Spherical mirror formula relating an object distance ‘u’, image distan

Spherical mirror formula relating an object distance ‘u’, image distance ‘v’ and focal length of mirror ‘f’ may be applied to a plane mirror when

focal length goes to infinity.
focal length goes to zero.
image distance goes to zero.
image distance goes to infinity.
This question was previously asked in
UPSC NDA-2 – 2021
The correct answer is A) focal length goes to infinity.
A plane mirror can be considered a spherical mirror with an infinitely large radius of curvature. Since the focal length of a spherical mirror is half its radius of curvature (f = R/2), the focal length of a plane mirror is also infinite.
The spherical mirror formula is 1/u + 1/v = 1/f. If f goes to infinity, then 1/f goes to zero. The formula becomes 1/u + 1/v = 0, which implies v = -u. This relationship (image distance is the negative of object distance, indicating a virtual image at the same distance behind the mirror as the object is in front) is consistent with the properties of a plane mirror.