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

Step-by-step solution

Using mirror formula, 1 f = 1 u + 1 v or, -1 f = -1 u + 1 v [ u & f negative for concave mirror aligned & 1 v = 1 u - 1 f 1 v = f-u u f & v= u f u-f aligned Length of image, aligned & L =|v|-|f|=v= u f u-f -f & ~L = u f-f(u-f) u-f & = u f-u f+f^2 u-f = f^2 u-f aligned