The Optical Communications Reference

1.1.4. Prisms in optical systems

Prisms serve three main purposes in optical systems: (i)

to fold the optical axis; (ii) to invert the image; and (iii)

to disperse light of different wavelengths. Here we will

consider the first two purposes. It is quite understand-

able that both are achieved due to reflection of rays on

one or several faces of the prism. So, it is worth keeping

in mind how the system of plane reflectors (plane mir-

rors) can be treated (e.g., see Problem P.1.1.14).

A great variety of prisms are commonly used in nu-

merous optical architectures. Only a few simple cases are

described below.

Right-angle prism. This is intended for changing the

direction of the optical axis through 90



. The cross-sec-

tion of this prism is shown in Fig. 1.1.27a. The rays

coming from the object (the arrow 1–2) strike the input

face AB at 90



and after reflection from the hypotenuse

side emerge along the normal to the face BC. It can be

seen that beyond the prism the object is inverted. The

shortcoming of this prism is revealed if the incoming light

is not normal to the prism face. In this case the angle

between incoming and outgoing rays differs from 90



.

Another issue is concerned with the total reflection of

rays on face AC: it might happen that for some tilted rays

total reflection does not occur. In such a case a reflecting

coating on AC is required.

Penta-prism. This prism has effe ctively four faces with

an angle of 90



between AB and BC and 45



between the

two other sides (Fig. 1.1.27b). The shortcoming of the

right-angle prism does not occur here, i.e., the outgoing

beam is always at 90



to the input beam, independent of

the angle of incidence. Also, the object is not inverted.

This results from a double reflection in the prism and is

evidence of the common rule for any prism or system

with reflectors; namely, the image is not inverted if the

number of reflections is even.

Dove prism. The angles A and D are of 45



and the

input and output beams are usually parallel to the basis

face AD (Fig. 1.1.27c). While traveling through the

prism the beams are inverted. Another featu re of this

prism is its ability to rotate an image: when the prism is

inserted in an imaging system rotated around the input

beam with angular speed u the image in the system will

be rotated at a speed 2u.

If it is necessary to invert beams around two axes

a combination of prisms, like the Amici prism shown in

Fig. 1.1.28, can be exploited. This prism is actually

a right-angle prism with an additional ‘‘roof’’ (for this

reason it is also called the roof-prism). As a result the

beams are inverted in both directions: upside-down and

left-right.

In general, any prism inserted in an imaging system

makes the optical path longer. This effect should be

taken into account if a system designed for an unbent

configuration has to be bent to a more compact size using

prisms and mirrors. With regard to its influence on image

quality and optical aberrations the prism acts as a block of

glass with parallel faces. As was demonstrated earlier (see

Problem P.1.1.6 where the propagation of a divergent–

convergent beam through a glass slab of thickness t was

considered) the block of glass causes a lengthening of the

optical path by (n  1)t/n compared to the ray tracing in

air. Therefore instead of tracing the rays through the slab

and calculating the refraction at the entrance and exit

surfaces one can replace a real plate by a virtual ‘‘air slab’’

of reduced thickness, t/n, and perform ray tracing for air

only. To apply this approach to prisms we have to find the

slab equivalent to the prism with regard to the ray path

inside the glass. This can be done by the following pro-

cedure based on unfolded diagrams (see Fig. 1.1.29). We

start moving along the incident ray until the first re-

flection occurs. Then we build the mirror image of the

prism and the rays and proceed moving further along the

initial direction until the second reflecte d surface is met.

Then again we build the mirror image of the configura-

tion, including the ray path, and proceed further until the

initial ray leaves the last (exit) face of the prism. Details

of the procedure can be seen in Problem P.1.1.15.

Creating unfolded diagrams is aimed at calculating the

thickness, t

e

, of the equivalent glass block. For the cases

depicted in Fig. 1.1.29:

(a) right-angle prism with an entrance face of size

a: t

e

¼ a;

Fig. 1.1.27 Layout of different prisms: (a) right-angle prism;

(b) penta-prism; (c) Dove prism.

Fig. 1.1.28 Amici prism.

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Geometrical optics CHAPTER 1.1