Question

Why the focal lenght of convex lens is always +ve and concave lens is always -ve?

Answer 1

Now the convex lens converges the incident rays. Hence the rays converge to a single point infront of the lens. So the image distance is positive here.

as if we go through cartisian plane you will get it

Answer 2

when the focus is towards the direction where the light is goes then the direction of the side is considered as positive ,

so when we see the case of convex lens the light rays Travels and bends towards the focus i.e. on the right side hence making the focal length positive .

now taking the case of concave lens ;

when the light ray passes through concave lens the light diverges and hence cannot meet .

and it makes the image at the left side making the focal length negative .