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 magnification to 0.26, the object is moved further away from the mirror. Calculate the distance through which the object should be moved.
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