Chapter 10: Formula Reference — Optics
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Optics deals with the behaviour of light — its reflection, refraction, and the images formed by mirrors and lenses. Light is an electromagnetic wave and, unlike sound, can travel through a vacuum; its speed in vacuum, c ≈ 3 × 10⁸ m/s, is one of the fundamental constants of nature and is itself used to define the metre, as noted in Chapter 3.
10.1 Reflection of Light
Quantity / Law | Formula | Notes |
|---|---|---|
Laws of reflection | Angle of incidence = Angle of reflection | Incident ray, reflected ray, and normal all lie in the same plane |
Mirror formula | 1/v + 1/u = 1/f | u = object distance, v = image distance, f = focal length (all in metres, with sign convention) |
Magnification (mirror) | m = −v/u = h'/h | h' = image height, h = object height |
Focal length and radius of curvature | f = R/2 | R = radius of curvature of the mirror |
Refraction is the bending of light as it passes from one transparent medium into another of different optical density, caused by the change in the speed of light between the two media. The extent of bending is governed quantitatively by Snell's law, and the same underlying physics explains why a lens can form real or virtual images, as described by the lens formula below.
10.2 Refraction of Light
Quantity / Law | Formula | Notes |
|---|---|---|
Snell's Law | n = sin i / sin r | n = refractive index, i = angle of incidence, r = angle of refraction |
Refractive index (in terms of speed) | n = c/v | c = speed of light in vacuum, v = speed of light in the medium |
Lens formula | 1/v − 1/u = 1/f | u = object distance, v = image distance, f = focal length |
Magnification (lens) | m = v/u = h'/h | h' = image height, h = object height |
Lens-maker's formula | 1/f = (n − 1)(1/R₁ − 1/R₂) | R₁, R₂ = radii of curvature of the two lens surfaces |
Power of a lens | P = 1/f (f in metres) | P in dioptre (D); converging (convex) lens has positive power, diverging (concave) lens has negative power |
Power of combination of lenses (in contact) | P = P₁ + P₂ + P₃ + ... | Powers add algebraically |
10.3 Human Eye and Optical Instruments — Quick Facts
- Myopia (short-sightedness / near-sightedness): distant objects appear blurred; corrected using a concave (diverging) lens.
- Hypermetropia (long-sightedness / far-sightedness): nearby objects appear blurred; corrected using a convex (converging) lens.
- Presbyopia: age-related loss of the eye's accommodation power; usually corrected using bifocal lenses.
- Astigmatism: caused by irregular curvature of the cornea or lens; corrected using a cylindrical lens.
- Near point of the normal human eye (least distance of distinct vision): about 25 cm.
- Far point of the normal human eye: infinity.
- Dispersion of light: splitting of white light into its constituent colours (VIBGYOR) on passing through a prism, due to different wavelengths refracting by different amounts.
- Scattering of light: Rayleigh scattering of shorter wavelengths (blue) by atmospheric particles explains why the sky appears blue; the reddish colour of the sky at sunrise/sunset is also explained by scattering.
- Total internal reflection: occurs when light travels from a denser to a rarer medium at an angle greater than the critical angle; it is the principle behind optical fibres.