Reflection and Refraction of Light: Mirrors, Snell's Law and Lenses
This section covers plane and spherical mirrors, the mirror equation with the Cartesian sign convention, Snell's law, total internal reflection and thin lenses.
Mirrors
Laws of reflection: the angle of incidence equals the angle of reflection, and the incident ray, reflected ray and normal lie in one plane. For a spherical mirror f = R/2, and 1/v + 1/u = 1/f with m = −v/u, distances measured from the pole, those along the incident light being negative. A concave mirror gives a real, inverted image for an object beyond F and is used in headlights and shaving mirrors; a convex mirror always gives a virtual, diminished image and serves as a rear-view mirror.
Refraction and lenses
Snell's law: n₁ sin i = n₂ sin r; absolute refractive index n = c/v = sin i / sin r. Going from a denser to a rarer medium, when i exceeds the critical angle C, where sin C = 1/n, total internal reflection occurs - this is why optical fibres guide light and diamonds sparkle. For a lens, 1/v − 1/u = 1/f and power P = 1/f in dioptres.
Worked example
An object is 20 cm in front of a concave mirror of focal length 15 cm. With u = −20 cm and f = −15 cm: 1/v = 1/f − 1/u = −1/15 + 1/20 = −1/60, so v = −60 cm. The image is 60 cm in front of the mirror and real; m = −v/u = −(−60)/(−20) = −3, so it is inverted and three times larger.
Traps that cost marks
- Dropping the minus signs of u, v or f.
- Using f = 2R instead of R/2.
- Applying the lens formula to a mirror.
- Forgetting that a plane mirror image is virtual and laterally inverted.