Light - Reflection and Refraction
Light - Reflection and Refraction tests the mirror and lens formulae, ray diagrams, the sign convention and refractive index. Numerical questions with a wrong sign lose the whole mark, so practise the convention until it is automatic.
Rules
New Cartesian sign convention: distances are measured from the pole or optical centre; against the incident light is negative, along it positive; heights above the principal axis are positive. Mirror formula 1/v + 1/u = 1/f; lens formula 1/v - 1/u = 1/f. Magnification m = h'/h = -v/u for mirrors, v/u for lenses. Power P = 1/f in metres, unit dioptre.
Refraction: n = c/v = sin i / sin r; a ray entering a denser medium bends towards the normal.
Mirror facts
A concave mirror has negative f and converges; it forms real inverted images except when the object lies inside F. A convex mirror has positive f, diverges, and always gives a virtual, erect, diminished image, so it is used as a rear-view mirror.
Worked example
An object stands 20 cm in front of a concave mirror of focal length 10 cm. u = -20, f = -10. Then 1/v = 1/f - 1/u = -1/10 + 1/20 = -1/20, so v = -20 cm. m = -v/u = -(-20)/(-20) = -1: the image is real, inverted and the same size, because the object is at the centre of curvature.
Traps
Dropping minus signs; using m = v/u for a mirror; saying a convex mirror forms a real image; forgetting the power of a diverging lens is negative.