Light: Reflection, Refraction, Total Internal Reflection and Lenses

Light is the largest subtopic in Waves and the most diagram-heavy in the whole 0625 syllabus. Examiners test it through ray diagrams, two refractive-index equations and lens constructions. These marks reward a sharp pencil and a fixed method.

What are the rules for reflection and refraction of light?

Reflection: the angle of incidence equals the angle of reflection, both measured from the normal. The image in a plane mirror has four properties: same size as the object, same distance behind the mirror as the object is in front, virtual (cannot be formed on a screen), and laterally inverted. All four are standard recall marks.

Refraction: light bends towards the normal when it slows down entering a denser medium (air to glass), and away from the normal when it speeds up leaving. Extended candidates quantify this with refractive index.

Quantity	Symbol	Unit
Angle of incidence	$i$	degree (°)
Angle of refraction	$r$	degree (°)
Critical angle	$c$	degree (°)
Refractive index	$n$	no unit

In words: refractive index = sine of the angle of incidence ÷ sine of the angle of refraction. In symbols: $n = \dfrac{\sin i}{\sin r}$. The critical-angle relationship: $n = \dfrac{1}{\sin c}$.

Total internal reflection happens when light inside the denser medium hits the boundary at an angle greater than the critical angle. All the light reflects back inside. Optical fibres exploit this to carry telephone and broadband signals as light pulses bouncing along a glass core. White light passing through a prism disperses into a spectrum because each colour refracts by a different amount. Light of a single frequency is called monochromatic.

How do you draw lens ray diagrams that score full marks?

A thin converging lens brings parallel rays to a focus at the principal focus, F. The distance from lens to F is the focal length. Use two construction rays from the top of the object: one parallel to the axis, refracting through F; one straight through the centre of the lens. Where they cross, the image forms. Object beyond F: image is real and inverted. Object closer than F: the rays diverge, and tracing them backwards gives an enlarged, upright, virtual image (the magnifying glass). Extended candidates also link lenses to vision: a diverging lens corrects short-sightedness; a converging lens corrects long-sightedness.

Worked Exam Question

A ray of light passes from air into glass. The angle of incidence is 45° and the angle of refraction is 28°. (a) Calculate the refractive index of the glass. [2] (b) Calculate the critical angle of the glass. [2]

Worked solution:

1. (a) Equation: $n = \dfrac{\sin i}{\sin r}$
2. Substitute: $n = \sin 45^\circ \div \sin 28^\circ = 0.7071 \div 0.4695$
3. Answer: $n = 1.5$ (2 significant figures)
4. (b) Equation: $n = \dfrac{1}{\sin c}$, so $\sin c = 1 \div 1.5 = 0.667$; $c = \sin^{-1}(0.667) = 42^\circ$ (2 significant figures)

Mark scheme:

• M1: $n = \dfrac{\sin i}{\sin r}$ with correct substitution
• A1: 1.5 (accept 1.51; no unit)
• M1: $\sin c = \dfrac{1}{n}$ used (error carried forward allowed)
• A1: $42^\circ$

Common Mistakes

• Measuring angles from the mirror or glass surface. Every angle is measured from the normal; mislabelled angles void the calculation.
• Forgetting the sines and computing $i \div r$. $45 \div 28$ gives 1.6, close enough to look right and still wrong (you must take the sines first).
• Giving refractive index a unit. It is a ratio of sines and has no unit.
• Drawing ray diagrams without arrows, or construction lines freehand. Arrows and ruler-straight rays are explicit mark-scheme requirements.
• Calling the plane-mirror image real. It is virtual, because no rays actually meet behind the mirror.

Exam Technique Tip

Set your calculator to degrees before the exam starts, and check it on every paper. A calculator left in radians turns $\sin 45^\circ$ into 0.851 and quietly destroys both marks. Then follow the routine: equation, substitution with the sine values written out, answer to 2 significant figures. Writing the intermediate sine values earns method marks even when the final keystroke slips.

How This Is Examined

Light appears on every paper, usually for more marks than any other Waves subtopic. Papers 1 and 2 test mirror-image properties, refraction direction and lens facts. Papers 3 and 4 demand ray diagrams and, on Extended only, the $n = \dfrac{\sin i}{\sin r}$ and $n = \dfrac{1}{\sin c}$ calculations, plus virtual-image lens constructions and sight correction. Core candidates describe total internal reflection qualitatively. Papers 5 and 6 feature the classic pins-and-glass-block or lens-and-screen experiments: tracing rays, measuring angles, finding focal length. There is a lot here, so we split light across two 1-to-1 sessions, diagrams first, calculations second. Mixing the two in one sitting is where self-study usually breaks down.