there was a question in which the object is place right side of a concave lens so I decided as usual like taking objects position as positive and considering the right face of the concave mirror so I take focal length also as positive but my answer was wrong I want the reason?
Imagine a bunch of rays travelling parallel to the principle axis and diverge after travelling through the lens. If you had to take the focal length to be positive you would have to trace it on the positive side which is not possible. When you trace the paths of the diverging rays to find which is the spot of convergence you end up at the focal point which is on the negative side by convention. A simple ray diagram should help you understand this