Laws of reflection: (1) incident ray, reflected ray and normal lie in the same plane; (2) angle of incidence = angle of reflection.
Plane mirror image: virtual, erect, same size, laterally inverted, as far behind the mirror as the object is in front.
Refraction: change in direction of light on passing from one medium to another because its speed changes. Refractive index n = speed of light in vacuum / speed in the medium = sin i / sin r (Snell's law).
Total internal reflection (TIR): a ray in a denser medium is completely reflected back when the angle of incidence is greater than the critical angle. Critical angle: angle of incidence in the denser medium for which the angle of refraction is 90°. sin c = 1/n.
Optical fibre: thin glass or plastic tube working on TIR. Uses: telecommunication, internet, endoscopy.
Lens: convex (converging, thick in the middle) and concave (diverging, thin in the middle). Focal length: distance from lens to principal focus. Power of lens P = 1/f in dioptre (D) with f in metres.
Dispersion: splitting of white light into seven colours by a prism because each colour is refracted by a different amount (violet most, red least).
Real image: formed by actual meeting of rays, can be taken on a screen, inverted. Virtual image: rays only appear to meet, cannot be taken on a screen, erect.
Gravitational lensing: bending of light by the gravity of a massive object (Einstein rings); used to study dark matter. Acoustic lensing: using materials to focus or spread sound (non-destructive testing).
Formulas
n = c/v. n = sin i / sin r. sin c = 1/n (or n2/n1). 1/f = 1/p + 1/q. Magnification m = q/p = hi/ho. Light speed in vacuum 3 × 10⁸ m/s.
Must-know points
Glass slab: ray bends towards the normal entering, away on leaving, emerges parallel to the incident ray but shifted sideways. Label incident ray, refracted ray, emergent ray, normal, angles i and r.
Conditions for TIR: light must travel from denser to rarer medium; angle of incidence must be greater than the critical angle. Examples: mirage, diamond sparkle, optical fibre, prism binoculars.
Three differences between real and virtual images: real can be received on a screen, virtual cannot; real is inverted, virtual is erect (for a lens); real is formed by actual intersection of rays, virtual by apparent intersection.
Image by magnifying glass (object inside the focal length): virtual, erect, magnified, on the same side as the object.
Convex lens ray diagrams: beyond 2F gives real, inverted, diminished image between F and 2F; at 2F gives real, inverted, same size at 2F; between F and 2F gives real, inverted, magnified beyond 2F; at F gives image at infinity; inside F gives virtual, erect, magnified image.
Magnification greater than 1 when object is between F and 2F (real) or inside F (virtual).
Human eye: cornea and lens focus light on the retina, which has rods (dim light, about 100 million) and cones (colour, about 6 million). Short-sightedness (myopia): far objects blurred, corrected with concave lens. Long-sightedness (hypermetropia): near objects blurred, corrected with convex lens. Draw ray diagrams with and without the lens.
Visible spectrum about 400 to 750 nm. Rainbow: refraction, TIR and dispersion in raindrops. Object in water looks raised because of refraction.
Past-paper questions with model answers
What is refractive index? Calculate it if the speed of light in the medium is 2 × 10⁸ m/s: n = 3 × 10⁸ / 2 × 10⁸ = 1.5.
Labelled sketch of refraction through a parallel-sided glass slab (3 marks).
Snell's law with mathematical expression: n = sin i / sin r.
Critical angle with formula, conditions for TIR (5 marks, Section C).
Object 2 cm from a convex lens, image 6 cm away (virtual): 1/f = 1/2 − 1/6 = 1/3, f = 3 cm, m = 6/2 = 3.
Image 10 cm, object 5 cm: m = 2; m greater than 1 when the object is within 2F (between F and 2F or inside F).
M = 0.5, object 2 cm tall at 5 cm: q = M p = 2.5 cm, image height = 0.5 × 2 = 1 cm.
Characteristics of image by magnifying glass; three differences between real and virtual images.
Lenses for long and short sight with diagrams; ray diagram of convex lens for object beyond 2F and at F (Section C); optical fibre principle and two advantages (no loss, light weight, no interference).