Chapter VII The Diagonal
RAYS OF LIGHT from a distant star, upon reaching the earth,
are sensibly parallel, and the rays that strike the surface of our
paraboloidal mirror are contained in a cylinder 6" in diameter. They are then converged by reflection to form a point image of the star at the focus of the mirror. If a strip of screen is stretched across
the focus, and if other stars are present in the field, their images
will be observed on the screen extending a number of degrees on either side of the optical axis. The focal surface thus formed is not actually flat, but is a section of a sphere, concave toward the mirror (Fig. 44). But all the star images will not be of equal quality, and only the one that lies on the axis
Fig. 44. The mirror can (in the absence of a tube) image a broad area of the sky on the focal surface. will be perfect. Because of the oblique aberrations known as coma and astigmatism (see Chapter XIII), present to a greater or lesser degree in most optical systems, the images deteriorate as they lie farther from the axis, with the result that only a very small part of the field is fit for useful study. In order to deflect this useful field to one side, so that the observer will not obstruct the incoming rays, a secondary mirror or diagonal is placed a short distance inside of focus, at an angle of 45°. The optical axis is thus deflected by 90°, and the rays from the primary mirror are diverted to form the image in the secondary focal plane (see Fig. 47).
The plane reflecting surface of the secondary may also be produced by total internal reflection from a right-angle prism. We shall briefly discuss the merits of a prism and then consider the dimensions of the diagonal mirror called for in the standard design we have adopted. Fig. 45. Displacement of the focal plane due to refraction in a prism.
The objections to a prism diagonal are its greater cost and difficulty of mounting, and the fact that it must necessarily offer a four-cornered obstruction to the light. The glass prism surfaces are easier to keep clean than the aluminized surface of the diagonal, and so are more enduring. In reflective ability both are, ordinarily, about equal. At the 45° angle, the aluminized diagonal reflects about 90 per cent of the light coming from the mirror. Normally, the entrance and exit faces of the prism reflect about four per cent (the hypotenuse face is internally totally reflecting), and there may be a loss of about two per cent due to absorption; about 90 percent of the original light is therefore transmitted by the prism. However, if its entrance and exit faces are given an anti-reflection fluoride coating, the losses there will be reduced to a fraction of one per cent, and there is then no question of the superior reflectivity of such a prism.
When a prism is employed, refraction of the converging rays at both of its faces will cause an outward displacement of the focal plane, as shown in Fig. 45. For crown glass of refractive index 1.5, this displacement amounts to one third of the total path length of the axial ray through the prism. (Of course, no axial ray actually enters into the image, as it is obstructed by the prism.)
How large the diagonal |
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