(a) For concave mirror. f < 0, u < 0
∴ 2f < u < f ⇒ 1/2f > 1/u > 1/f
⇒ -1/2f < -1/u < -1/f
⇒ 1/f - 1/2f < 1/f - 1/u < 1/f - 1/f
∴ According to equation, 1/v = 1/f - 1/u
∴ v is negative. Therefore image formed is real and lies beyond 2f
(b) For convex mirror, f > 0, u < 0
As, 1/v = 1/f - 1/u
∴ v is positive. Therefore image formed is virtual and is at the back of the mirror.
(c) For convex mirror, f > 0, u < 0.
∴ 1/v = 1/f - 1/u ∴ 1/v > 1/f or, v < f
therefore image is located between the pole and the focus.
Also v < u, hence image is diminished.
(d) For concave mirror, f < 0,
Since the object is placed between the pole and focus
∴ f < u < 0 ∴ (1/f - 1/u) > 0
Also, 1/f - 1/u = 1/v
∴ 1/v > 0 or v is positive, on the right side of mirror hence it must be virtual.
∴ v > u, ∴ image is enlarged.