OPTICS. ag 
the incident ray with a perpendicular to the surface at the point of incidence, 
will be equal to the angle formed by the reflected ray with this same 
perpendicular. Thus, in pl. 21, fig. 5, suppose a ray to come in the 
direction d/, forming an angle, d/p, with the perpendicular /p, the reflected 
ray will be /r, making the angle d/p = pir. The former is called the angle 
of incidence, the latter the angle of reflection. Rays reflected in this manner 
are said to be regularly reflected. There are, in addition, rays that are 
irregularly reflected, or scattered in all directions from the radiant beam. 
The intensity of this scattered light is in proportion to the want of polish of 
the reflector. 
To prove the preceding proposition respecting regularly reflected light, 
the following method may be employed. Take a vertical graduated circle, 
C, (an altitude circle) fig. 6, about whose axis a telescope, /, moves. Have 
also an artificial horizon of mercury or linseed oil,in a wooden vessel ; then 
sight with the telescope, first at a star and then at its image reflected in the 
artificial horizon. On measuring the angles which the sight lines oe and 0’ 
form with the horizontal line cf, it will be found that they are equal; 
whence, as eo is parallel to the incident ray cz, both coming from an infi- 
nitely distant star, it follows that the incident ray, ci, and the reflected ray, 
io’, make equal angles with the horizontal line, and consequently with the 
vertical or plumb line, pi. The three lines, cz, io’, and pi, evidently 
lie in one and the same plane, or the plane in which the telescope 
rotates. 
A plane mirror shows the images of objects lying before it, which images 
must be symmetrical with the object, in relation to the reflecting plane. In 
jig. 7, let m'm be a plane mirror, and / a luminous point before it, which 
sends to the mirror the ray Zi. This is reflected in the direction zc, and 
produces an impression upon an eye at c, as if it had come from a point, 2, 
in the direction ic, and behind the mirror, so that 7//= 71. An eye at c’ will 
observe the point / in the same point /’. Draw Ul’ cutting mm’ in &, Il’ will 
evidently be perpendicular to mm’, and be bisected at k. We thus find the 
image of a luminous point in a plane mirror by letting fall from the luminous 
point a perpendicular to the mirror, or the mirror produced, and taking on 
this perpendicular, behind the mirror, a distance equal to that of the point in 
front of it. As this proposition holds good for every point of an object 
emitting light, the image of such an object may be readily constructed. 
Thus, in fig. 8, ab is the image, in the mirror VW, of the arrow AB, and it 
is evident that the image and object are perfectly symmetrical, with respect 
to the plane of the mirror. ,The construction lines, Ak and ka, B/ and 61, 
exhibit the position of the image, while the other lines show the correctness 
of the figure with reference to the reflection of the rays of light. 
The intensity of the reflected light, whose direction may be ascertained 
in the most exact manner, depends on the one hand upon the medium in 
which the light moves and in which it falls, and on the other hand upon the 
angle of incidence: the more acute the angle the greater the number of rays 
reflected. 
If two plane mirrors be placed together at any angle, an object between 
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