Question

what is lens formula give its sign conventions and assumptions

Answer 1

Lens maker formula is a relation between the focL lenght (f), Refrective index of the material (n) and the. Radii of curvature of its surfaces (R1 And R2 ) of the lens, It is known as lens formula
The manufactures of the lense use this relation to design the lens of a given focal lenght and hence it is called so.

Answer 2

Lens formula is ;

(1/f) = (1/v) - (1/u)

the assumption is that the object distance 'u' is always been considered as negative.

The sign of 'f' is positive for convex lens whereas it is negative for concave lens.

The sign of 'v' is positive when the image is formed in front of the lens, that is a virtual and erect image.