Chapter 6: Light and Optics

6.1 Refraction of Light

• Refraction occurs because light bends when travelling between media of different optical densities, due to a change in velocity. (p.232)
• Refractive index, n = c/v (speed of light in vacuum ÷ speed of light in medium). (p.233)
• Snell's Law: n = sin i / sin r (or n₁ sin θ₁ = n₂ sin θ₂). (p.235)
• Refraction causes an object viewed through a denser medium to appear closer to the surface (real depth vs apparent depth). (p.237)
• n = H/h, where H = real depth and h = apparent depth. (p.239)

6.2 Total Internal Reflection

• Total internal reflection occurs when light travels from a denser to a less dense medium and the angle of incidence is greater than the critical angle. (p.242)
• Critical angle, c: the angle of incidence in the denser medium at which the angle of refraction equals 90°. (p.243)
• n = 1/sin c. The higher the refractive index, the smaller the critical angle. (p.244)
• Rainbow formation: refraction, dispersion, and total internal reflection of light in water droplets. (p.247)
• Mirage: caused by refraction of light through air layers of different temperature and optical density. (p.247)
• Applications: optical fibres (telecommunications, medical endoscopes), prism periscopes, cat's eye road reflectors. (p.248)

6.3 Image Formation by Lenses

• Convex lens: a converging lens with a real focal point. Concave lens: a diverging lens with a virtual focal point. (p.251)
• Key terms: optical centre (O), principal axis, axis of lens, focal point (F), object distance (u), image distance (v), focal length (f). (p.252)
• A convex lens forms images ranging from real/inverted/diminished (object beyond 2F) to virtual/upright/magnified (object within F), depending on object position. (p.256)
• A concave lens always produces a virtual, upright, diminished image, regardless of object position. (p.257)
• Linear magnification, m = h_i/h₀ = v/u (p.258)

6.4 Thin Lens Formula

• 1/f = 1/u + 1/v (p.261)
• Sign convention: convex/converging lens → f positive; concave/diverging lens → f negative; real image → v positive (opposite side of the object); virtual image → v negative (same side as the object). (p.261)

6.5 Optical Instruments

• Compound microscope: two convex lenses — short-focal-length objective lens and longer-focal-length eyepiece lens. The objective forms a real, inverted, magnified first image; the eyepiece then forms a virtual, magnified final image. (p.266)
• Telescope: objective lens (long f_o) and eyepiece lens (short f_e). At normal adjustment, lens separation = f_o + f_e, and magnification M = f_o/f_e. (p.267)
• Small lenses in smartphone cameras and CCTV form an image at the sensor; minimum device thickness is limited by the lens's focal length. (p.268)

6.6 Image Formation by Spherical Mirrors

• Key terms: centre of curvature (C), radius of curvature (r = 2f), pole (P), focal point (F). (p.271)
• Concave mirror: image characteristics range from real/inverted/diminished (object beyond C) to virtual/upright/magnified (object within F). (p.274)
• Convex mirror: always produces a virtual, upright, diminished image, with a wider field of vision than a plane mirror of the same size. (p.274)
• Applications of concave mirror: car headlight reflectors, dental mirrors, cosmetic mirrors. (p.275)
• Applications of convex mirror: vehicle rear-view mirrors, blind-spot mirrors, security mirrors in buildings. (p.276)