UPSC NDA 2 2021 General Ability Solved Paper

Concept:A plane mirror is equivalent to a spherical mirror with an infinite radius of curvature. Therefore, its focal length $f$ is also infinite. The spherical mirror formula $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ can then be applied by taking the limit $f \to \infty$.Explanation:The mirror formula $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ is valid for all spherical mirrors.A plane mirror can be treated as a part of an infinitely large spherical mirror.For such a mirror, the radius of curvature $R$ is infinite.Since focal length $f = \frac{R}{2}$, when $R \to \infty$, $f$ also tends to infinity.Thus, the formula applies to a plane mirror only when the focal length is taken as infinite.The other options are incorrect:• Focal length going to zero would imply a point-like mirror, not a plane.• Image distance going to zero or infinity does not make the formula applicable for a plane mirror.Therefore, option A is the correct choice.Answer:Option A: focal length goes to infinity.