Optics: Reflection, Refraction and Lenses
Light travels in straight lines in a uniform medium. Reflection follows the law that the angle of incidence equals the angle of reflection, both measured from the normal. Refraction occurs because light changes speed between media. Snell's law is n₁ sin θ₁ = n₂ sin θ₂, and the refractive index is n = c/v, where c is the speed of light in vacuum. Refractive index has no units.
When light travels from a denser to a less dense medium, total internal reflection can occur if the angle of incidence exceeds the critical angle C, given by sin C = n₂/n₁. This principle underlies optical fibres. Lenses and curved mirrors form images described by 1/f = 1/v + 1/u using a consistent sign convention, with magnification m = v/u. A converging (convex) lens can form real or virtual images; a diverging (concave) lens forms virtual images. Dispersion separates white light into colours because refractive index varies with wavelength.
Traps: angles are measured from the normal, not the surface; total internal reflection requires travel from higher to lower refractive index; sign conventions must be applied consistently; a virtual image cannot be projected onto a screen; and n = c/v gives a value greater than or equal to 1 for ordinary media.
Worked example: for glass with n = 1.50 in air, the critical angle satisfies sin C = 1/1.50 = 0.667, so C ≈ 41.8°. For a converging lens of focal length 10 cm with an object 30 cm away: 1/v = 1/10 − 1/30 = 1/15, so v = 15 cm and m = v/u = 0.5, giving a real, inverted, diminished image.