Use the mirror equation to show that:
(a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f.
(b) a convex mirror always produces a virtual image independent of the location of the object.
(c) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.
Mirror equation is given by,
a)
For a concave mirror, f is negative, i.e., f < 0
For a real object i.e., which is on the left side of the mirror,
For u between f and 2f implies that 1/u lies between 1/f and 1/2f
i.e., 
Implies, v is negative and greater than 2f. Therefore, image lies beyond 2f and it is real.
b)
Focal length is positive for convex mirror, i.e., f > 0.
For a real object on the left side of the mirror, u is negative.
That is, 
Since u is negative and f is positive so, 1/v should also be positive, so v must be positive.
Hence, image is virtual and lies behind the mirror.
c)
Using the mirror equation, we have
That is, the image is enlarged.
