Question

are the object distance and image distance always negative for concave and convex lens? if not how do we come to know whether the object and image distance is positive or negative?

Answer 1

Concave mirror:
sign conventions:
object distance = negative
image distance= negative.
convex mirror:
object distance= negative
image distance= positive.
All distance are measured from pole and .measurements in the direction of incident light are considered as positive and negative if measured in opposite direction of incident ray.

Answer 2

Object distance is always negative according to the sign convention,(as the object is placed in front of the lens).In the case of lenses image distance is always negative for concave lens as it forms only virtual image.But taking convex lens image distance is +ve for real image and -ve for virtual image.