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

Step-by-step solution

Given: A convex lens with focal length f = 1 3 m forms a real, inverted image with magnification m = -2 . From the magnification formula, m = v u , so -2 = v u , giving v = -2u . The lens formula 1 f = 1 v - 1 u is applied. Substituting f = 1 3 and v = -2u : 1 1/3 = 1 -2u - 1 u 3 = - 1 2u - 2 2u = - 3 2u Solving for u : 3 = - 3 2u 6u = -3 u = - 1 2 m The negative sign indicates the object is placed in front of the lens; the magnitude is 0.5 m . This corresponds to option C . Thus, C