10. Formula Reference and Sign Convention
Free study material · concepts, shortcuts & solved questions
For numerical questions on mirrors and lenses, the standard 'New Cartesian Sign Convention' is used almost universally in Indian school and competitive-exam physics. The essential rules are summarised below.
Rule | Convention |
|---|---|
Origin | The pole (mirror) or optical centre (lens) is taken as the origin |
Direction of incident light | Taken as the positive x-direction (left to right) |
Distances measured against incident light (to the left) | Taken as negative |
Distances measured with incident light (to the right) | Taken as positive |
Heights measured upward (above principal axis) | Taken as positive |
Heights measured downward (below principal axis) | Taken as negative |
Focal length of concave mirror | Negative |
Focal length of convex mirror | Positive |
Focal length of convex (converging) lens | Positive |
Focal length of concave (diverging) lens | Negative |
Quantity | Formula | Notes |
|---|---|---|
Laws of reflection | ∠i = ∠r | Angles measured from the normal |
Snell's Law (refraction) | sin i / sin r = n (constant) | n = refractive index of 2nd medium w.r.t. 1st |
Absolute refractive index | n = c / v | c = speed of light in vacuum; v = speed in medium |
Mirror formula | 1/v + 1/u = 1/f | f = R/2 for spherical mirrors |
Mirror magnification | m = −v/u = h′/h | Negative m = real & inverted image |
Lens formula | 1/v − 1/u = 1/f | u, v, f as per sign convention |
Lens magnification | m = v/u = h′/h | Positive m = virtual & erect image |
Power of a lens | P = 1/f (f in metres) | Unit: dioptre (D) |
Combined power of lenses in contact | P = P₁ + P₂ + P₃ + … | Algebraic sum |
Photon energy | E = hν | h = Planck's constant |
Wave equation | c = νλ | Applies to all EM waves |