An object is located to the left of a convex mirror whose focal length is -31 . The magnification produced by the mirror is = 0.35.To decrease...

The relation between the distance of the object do,
distance of the image di and the focal length is 1/do + 1/di = 1/f. The magnification is
given by m = -di/do.

Here, the magnification of the object
when it is placed in front of the mirror is 0.35. If the object distance is denoted by
do, we have 1/do + 1/di = -1/31.

0.35 =
-di/do

=> di =
-0.35*do

1/do - 1/0.35*do =
-1/31

=> do =
13*31/7

Using the procedure used above, if the
magnification has to be made 0.26 we have 1/do - 1/0.26*do =
-1/31

=> do =
37*31/13

Therefore the object has to be moved a distance
37*31/13 - 13*31/7 = 2790/91

The distance that the object
has to be moved away from the mirror is approximately 30.65