Light

Every optical angle — incidence, reflection and refraction — is measured between the ray and the normal, never between the ray and the surface. A ray making 30 degrees with a mirror has an angle of incidence of $90 - 30 = 60$ degrees. Read the angle off the surface and the law of reflection then places the reflected ray wrongly, so every later angle is wrong too.

Core properties: same size, same distance behind the mirror as the object is in front, laterally inverted, upright. (Extended) It is also virtual — the reflected rays only appear to come from it, no light reaches that point, so it cannot be caught on a screen. Locate it by extending the reflected rays backwards as dashed construction lines.

Going from air into a denser medium (glass, water) light slows down and bends towards the normal, so the angle of refraction is smaller than the angle of incidence. Candidates routinely draw the ray bending away from the normal, or passing straight through unchanged. It only continues undeviated when it meets the boundary along the normal ($i = 0$).

Take the sine of each angle first, then divide: $n = (\sin i)/(\sin r)$. From $i = 53$ and $r = 31$ degrees the value is $\sin 53^\circ / \sin 31^\circ = 0.799/0.515 = 1.55$ — not $53/31$. Keep $i$ in the less dense medium (air), $r$ in the denser one, and give $n$ with no unit — it is a ratio of sines. A larger $n$ bends light more; glass has $n \approx 1.5$.

Rearranging $n = (\sin i)/(\sin r)$ gives $\sin r = (\sin i)/n$ — that is $\sin r$, not $r$, so finish with the inverse sine: $\sin r = 0.382 \Rightarrow r = 22.5$ degrees. The same slip appears with the critical angle, which uses $\sin C = 1/n$ and not $\sin C = n$; writing $\sin C = 1.5$ has no solution at all.

The critical angle $C$ is the angle of incidence, in the denser medium, for which the angle of refraction is exactly 90 degrees. Answers that omit "angle of incidence" or omit "90 degrees" are incomplete. Total internal reflection happens only above $C$: at exactly $C$ the refracted ray grazes along the boundary, and below $C$ the light refracts out.

A real image from a converging lens is always inverted, but it is not always bigger. A distant object gives a diminished real image; enlargement needs the object between $f$ and $2f$. Use the examiner's term principal focus or focal point — "focus point" is not accepted. Give both descriptors every time: size and orientation.