a short linear object of length L lies on the axis of a spherical mirror of focal length f at a distance u from the mirror. what will be the axial length of the image ???

center of object is u distance apart from mirror...

now , one end is at u¹= u-L/2 &

 other end is at u₂ = u+L/2

1/v + 1/u = 1/f            (mirror formula)

v = fu/u-f       .................1

image for one end = v¹ = fu¹/u¹-f

image for other end = v₂ = fu₂/u₂-1

v¹-v₂ = length of image = f²(u₂-u¹)/(u¹-f)(u₂-f)

now solve this & get the ans