# 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...

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.

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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