3.54PH1 · Section 3: Waves

Refraction of light

Key learnings

Refraction: speed changes, not frequency
Refraction is the change in direction of light as it crosses a boundary because its speed changes; frequency (and colour) stay the same, so wavelength changes too. Air → glass: light slows and bends towards the normal; glass → air: it speeds up and bends away. A ray along the normal (0°) passes straight through. Refractive index $n = c/v$ , with $c = 3 \times 10^8$ m/s; glass $n \approx 1.5$ , water $n \approx 1.33$ . Larger $n$ = slower light = more bending.
Snell's law: n = sin i / sin r
Snell's law (air into a medium): $n = \dfrac{\sin i}{\sin r}$ , with $i$ = angle of incidence and $r$ = angle of refraction, both from the normal (formula-sheet form). General form: $n_1 \sin i = n_2 \sin r$ . Mark-scheme definition of $n$ : the ratio of $\sin i$ to $\sin r$ for a ray from air into the medium — two elements: the sines ratioed AND their order. Never write "how much light bends". Example: $i = 50°$ , $r = 30°$ gives $n = 1.53$ .
Critical angle and TIR: sin c = 1/n
Critical angle $c$ : the incidence angle in the denser medium at which the refracted ray grazes the surface (90°). Below $c$ light refracts out; above $c$ : total internal reflection (TIR), all light reflects back inside. $\sin c = \dfrac{1}{n}$ , so $c = \sin^{-1}(1/n)$ ; for glass $n = 1.5$ gives $c = 41.8°$ . TIR needs both: (1) denser → less dense medium, and (2) incidence angle above $c$ . Uses: optical fibres and reflecting prisms in periscopes and binoculars.

Common mistakes

Drawn from real examiner reports.

Angles measured from surface, not normal

Both $i$ and $r$ are measured from the normal (perpendicular to the boundary), never from the surface. Using the surface angle puts the complementary angle into $n = \sin i / \sin r$ and gives a wildly wrong $n$ — often below 1, impossible for a solid denser than air. Draw the dashed normal first. November 2024 Paper 1P Q6(c)(i) flagged exactly this.

November 2024 Paper 1P Q6(c)(i): many candidates measured the angle from the surface rather than from the normal, producing incorrect values when calculating or drawing the emergent ray direction.

TIR shown when entering a denser medium

TIR cannot happen when light enters a denser medium (air → glass): refraction always occurs and the ray bends towards the normal, with no critical angle to exceed. In June 2024 Paper 1P Q8 many candidates drew ray B undergoing TIR while entering glass — a zero-scoring physics error. Always check: is the ray leaving the denser (glass) side? Only then can TIR occur.

June 2024 Paper 1P Q8: some candidates showed ray B (moving from air into glass, i.e. entering a denser medium) undergoing total internal reflection — this is physically impossible and scored zero for that ray.

TIR description misses one condition

Describing TIR, most candidates state only "angle greater than the critical angle" and omit the direction. Both conditions are required: (a) from a denser to a less dense medium, AND (b) angle of incidence greater than the critical angle. November 2024 Paper 1P Q6(b)(iii) called this "surprisingly challenging" — a vague "the light reflects" scores nothing.

November 2024 Paper 1P Q6(b)(iii): description of total internal reflection was "surprisingly challenging"; most candidates missed at least one of the two required conditions (dense-to-less-dense medium AND angle exceeding critical angle).

Vague refractive-index definition

For "define refractive index", "how much a material bends light" earns nothing. Give a two-element form: the ratio of $\sin i$ to $\sin r$ (air into the medium), OR the ratio of the speed of light in vacuum to the speed in the medium ( $n = c/v$ ). State both quantities AND the correct order — inverting the ratio gives $n < 1$ , which is impossible.

Using sin c = n instead of 1/n

Computing the critical angle, do not write $\sin c = n$ . The formula is $\sin c = \dfrac{1}{n}$ . Using $\sin c = 1.5$ is impossible (a sine cannot exceed 1) and the step collapses. Take $c = \sin^{-1}(1/n)$ ; for $n = 1.5$ , $c = \sin^{-1}(0.667) = 41.8°$ .

(general exam technique)

Radians mode or forgetting inverse sine

Two calculator slips: (1) working in radians — set degree mode, or $\sin^{-1}(0.66)$ returns nonsense; (2) forgetting to rearrange or to take $\sin^{-1}$ , leaving the answer as a sine value like 0.38 instead of the angle 22.5°. Check: entering a denser medium gives $r < i$ .

(general exam technique)

Exam tips

For "explain", add a calculation and a reason
When the command word is explain, drawing alone scores about half. Add labelled angles from the normal, a calculation ( $n = \sin i / \sin r$ or $\sin c = 1/n$ ), and a reason linking the result to the bending direction. June 2024 Paper 1P Q8 penalised missing calculations.
Draw the normal first, convert surface angles
Always draw the dashed normal first, then measure $i$ and $r$ to it. If a question gives the angle to the surface, convert: angle from normal $= 90° - \text{surface angle}$ before substituting into Snell's law.
Sanity-check the bending direction
Check every refraction answer by direction: entering a denser medium ( $n > 1$ ) bends the ray towards the normal, so $r < i$ ; leaving it bends away, so $r > i$ . If your $r$ comes out on the wrong side of $i$ , you have inverted the formula.
Emergent ray parallel for a parallel block
For a rectangular (parallel-sided) block, the emergent ray leaves parallel to the original incident ray, just laterally shifted. Drawing it at a random angle loses the mark. Mark both normals; the ray bends towards the normal on entry and away on exit.

Revision notes