Reflection is the bouncing back of light when it hits a surface. Laws of Reflection: (1) Angle of incidence = Angle of reflection. (2) The incident ray, reflected ray, and normal all lie in the same plane. Types of reflection: Regular (specular) reflection — smooth surfaces (mirror); Irregular (diffuse) reflection — rough surfaces. Image in a plane mirror: virtual, erect, laterally inverted, same size as object, at same distance behind mirror as object is in front.

Spherical mirrors are cut from a hollow sphere. Concave mirror: reflecting surface curves inward (cave); used in torches, vehicle headlights, shaving mirrors, solar cookers. Convex mirror: reflecting surface curves outward; used as rear-view mirrors (gives wider field of view). Key terms: Centre of curvature (C), Radius of curvature (R), Principal focus (F), Focal length (f) — f = R/2, Pole (P), Principal axis. Mirror formula: 1/v + 1/u = 1/f. Magnification: m = -v/u = h'/h. Sign convention: all distances measured from pole; distances in direction of incident light are positive. Concave mirror can form real/inverted images (when object beyond F) or virtual/erect (when object between P and F).

Refraction is the bending of light when it passes from one medium to another, caused by the change in speed of light. Light bends toward the normal when entering a denser medium (speed decreases). Light bends away from the normal when entering a rarer medium (speed increases). Snell's Law: n₁ sin θ₁ = n₂ sin θ₂. Refractive index (n) = speed of light in vacuum / speed of light in medium = c/v. Absolute refractive index of water ≈ 1.33; glass ≈ 1.5. Apparent depth: objects in water appear shallower than actual depth. Refraction causes: bending of a pencil in water, twinkling of stars, early sunrise and delayed sunset.

A lens is a transparent material (glass) that refracts light. Convex (converging) lens: thicker in middle; converges light rays; used in magnifying glass, spectacles for hypermetropia, cameras, microscopes, telescopes. Concave (diverging) lens: thinner in middle; diverges light rays; used in spectacles for myopia. Key terms: Optical centre (O), Principal foci (F₁, F₂), Focal length (f), Power of lens (P = 1/f in dioptres). Lens formula: 1/v - 1/u = 1/f. Magnification: m = v/u. A convex lens forms real inverted images (object beyond F) or virtual erect magnified images (object between O and F). Power is positive for convex, negative for concave lenses.

The human eye works like a camera. Cornea (outer transparent layer), Iris (controls pupil size/amount of light), Pupil (opening), Lens (flexible, focuses image), Retina (screen with rods — dim light, cones — colour), Optic nerve (transmits signals to brain). Accommodation: ability of the eye to adjust focal length by changing lens curvature — controlled by ciliary muscles. Near point: 25 cm; Far point: infinity. Defects of vision: Myopia (short-sightedness) — image forms in front of retina; corrected by concave lens. Hypermetropia (long-sightedness) — image forms behind retina; corrected by convex lens. Presbyopia — loss of accommodation with age; corrected by bifocal lenses. Astigmatism — uneven curvature of cornea; corrected by cylindrical lenses.

Dispersion: splitting of white light into its component colours (VIBGYOR) by a prism, due to different refractive indices for different wavelengths. Violet deviates the most; Red deviates the least. Rainbow: formed when sunlight is dispersed by raindrops (refraction + internal reflection + refraction). Scattering of light (Tyndall effect): light scattered by colloidal particles. Why sky is blue: shorter wavelengths (blue) scattered more by atmospheric particles (Rayleigh scattering). Why sunrise/sunset appear red: at horizon, light travels through more atmosphere; blue light scattered away, only red/orange reaches eyes. Why danger signals are red: red light has longest wavelength — least scattered, visible from far distance.

Object at infinity: image at F, real, inverted, highly diminished. Beyond C: between F and C, real, inverted, diminished. At C: at C, real, inverted, same size. Between C and F: beyond C, real, inverted, enlarged. At F: at infinity, real, inverted, highly enlarged. Between F and P: behind the mirror, virtual, erect, enlarged. A concave mirror forms a virtual, erect, enlarged image only when the object is between the pole and the focus (used as a shaving mirror).

New Cartesian sign convention: the pole is the origin; the principal axis is the x-axis; distances measured in the direction of incident light are positive and against it are negative; heights above the axis are positive, below are negative. Mirror formula: 1/v + 1/u = 1/f. For a spherical mirror f = R/2. Magnification m = h'/h = −v/u. For a concave mirror f is negative; for a convex mirror f is positive. Negative m means the image is real and inverted; positive m means virtual and erect.

Refraction is the bending of light when it passes from one transparent medium to another. Laws: (1) the incident ray, refracted ray and normal lie in the same plane; (2) sin i / sin r = constant (Snell's law) for a given pair of media. Light bends towards the normal when it enters a denser medium and away from the normal when entering a rarer medium. Absolute refractive index n = speed of light in vacuum (c) ÷ speed in the medium (v). Examples: water 1.33, glass about 1.5, diamond 2.42 (the highest). A medium with a higher n is optically denser.

Object at infinity: image at F₂, real, inverted, highly diminished. Beyond 2F₁: between F₂ and 2F₂, real, inverted, diminished. At 2F₁: at 2F₂, real, inverted, same size. Between F₁ and 2F₁: beyond 2F₂, real, inverted, enlarged. At F₁: at infinity, real, inverted, highly enlarged. Between F₁ and the optical centre: same side as object, virtual, erect, enlarged (used as a magnifying glass). A concave lens always forms a virtual, erect, diminished image between the optical centre and F₁.

Lens formula: 1/v − 1/u = 1/f. Magnification m = h'/h = v/u. Power of a lens P = 1/f (f in metres); unit dioptre (D). A convex lens has positive power and positive focal length; a concave lens has negative power and negative focal length. Power of lenses in contact: P = P₁ + P₂. Example: f = +50 cm gives P = +2 D. Opticians use power to prescribe spectacles; a lens of power +1 D has focal length 1 m.

Myopia (near-sightedness): distant objects appear blurred; the image forms in front of the retina because the eyeball is too long or the lens is too curved; corrected by a concave lens. Hypermetropia (far-sightedness): near objects appear blurred; the image forms behind the retina; corrected by a convex lens. Presbyopia: weakening of ciliary muscles and loss of flexibility of the lens with age, causing both near and distant vision problems; corrected using bifocal lenses. Cataract: the lens becomes cloudy and is replaced surgically.

Refraction of light by the Earth's atmosphere is atmospheric refraction. Twinkling of stars: starlight passes through layers of air of varying density, so its apparent position keeps shifting and brightness fluctuates; stars are point sources so they appear to twinkle; planets are nearer extended sources, so the variations average out and they do not twinkle. Advance sunrise and delayed sunset: refraction lets us see the Sun about 2 minutes before it actually rises and about 2 minutes after it sets, so the day is about 4 minutes longer.

Tyndall effect is the scattering of light by colloidal particles, and it makes the path of a light beam visible. The sky appears blue because molecules of air and fine particles scatter the shorter wavelengths (blue) much more than the longer wavelengths (red). At sunrise and sunset the Sun is near the horizon and its light travels a longer path through the atmosphere, so most blue light is scattered away and the red reaches us. Red is used in danger signals because it is the least scattered. For an astronaut, the sky looks dark because there is no atmosphere to scatter light.

Mirror: 1/v + 1/u = 1/f; f = R/2; m = −v/u. Lens: 1/v − 1/u = 1/f; m = v/u; P = 1/f. Snell's law: sin i / sin r = n₂₁; n = c/v. Concave mirror: f negative; convex mirror: f positive. Convex lens: f positive; concave lens: f negative. Rainbow: dispersion, refraction and internal reflection of sunlight in water droplets. Near point of normal eye: 25 cm; far point: infinity.