Question
What is lens formula? Give its sign conventions and assumptions.

Answer

If u is the distance of object and v, the distance of image from optical centre of the lens, then focal length fis related to u and v by $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ which is called lens formula. The formula is equally applicable t to convex, concave or any other type of lens. (e.g. concavo-convex, plano-convex, convexo-concave, plano-concave etc.)
Sign Conventions:
(1) The object is always placed to the left of the lens.
(2) All distances parallel to principal axis are measured from optical centre of the lens.
(3) All distance measured to the right of optical centre (along x-axis) are taken as positive while those measured to the left of optical centre (along x-axis) are taken as negative.
(4) Distance measured perpendicular to and above the principal axis (along y axis) are taken as positive.
(5) Distance measure perpendicular to and below the principal axis (y'-axis) are taken as negative.
Assumptions (1) Object is taken on principal axis. (2) The lens is thin.

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