An infinitely long rod lies along the axis of a concave mirror of focal length f . The near end of the rod is at a distance u > f from the mirror. Its image will have a length

Step-by-step solution

1 v + 1 u = 1 f ⇒ let v 1 = distance of near end of image 1 v 1 + 1 - u = 1 - f ⇒ 1 v 1 = 1 u + 1 - f ⇒ 1 v 1 = f - u u f v 1 = u f f - u ⇒ 1 v 2 + 1 ∞ = 1 - f ⇒ v 2 = - f ( v 2 = the distance of last end of image ) Length of Image ⇒ v 1 - v 2 = u f f - u - - f ⇒ v 1 - v 2 = u f - u f + f 2 u - f v 1 - v 2 = f 2 u - f