=369. Concave Mirrors.=--Another useful piece of physical apparatus is the concave spherical mirror. It is frequently made from plano-convex lenses by silvering the convex surface of the lens, thus making a concave reflecting surface from the inner surface of the silvered part; they are also made by polishing the inner surfaces of metallic spherical shells. The concave mirror is represented in section in Fig. 359 by the curve _MN_; _C_ is the _center of curvature_ or the center of the surface of which this mirror _MN_ is a part; the line _VC_ through the center _V_ of the mirror is called the _principal axis_; while any other line passing through _C_ is called a _secondary axis_. The point midway between the vertex _V_ and center of curvature _C_ is called the _principal focus_, _F_. It is the point through which parallel incident rays pass after reflection. The angle _MCN_ which the curve of the mirror subtends at the center is called the aperture of the mirror. We learned in Art. 361, the angle of reflection of a ray of light is always equal to the angle of incidence no matter what the nature of the reflecting surface may be. If the reflecting surface is a regular concave surface, like the inner surface of a sphere, the rays of light coming from a point source may after reflection come to a focus, forming a real image. The two extreme points of an object should be selected for locating its image; Fig. 360 shows the construction. The real images formed by concave mirrors are always inverted. The principal focus of a concave mirror may be observed by holding the mirror in a beam of sunlight entering a darkened room. The sun's rays after reflection converge to form a small, round, intense spot of light, which is a real image of the sun, located at the principal focus of the mirror. The distance of the principal focus from the mirror is the least distance that a real image can be formed in front of a concave mirror. =370. Virtual Images by Concave Mirrors.=--When light comes from a small point situated between a concave mirror and its principal focus, the reflected rays are divergent and hence no real image of the object can be found in front of the mirror. But if the rays are extended behind the mirror they will meet in a point called the _virtual focus_. This is the point from which they appear to come. Any image of an object situated between the principal focus and a concave mirror is therefore a virtual image, erect and larger than the object. (See Fig. 361.) [Illustration: FIG. 361.--Virtual image formed by a concave mirror.]