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Spherical Mirror
 
A spherical mirror is a reflecting mirror that has the shape of a spherical segment. The surface of the mirror is a part of the sphere, which is called the center of curvature. The point at the center of the mirror surface is called the vertex of the mirror. The line passing through the center of curvature and the vertex of the mirror is called the optic axis.

Spherical mirrors can be convex and concave.

If the incoming rays are parallel to the optic axis, they converge at a locus that is called the focal point. The distance between the focal point and the vertex of the mirror is called the focal length. A concave mirror has a real focal point. It is located between the center and the vertex.

The focal point of a convex mirror is a virtual one. The incoming rays parallel to the optic axis are not reflected through the focal point. Instead, they diverge as though they had come from the focal point. The focal length of a concave mirror is f > 0, and the focal length of a convex mirror is f < 0. In both cases, the magnitude of the focal length is one half of the curvature?s radius: f = R/2.

Spherical mirrors, like lenses, can reproduce images of objects. These images can be erect and inverted, real and virtual. The position of the image can be determined by graphical methods. To do this, one can use properties of the rays passing through the center of the mirror or its focal point, as well as properties of the rays that are parallel to the axis.

The position of the image can also be found by the following formula:

1/s + 1/s' = 1/f.

Note the similarity with the thin lens formula.

The rules for determining signs of s and s' are the same as the rules used for determining the sign of a thin lens:

s > 0 and s' > 0 for real objects and images;

s < 0 and s' < 0 for virtual objects and images.

The lateral magnification of a spherical mirror is given by m = h/h' = - s/s'. Here, h and h' are the sizes of the object and its image.

The signs in this formula are such that for an erect image, m > 0; and for an inverted image, m < 0.

 
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