Plane-Parallel Plate

Plane-Parallel Plate

 

a layer of a homogeneous medium that is bounded by parallel surfaces and is transparent for some range of wavelengths λ of optical radiation. The optical path of a light ray in a plane-parallel plate is nd, where d is the geometrical thickness of the plate, and n = n(λ) is the refractive index of the material of the plate. Suppose the angle of incidence i of a light ray on a plane-parallel plate is nonzero (Figure 1). When the ray passes through the plate, it preserves its direction as a result of being refracted twice at the surfaces of the plate but is displaced by the distance §L. The larger are i, d, and n, the greater is §L. When a plane-parallel plate is inserted into the path of a beam of rays forming an optical image of a point, the image is displaced by the distance δl. For a paraxial beam of rays whose axis is normal to the plate, δl = d(l — 1/n).

Figure 1. Paths of light rays through a plane-parallel plate: (d) thickness of the plate, (n) refractive index of the material of the plate, (δl) plate-induced displacement of the image of a point along the axis perpendicular to the plate, (δL) transverse displacement of a ray incident on the plate at an oblique angle i; when i is large, the spherical aberration of the plate contributes to SI the additional displacement δs’ along the axis

Since optical objects that are not infinitely distant always emit beams of rays with i ≠ 0, a plane-parallel plate used as an optical element has aberrations, in particular, spherical aberration, chromatic aberration, and astigmatism. For sufficiently distant objects and sufficiently small d these aberrations are insignificant. When plane-parallel plates and reflecting prisms that are optically equivalent to such plates are incorporated in optical systems, these aberrations must be taken into account and corrected.

Plane-parallel plates are used as protective glass for windows and light filters (plane-parallel plates of colored materials). They are also used in goniometric devices (when the angular displacements of the image are small), in some interferometers, and as optical compensators.

References in periodicals archive ?
Other topics include the law of refraction as the foundation of geometrical optics, the transition from a thin to a thick lens, systems with two separated components, the single-image mirror, the plane-parallel plate, and details of a hybrid lens.
Some optical properties of the two plane-parallel plates cut from the crystal are described in Syuy et al.