points . For ideal systems, the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points; in fact only four points are necessary: the focal points and either the principal or nodal points . The only ideal system that has been achieved in practice is the plane mirror, however the cardinal points are widely used to approximate the behavior of real optical systems . Cardinal points provide a way to analytically simplify a system with many components, allowing the imaging characteristics of the system to be approximately determined with simple calculations . </P> <P> The cardinal points lie on the optical axis of the optical system . Each point is defined by the effect the optical system has on rays that pass through that point, in the paraxial approximation . The paraxial approximation assumes that rays travel at shallow angles with respect to the optical axis, so that sin ⁡ θ ≈ θ (\ displaystyle \ sin \ theta \ approx \ theta) and cos ⁡ θ ≈ 1 (\ displaystyle \ cos \ theta \ approx 1). Aperture effects are ignored: rays that do not pass through the aperture stop of the system are not considered in the discussion below . </P>

What are cardinal points of a thick lens