Q.At which positions of the objects do spherical mirrors produce

[!TLDR] A concave mirror gives a diminished (or same-size) image whenever the object is beyond f (u>2f, or u=2f), and a magnified image whenever the object is between f and 2f, or inside f. [!ANSWER] Diminished: object bey …

For a concave mirror (a convex mirror ALWAYS gives a diminished image, regardless of object position, so this question is really about the concave mirror's range of behaviour): (i) a DIMINISHED image forms whenever the object lies beyond the centre of curvature, i.e. for u greater than 2f in magnitude (object distance more than twice the focal length) -- the image is real, inverted, and smaller than the object, forming between f and 2f. At exactly u=2f the image is the same size (m=1), which can also be treated as the diminished/magnified boundary. …

Use the concave-mirror object-position table: diminished images occur only for objects beyond 2f; magnified images occur for objects either between f an …

Forgetting that 'magnified' covers two genuinely different situations (real magnified beyond 2f, and virtual ma …