A convex lens of focal length 1 3 ~m forms a real, inverted image twice the size of the object. The distance of the object from the lens is

Step-by-step solution

The lens formula and magnification relationships determine the object position. Given a convex lens with focal length f = + 1 3 m producing a real, inverted image twice the object size, magnification is m = -2 . Magnification relates object and image distances as m = v/u , yielding v = -2u . Substituting into the lens formula 1 v - 1 u = 1 f gives: 1 -2u - 1 u = 3 Combining terms: - 3 2u = 3 Solving: u = - 1 2 m The magnitude 0.5 m matches option A .