A convex mirror of focal length 30 cm produces an image that is one-third the size of the object. The distance of the object from the pole of the mirror is

Step-by-step solution

For a convex mirror, the image formed is always virtual and erect, so the transverse magnification is positive. Given m = + 1 3 and f = +30 cm. We know that m = - v u 1 3 = - v u v = - u 3 Using the spherical mirror formula: 1 v + 1 u = 1 f 1 - u 3 + 1 u = 1 30 - 3 u + 1 u = 1 30 - 2 u = 1 30 u = -60 cm The distance of the object from the mirror is |u| = 60 cm. Answer: 60 cm