Page 171 - Modern Optical Engineering The Design of Optical Systems

154 Chapter Seven

The procedure is now repeated for the other prism; an air space is
left between the two to allow for the mounting plate to which both
prisms are to be fastened. In Fig. 7.39b, the system is drawn to scale,
with the prism blocks expanded to their true length. The reason for the
ground slot usually cut into the hypotenuse faces of Porro prisms can
be understood from an examination of the unfolded drawings. Light
rays from outside the desired field of view can be reflected (by total
internal reflection) from these faces back into the field where they are
quite annoying; the slot intercepts these rays as they graze along the
hypotenuse.

7.17 Analysis of Fabrication Errors
The effects produced by errors in prism angles (due to manufacturing
tolerances) are readily analyzed. Such angular errors can be treated as
equivalent to the rotation of a reflecting surface from its nominal posi-
tion, and/or the addition of a thin refracting prism to the system.
As an example, consider the right-angle prism shown in Fig. 7.40
and assume that the upper 45° angle is too large by and that the
lower 45° angle is too small by . A ray normal to the entrance face will
make an angle of incidence of 45° at the hypotenuse; the angle of
reflection will then be 45° and the ray will be reflected through an
angle of 90° 2 . Thus, rotating the reflecting face through has
introduced an error of 2 in the direction of the ray.
At the exit face, the ray has an angle of incidence of 2 and, if the
prism index is 1.5, an angle of refraction of 3 . Thus, the total deviation
of the ray from its nominal direction is 3 . Also, since the ray has been
deviated through an angle by refraction at this surface, the ray will
be dispersed and spread out into a spectrum subtending an angle of
/V according to Eq. 7.11.

Figure 7.40 The passage of a ray
through a right-angle prism the
hypotenuse face of which is tilted
from its proper position by a
small angle . After reflection,
the ray is deviated by 2 ; this is
increased to 3 (or 2n ) by
refraction at the exit face.