Sign convention errors cause more wrong answers in NEET ray optics than any other single source. Here are the eight most critical rules and their common violation patterns.

Rule 1: u is ALWAYS negative. Object is always to the left of the optical element → left direction = negative. There are no exceptions. Writing u = +20 cm for any real object is always wrong.

Rule 2: Concave mirror has f NEGATIVE. The principal focus of a concave mirror is in front of the mirror (to the left). Left = negative. Therefore f = −|f| for any concave mirror. Using f = +15 cm for a concave mirror is the #1 error in NEET optics.

Rule 3: Convex mirror has f POSITIVE. Focus is behind the mirror (to the right). Right = positive. f = +|f| for convex mirrors.

Rule 4: Convex lens has f POSITIVE; Concave lens has f NEGATIVE. Convex lens focuses transmitted light to the right (positive direction) → f > 0. Concave lens focuses appear to diverge from the left → f < 0.

Rule 5: Mirror formula uses PLUS; Lens formula uses MINUS. Mirror: 1/v + 1/u = 1/f. Lens: 1/v − 1/u = 1/f. Interchanging these formulas gives wrong v even if all signs are correct.

Rule 6: Mirror magnification has MINUS; Lens has NO minus. Mirror: m = −v/u. Lens: m = v/u. Applying the mirror formula to a lens flips the sign of m — predicting erect when inverted, or vice versa.

Rule 7: For mirrors, real image means v NEGATIVE; for lenses, real image means v POSITIVE. These are opposite conventions. Mirror real image: v < 0 (in front). Lens real image: v > 0 (other side).

Rule 8: In lensmaker's equation, biconvex lens has $R_{1}$ positive and $R_{2}$ negative. For a biconvex lens: $R_{1}$ = +R (curvature toward incident light), $R_{2}$ = −R (curvature away from incident light). Using $R_{2}$ = +R gives 1/$R_{1}$ − 1/$R_{2}$ = 0 (infinite focal length) — catastrophically wrong.