When an object is placed 40 cm away from a spherical mirror an image of magnification 1/2 is produced. To obtain an image with magnification of 1/3, the object is to be moved :

Solution

Physics sir · 4 steps

An erect, half-size image means a convex mirror: find f from the first image, then reuse it for the second.

1. Which mirror. A positive magnification smaller than 1 means an erect, diminished image. Only a convex mirror gives that for a real object. Take u negative and f positive (convex).

   m = -v/u = f/(f-u)

2. Find f. With u = -40 cm and m = 1/2: f/(f+40) = 1/2, so 2f = f + 40 and f = +40 cm.
3. New distance. For m = 1/3: 40/(40-u) = 1/3, so 40 - u = 120 and u = -80 cm. The object now sits 80 cm in front of the mirror.
4. So. The object moves from 40 cm to 80 cm, that is, 40 cm away from the mirror, option (d).

The idea to keep. For a mirror, m = f/(f-u) links magnification straight to object distance. Use the first image to get f, then reuse that f for the second image.

Answer from the NTA final answer key. Solution by PrepWiser.