Natural Phenomena: Light, Reflection, Refraction and the Human Eye
Natural Phenomena (light) tests reflection, refraction, mirrors, lenses and the human eye, with numericals and ray-reasoning questions.
Reflection and mirrors
Light reflects so that the angle of incidence equals the angle of reflection, and the incident ray, reflected ray and normal lie in one plane. For spherical mirrors, use the sign convention: distances are measured from the pole, and distances against incident light are negative. Mirror formula: 1/v + 1/u = 1/f, with f = R/2; magnification m = −v/u. A concave mirror can form real or virtual images; a convex mirror always forms a diminished, virtual, erect image and is used as a rear-view mirror.
Refraction, lenses and the eye
Refraction occurs because light changes speed between media. Refractive index n = c/v; Snell's law n₁ sin i = n₂ sin r. Lens formula: 1/v − 1/u = 1/f; power P = 1/f in metres, unit dioptre. A convex lens converges and can form real or virtual images; a concave lens diverges. The human eye focuses with the cornea and lens onto the retina; rods detect dim light, cones colour. Accommodation is the lens changing shape. Myopia is corrected by a concave lens, hypermetropia by a convex lens.
Worked example
An object is 20 cm in front of a concave mirror of focal length 10 cm. Take u = −20 cm, f = −10 cm. 1/v = 1/f − 1/u = −1/10 + 1/20 = −1/20, so v = −20 cm. The image is real, inverted and 20 cm in front of the mirror; m = −v/u = −(−20)/(−20) = −1, so it is the same size. The object is at the centre of curvature, so the image forms there.
Traps
Wrong signs in the mirror or lens formula cause most errors. Power is in dioptres only when focal length is in metres. A convex lens is not always a magnifying glass; the object must be within the focal length. Myopia is corrected with a concave lens, not convex.