if an object is placed to the left of a concave mirror beyond it's focal point..........?

Question

if an object is placed to the left of a concave mirror beyond it's focal point..........In which direction will the image move when the object is moved farther to the left?

Answer 1

The image will be formed further to the left of the concave mirror and will be enlarged ( magnified) and inverted.
There are some rules that you can use to sketch the image of an object as formed by curved mirrors.
1. Rays of light through the Focal point are reflected back parrallel to the axis of the mirror ( ie. the line through the center of curvature though the principal focus to the circumference of the mirror)
2. Rays parallel to the axis described above will be reflected through the principal focus
3.Rays throught the center of curvature will be reflected back on the same path.
Where all these rays intersect, that is where the image is formed.
Hope this answers your question.

Answer 2

The image will move to the right, getting closer to the mirror. An object at infinite distance will form an image at the mirror's focal point. An object at exactly twice the focal length will form an image at twice the focal length, right on top of itself. An object at the focal point would form an image at infinite distance. So it is like a teeter-totter. As the object gets closer to the mirror, the image gets farther, and as the object gets farther, the image gets closer. If your object is left of the mirror and beyond the focal point then moving it farther left is moving it farther from the mirror, so the image moves closer, which is to the right in this example.