The slightly less cool thing about a spherical reflector (as opposed to a parabolic reflector, for example) is that it focuses to a line rather than a point.

This can be corrected for either by making your receiving antenna in the shape of a line, though this severely limits the range of frequencies you can be monitoring at any given time (Arecibo Observatory with its 305-m spherical dish used to have a system of several line feeds that could be swapped in and out for different observing purposes before it switched to the second correcting option...), or by implementing a series of secondary reflectors that can then focus the line signal down to a point.
As suggested longwinter's writeup, a spherical mirror will not produce as sharp an image as a plane mirror will due to the lack of a definite focal point. However, if the mirror is small relative to its radius of curvature, the reflected rays will cross at very nearly a single point. This is known as the focal point and the diistance from it along the principal axis to the mirror is the focal length. The focal length is half the radius of curvature. However, this only holds if the angle of reflection is small. So,

f = r / 2

The image formed from a concave spherical mirror is always magnified. If the object lies between the focal point and the mirror, then the image is virtual (behind the mirror) and upright. Conversely, if the object lies beyond the focal point, the image is real, and inverted.

Although not necessarily spherical, a spoon is an everyday example of this phenomenon. When you look at the reflection of your face on the inside of a spoon, it's upside down. This indicates that the focal point lies between your face and the spoon. If you were to move your face closer to the spoon (and the spoon was big enough that you could still see the inside) the image would become non-inverted once your face passed the focal point.
Shaving mirrors which magnify the image are spherical concave reflectors. However the radius of curvature is large enough that your face is still the right way up when you look in the mirror. If you look at a shaving mirror from several metres away, the image will be inverted.

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