Principal Planes
With a thick lens, the concept of principal surfaces is introduced. A light ray traced from the object, through the first focal point (F1), consists of three segments, as seen in Figure 5: the first, in air, from the object point to the lens; the second, within the lens; and the third, in air, after the lens and parallel to the optical axis. If the entering and emerging rays are extended, they will intersect in a locus of points that form the primary (or front) principal surface (H1). Near the axis, this surface becomes nearly flat and commonly is called the front principal plane. In a similar manner, rays incident parallel to the axis of the lens exit through the back principal plane (H2) and intersect the back focal point (F2). The secondary (or back) principal plane is defined by the intersection of these incident and emergent rays. The principal planes represent a single imaginary surface of refraction that replaces the real surfaces of the lens.
Although H1 and H2 are located at different positions within the system, this separation is “invisible” to the ray. For the purpose of ray-tracing, a ray of height yh at H1 can be directly translated to H2; its height remains yh. Also, when the lens is used at unit magnification (1x), the principal planes are conjugate to each other.
Figure 5
The principal planes serve as the references for the location of the front focal point, back focal point, object and image positions. Both the lensmaker’s and the lens formulae involve the effective focal length f, which is measured from H1 and H2.While the principal planes are useful in lens design calculations, their usefulness in a physical setup is limited because either plane may lie inside or outside the lens itself. In a physical setup, the front focal length (FF) and the back focal length (BF) are more useful than the principal planes. The front focal length is measured from the front focal point to the vertex of the first surface of the lens; the back focal length is measured from the vertex of the last surface of the lens to the back focal point.
