Question

in the sign convention the distance of the image is positive but in some case why do they use negative sign?? ​

Answer 1

this depends on the direction of ray of light. so due to this the sign changes. in the position

Answer 2

So the image distance is positive here. you can easily verify that the focal length is in the positive x direction for a convex lens while it is along the negative x direction for a concave lens. So f is positive for a convex lens and negative for a concave lens. The reason is the sign altering of v.