39
When is between and , the reflexion of the whole circle gives two complete hyperbolas in Fig. 52.
In the first place, the semi-circle gives the portion of hyperbola . The part gives the infinite branches and the conjugate hyperbola and the former hyperbola is completed by the reflexions at considered as convex mirrors. The part of the object has for its images the hyperbola and part of namely, the infinite parts of the line outside the circle are represented by and by the remaining parts have for images only and
46.In all that has preceded, we have confined our attention to sections of the mirror, object, and image; but of course the reader will not find the smallest difficulty in inferring that the image of a plane object, made by a spherical mirror, is, according to circumstances, a portion of a sphere, a spheroid, a parabolic or hyperbolic conoid, or a plane.
47.By referring to the figures, it will readily be seen that when the mirror is concave, the image is, in most cases,[1] inverted with respect to the object: a convex mirror always gives an erect image.
48.It will also be seen, that when the image is inverted, it is what is called a real image: when erect, it is imaginary.
49.Let the object presented to a concave mirror be a portion of its own sphere, (Fig. 53.)
Since rays proceeding from the extremity of the diameter, are reflected to making two-thirds of and that all points of the object are equally distant from the centre, it will readily be seen that the image of the portion of sphere represented by is a corresponding portion of sphere, having its radius one-third of that of the mirror.
50.Suppose now the object be a portion of any other sphere.
- ↑ When the object is between the mirror and the principal focus, the object is erect, otherwise not.
