Question

what are sign conventions and assumptions of lens formula

Answer 1

you can easily proceed sign convention for lens by co-ordinate method .

put the lens in the origin of co-ordinate axes .
now, left side of lens is negative part and right side of lens is positive part .

1) you always put object in left side e.g.
object distance from lens is negative .

2) focal length depend on nature of lens
if convex then focal length will be positive and if lens is concave then focal length will be negative .

3) if image distance from lens is positive it means , image form right side of lens
and vice -versa

this is some basic rule for finding sign of v , u and f

Answer 2

for understanding sign convention you need to assume that the optical centre is at the origin of a Cartesian plane...
1.so object on the left of optical centre will be negative
2.object on right will be positive
3.object above principal axis will be positive
4.object below principal axis will be negative.
5.focal length of concave lens is negative and convex lens is positive ...

or other method is as follows. .
1.when object is in direction of the light rays then positive distance and if in opposite direction then negative distance.
2.u is always positive..