114 PHYSICS. 
visible will be that of an object from which the ray, fB, comes. The 
angle which the two sight-lines, Be and Bf, from the two objects make with 
each other, is precisely twice the amount of the angle by which the planes 
of the two mirrors are now inclined to each other. It would be very easy 
to show that the angle eBf is twice as great as gBh. Pl. 21, fig. 15, 
represents a reflecting sextant of the simplest construction. For full 
particulars respecting this instrument in its various forms, as also for a 
more complete illustration of its theory, we must refer our readers to that 
part of our work where the sextant is treated of at length.—(Pp. 66 and 
165.) 
If a ray of light impinge upon any polished curved surface, it will be 
reflected as from a plane tangent to the surface at the point of incidence. 
A luminous point at the centre of a sphere emits rays which are all reflected 
back again to this centre. If the luminous point lie in one focus of an 
ellipsoid, its rays will be reflected to the other focus, and then back again by 
reflection to the first. If the luminous point be placed in the focus of a 
paraboloid, the rays will be reflected parallel to the axis: if a number of 
rays be incident parallel to the axis, they will be reflected to the focus. 
Spherical mirrors are either concave or convex. A spherical convex 
mirror is a part of a sphere polished externally ; a spherical concave mirror 
is part of a sphere polished internally. The centre, c (fig.77), of the sphere 
is called the centre of curvature ; the line ca, connecting it with the centre 
of the mirror, is called the axis of the mirror; the angle mcm’, formed by 
lines drawn from the centre of curvature to exterior points diametrically 
opposite to each other, is called the aperture of the mirror. If a luminous 
point be placed at the centre of curvature, all its rays will be reflected back 
to it again. If the radiant be at a very great distance from the mirror, its 
rays striking the mirror may be considered as parallel to each other. Rays 
falling upon the mirror parallel to each other (jig. 16) are reflected to a 
common point, c, called the focus of parallel rays, situated half way between 
the centre of curvature and the centre of the mirror (fig. 17). This is 
strictly true, however, only of those rays which are very near and parallel 
to the axis: the more they are removed from the axis, the nearer to the 
mirror is the focus. The focus of parallel rays, striking the mirror at a 
distance of 60° from the axis, will lie in the centre of the mirror itself. If 
all the parallel rays impinging upon a mirror are to be reflected to the same 
point, its aperture must not amount to more than from 8° to 10°; in this 
case all the rays may be considered as central. If the luminous point be 
not at an infinite distance, but a point, m, of the axis itself (fig. 16), the 
focus will be nearer the centre of curvature than the centre of the mirror ; 
if placed at the centre of curvature, the focus will be there also. If the 
radiant be placed between the focus of parallel central rays and the centre 
of curvature, the focus will be further from the mirror than this centre, and 
will recede more and more as the radiant approaches the centre of parallel 
rays. In this focus the radiant will emit rays which will be reflected in 
lines parallel to the axis and to eaeh other, and there will be no 
convergence to a focus at all. If the radiant be between the focus of 
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