An object is placed perpendicular to the principal axis of a convex mirror with radius of curvature of 40 cm. The position of the object from the pole of the mirror is 60 cm. Find the position of the image formed and its magnification.-15 cm and 0.5 respectively+15 cm and 0.25 respectively+12 cm and 0.5 respectively-12 cm and 0.25 respectively

To solve this problem, we need to use the mirror formula and the magnification formula.

The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.

The magnification formula is m = -v/u, where m is the magnification, v is the image distance, and u is the object distance.

Step 1: Calculate the focal length. For a convex mirror, the focal length is negative and is half of the radius of curvature. So, f = -R/2 = -40/2 = -20 cm.

Step 2: Substitute the values of f and u into the mirror formula to find v. So, 1/-20 = 1/v - 1/-60. Solving this equation gives v = +15 cm.

Step 3: Substitute the values of v and u into the magnification formula to find m. So, m = -v/u = -(+15)/-60 = 0.25.

So, the position of the image formed is +15 cm and its magnification is 0.25. Therefore, the correct answer is "+15 cm and 0.25 respectively".