PRISM LIGHT TRANSMISSION PATH

Prisms are used to fold light paths, manipulate image direction and size, and diffract light. In many applications, combinations of prisms are used to achieve several of these effects. In order to design components that contain multiple prisms, it is important to know the incidence, propagation, and exit position of light through each prism, as well as the length of the optical path of light as it passes through the prism. This can be easily modeled using prism tunnel diagrams.

A prism tunnel diagram is a two-dimensional (2D) diagram that shows the path of light through a prism. This technique is used to visualize the total path length of light through a prism. In this diagram, the prism is represented by a characteristic, proportional cross-section. Light starts outside the prism and enters through one of the faces. Inside the prism, the light comes into contact with the other side of the prism. If light strikes a new surface at an Angle equal to or greater than the critical Angle (related to the refractive index of the interfacial medium), or if the surface is coated with an appropriate specular coating, the light will be fully internally reflected or nearly internally reflected. When light is reflected from that surface, the cross section representing the prism is flipped over to the line representing the reflective surface of the prism, making it appear that the light passes directly through the next cross section without changing its original direction across the first cross section. If the light enters at an Angle not greater than or equal to the critical Angle, and the surface is not mirrored, the light will pass through that surface and leave the prism. The prism tunnel diagram of the pentaprism is shown in Figure 1, next to the typical ray path diagram.

（Figure 1: Top: Typical ray path diagram of pentaprism. Bottom: Prism tunnel diagram of light path through the same pentaprism）

The tunnel diagram helps to show the net aperture of the prism and can specify where the vignetting occurs, thus determining the prism's field of view. A prism can have multiple unique tunnel diagrams for different light paths through the prism. When light enters the prism at a variety of different faces and angles, unique diagrams can be made. For example, Dove prisms are often used in several different orientations to achieve different types of image transformations. Each of these different light trajectories through the prism has a different tunnel diagram (Table 1).

（Table 1: Common Dove prism tunnel diagram）

The light in the above and below images enters and exits on the same plane, but at different angles. In addition, the first diagram has only one reflector, while the second and third diagrams have two and three reflectors, respectively.

In the two-dimensional ray path diagram, add a "V" symbol to indicate the part where the two faces of the ridge or prism meet at a 90° Angle and represent the "rooflike" shape (Figure 2). This leads to additional reflections, changing the parity or chirality of the image.

（Figure 2: A "V" symbol has been added to the 2D view of the topped surface of the Amici prism to distinguish it from the untopped surface）

Shorten the distance

Light passing through a planar parallel plate will experience an image shift due to refraction (Figure 3). The image offset is a function of the plate thickness (t) and its refractive index (n).

（Figure 3: Image offset caused by planar parallel plates）

Image offset through the glass can be compensated by replacing the actual path length with the reduced distance. The actual path length (L) in the glass is divided by n to get the reduced distance. This is usually done in a prism tunnel diagram to determine the air space equivalent path length through the prism (Figure 3).