Law of reflection (i = r) and mirror image
Law of reflection: angle of incidence = angle of reflection, both measured from the normal: . A ray at 50° to the surface has , so .
Plane mirror image — VUSLD: Virtual (not projectable), Upright, Same size (magnification = 1), Laterally inverted (left–right swapped), same Distance behind as the object is in front. Specular (smooth) = clear image; diffuse (rough) scatters rays, no image (though holds at each point).
Refraction, refractive index and TIR
Refraction: light bends at a boundary as its speed changes; frequency and colour stay the same. Air → glass: bends towards the normal (); glass → air: bends away ().
Refractive index: ; e.g. . Critical angle: .
TIR needs BOTH: denser → less-dense AND ; then all light reflects, no refracted ray. Uses: optical fibres (telecoms, endoscopes), reflecting prisms.
Dispersion and (E) lenses
Dispersion: a glass prism splits white light into a spectrum — called dispersion, not refraction/diffraction. Colours: red → violet (ROYGBIV), red least, violet most refracted.
(E) Each colour has a different — violet highest (bends most), red lowest. A converging lens brings parallel rays to the principal focus (focal length ); object inside gives a virtual, magnified image. A diverging lens always gives a virtual, upright, diminished image.
Drawn from real examiner reports.
Measure angles from the normal, not surface
Angle of incidence and refraction are measured from the normal (perpendicular to the surface), never from the surface. A ray at 50° to the surface has . Feeding the surface angle into gives a wrong — often below 1, impossible for glass. Fix: draw the dashed normal first, then measure to it.
June 2024 Paper 31 Q7(a)(ii): most common error was 50° (angle from the surface) instead of the correct 40° (angle from the normal).
TIR needs both conditions; no refracted ray
Two traps. (1) Stating only one condition: full marks need BOTH — light goes from a denser to a less dense medium AND exceeds the critical angle . (2) Believing a refracted ray survives past : at TIR all light reflects back and there is no refracted ray. "The angle is large" alone scores partial marks.
June 2024 Paper 21 Q19 (Extended MCQ): most candidates chose an option showing a refracted ray past the critical angle; Paper 32 Q7(c): only stronger candidates gave both conditions.
Prism spectrum is dispersion, not refraction
The splitting of white light by a prism is dispersion. The common wrong answers are refraction (that is the mechanism, not the name) and diffraction (the spreading of waves through a gap or round an obstacle — a different effect). Learn the term: dispersion = white light separated into a spectrum by a prism.
June 2024 Paper 31 Q7(c)(i): most common wrong answers were refraction and diffraction instead of dispersion.
Define refractive index by the two sines
"A measure of how much a material bends light" earns nothing. The mark scheme needs a two-element definition: — the ratio of of the angle of incidence (in air) to of the angle of refraction (in the medium). Also accepted: (speed in vacuum ÷ speed in the medium). Both forms give as a pure number, no unit.
June 2024 Paper 22 Q20: many candidates could not link the definition of refractive index to its equation.
Mirror image is laterally inverted, upright
A plane mirror image is upright, not upside-down. It is laterally inverted — left and right are swapped (which is why AMBULANCE is written reversed on the front of the vehicle). Writing "inverted" alone implies upside-down, which is wrong for a plane mirror. The image is also virtual, the same size, and as far behind the mirror as the object is in front.
Prism ray is not parallel; block ray is
A prism has non-parallel sides, so the emergent ray is not parallel to the incident ray and the colours disperse. A rectangular block has parallel sides: the ray bends at each surface but the emergent ray leaves parallel to the incident ray (just shifted sideways), with no net dispersion. Do not draw a prism's output like a block's.
Write the equation before substituting
Write the formula in symbols or words first — e.g. — then substitute the numbers. Method marks are awarded for the correct equation even if the arithmetic is wrong (June 2024 Paper 41 key messages).
Put a unit on every numerical answer
Every numerical answer needs its unit — speed in m/s, angle in ° — and state that has no unit. In June 2024 Paper 41 Q4(b) many candidates omitted m/s on the speed of light in glass and lost the mark.
State BOTH TIR conditions separately
Asked for the conditions for TIR, write two separate points: (1) light travels from a denser to a less dense medium; (2) the angle of incidence exceeds the critical angle. Merging them into one sentence, or giving only one, loses a mark.
Draw the dashed normal first
In any optics diagram, draw the dashed normal at the boundary before any ray — this stops you measuring from the surface. For "explain" answers give cause + mechanism + effect; "light slows down" alone scores 1 of 3 marks.
| Quantity | Formula | Symbols |
|---|---|---|
| Reflection | , = angles of incidence, reflection (from normal) | |
| Refractive index (Snell) | = incidence in air; = refraction in medium | |
| Refractive index (speed) | m s; = speed in medium | |
| Critical angle | = critical angle, inside denser medium | |
| Snell's law (E, general) | , = refractive indices of the two media |
Angles always from the normal, in degrees.
Define refractive index.
A ray of light passes from air into a glass block. The angle of incidence is 40° and the angle of refraction inside the glass is 25°.
(a) State the equation relating refractive index, angle of incidence, and angle of refraction.
(b) Calculate the refractive index of the glass. Give your answer to 2 significant figures.