Question

why the aperture of spherical mirror should be smaller than the radius of curvature​

Answer 1

Answer:

Spherical mirrors do not focus parallel light rays to a single focal point. The focus actually lies on a surface called a caustic. ... The point of using an aperture much smaller that the radius of the mirror is to restrict the incoming light to a region where rays do (almost) come to a single focal point.

Answer 2

Answer:

For a spherical mirror, the diameter of the aperture cannot be more than twice the radius of curvature. Such a mirror would have a significant spherical aberration. A large aperture mirror that can focus parallel incident light into a point would need to have a parabolic shape, such a lens would have no (theoretical) limit on its size. Spherical mirrors do not focus parallel light rays to a single focal point. The point of using an aperture much smaller that the radius of the mirror is to restrict the incoming light to a region where rays do come to a single focal point

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