Question

how do you find the minimum limiting of object distance for real image

Answer 1

For concave mirror the cases for which a real image is obtained is

When object is at infinity then real image is formed at focus
When object is in between infinity and C then real image is formed between focus and C

When object is in between C and focus then real image is formed between C and infinity.

So the maximum distance between real object and real image for concave mirror is infinity.