IGCSE Physics Light notes

The normal is the line drawn at 90° to a surface at the point where the ray hits. All light angles are measured from the normal, never from the surface. The angle of incidence i sits between the incoming ray and the normal; the angle of reflection r sits between the reflected ray and the normal.

A plane mirror forms an image with three fixed properties: it is the same size as the object, the same distance behind the mirror as the object is in front, and virtual — the rays only appear to come from it. Trace two rays from the object, reflect them, and extend the reflected rays backwards behind the mirror with dashed lines: they cross at the image point. A virtual image cannot be projected onto a screen, because no real light actually passes through that point.

Light travels at different speeds in different materials. Crossing from air into glass it slows down, so the ray bends towards the normal; leaving glass into air it speeds up and bends away from the normal. The classic experiment: shine a ray into a rectangular glass block, mark the entry and exit points, remove the block and join the dots — the ray inside runs along the normal direction only if it entered along the normal.

Going the other way — glass to air — there is a limit. The critical angle c is the angle of incidence (in the denser medium) at which the refracted ray skims exactly along the boundary (refracted at 90°). At angles beyond c, no light escapes at all: it is all reflected back inside. This is total internal reflection, and it needs two conditions: light travelling in the denser medium, and an angle of incidence greater than the critical angle. Everyday examples: the sparkle of a diamond cut to trap light, and the mirror-like silvered surface seen by a diver looking up at steep angles.

Supplement: the refractive index n of a medium measures how much slower light travels in it: n = (speed of light in vacuum or air) ÷ (speed in the medium). For angles, n = sin i / sin r (air to medium). At the critical angle, r = 90°, which gives n = 1 / sin c. Glass with n = 1.5 has c = sin⁻¹(1/1.5) ≈ 42°.

Supplement: an optical fibre is a thin, flexible glass thread. Light enters end-on, meets the wall beyond the critical angle every time it bounces, and is trapped by total internal reflection along the whole fibre — even round corners. Fibres carry telephone and internet traffic as pulses of light over huge distances with little loss, which is why they dominate telecommunications.

A converging lens is thicker in the middle: parallel rays passing through it are bent inwards to cross at the principal focus (focal point). A diverging lens is thinner in the middle: parallel rays spread outwards, appearing to have come from a principal focus in front of the lens. The focal length is the distance from the lens centre to the principal focus; the principal axis is the line through the lens centre at right angles to it.

For a converging lens with an object beyond the focal length, two rays locate the image: (1) a ray parallel to the principal axis refracts through the far focal point; (2) a ray straight through the centre of the lens carries on unbent. Where they cross is the image. Depending on where the object sits, the image is inverted (upside down) and real — light actually passes through it, so it can be caught on a screen — and may be enlarged, same size or diminished.

Put the object inside the focal length and the refracted rays diverge — they never cross. Extrapolated backwards, they meet behind the object, forming an upright, enlarged, virtual image (Supplement). This is exactly how a magnifying glass works: hold it closer to the page than its focal length and the page’s virtual image is bigger and the right way up.

Supplement: the eye’s own lens focuses light onto the retina. In short sight the eye focuses light in front of the retina for distant objects, so a diverging lens weakens the eye’s convergence first; in long sight the eye focuses behind the retina (even for near objects), so a converging lens adds convergence. Spectacle lenses pre-bend the rays so the eye’s own lens can finish the job on the retina.

White light is a mixture of colours. In a glass prism each colour travels at a slightly different speed, so each refracts by a different amount — violet the most, red the least. The prism therefore fans the ray out into the visible spectrum: red, orange, yellow, green, blue, indigo, violet. This splitting is called dispersion. In order of wavelength, red is longest and violet shortest; in order of frequency, violet is highest and red lowest.

Supplement: light of a single frequency (a single colour, with no spread) is called monochromatic. Laser light is close to perfectly monochromatic; white light is the opposite — a blend of every visible frequency at once.