Light and sound

Every angle — incidence, reflection, refraction and the critical angle — is measured from the normal, never from the surface. Candidates lost marks for measuring from the surface and for measuring the wrong angle altogether. Always draw the normal first as a dashed perpendicular line, then take the smaller angle between the ray and that normal.

Refractive index uses $n = \dfrac{\sin i}{\sin r}$ — you must take the sine of each angle. The persistent error is dividing the angles directly ($i \div r$), which is wrong even when the correct formula was written down. Keep the incidence angle (in air) on top: for glass $n > 1$, so writing $\sin r / \sin i$ turns it upside down (a value below 1).

Leaving a denser medium (glass to air), the ray bends away from the normal, so the angle of refraction is larger than the angle of incidence. Only about a quarter of candidates drew this correctly. The ray cannot emerge at 90 degrees to the normal or run along the boundary — that is the critical-angle case, not ordinary refraction.

Describing TIR is a classic marks-loser: "the light bounces back inside" scores nothing. The mark scheme needs the light in the more dense medium, the angle greater than the critical angle, and then all the light reflected (none refracted out). Examiners found it "surprisingly challenging" and usually too imprecise; state both conditions clearly.

A critical angle and TIR exist only for light going from a denser to a less dense medium. Candidates wastefully calculated a critical angle when the light was entering a medium of higher refractive index, where TIR cannot occur — an irrelevant calculation earning nothing. Check the direction of travel before reaching for $\sin c = 1/n$.

After $\sin c = \dfrac{1}{n}$ you must take the inverse sine ($c = \sin^{-1}(1/n)$) to reach the angle — stopping at $1/n$ leaves no answer. The same applies to a refraction angle: rearrange to $\sin r$, then apply $\sin^{-1}$. Weaker candidates could compute $1/n$ but not complete the inverse-sine step.