Not given in the exam, recall it.
What it is for
Refractive index (Snell's law) is used in Light and Optics (SPM Physics Form 4). Keep the SI units in every line of working. Light and Optics
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| n | refractive index (no unit, ratio) | , |
| i | angle of incidence | ° |
| r | angle of refraction | ° |
Rearrangements
sin i = n sin rsin r = sin i / n
Worked example
Common trap
Understanding Snell’s law
Snell’s law, n = sin i / sin r, gives the refractive index of a medium from the angles a ray makes as it crosses a boundary. n is the refractive index, a pure ratio with no unit. i is the angle of incidence and r is the angle of refraction, both measured in degrees (°) from the normal, the line perpendicular to the surface.
A denser optical medium bends light more, giving a larger n. Because the ray bends towards the normal on entering a denser medium, r is smaller than i there, so sin i / sin r is greater than 1.
Rearrange to find an angle: sin i = n sin r or sin r = sin i / n. Take the inverse sine at the end to recover the angle itself.
A worked example, step by step
A ray of light travels from air into water of refractive index n = 1.33, striking the surface at an angle of incidence i = 45°. Find the angle of refraction r.
Rearrange Snell’s law to make sin r the subject:
sin r = sin i / n = sin 45° / 1.33 = 0.707 / 1.33 = 0.532.
Take the inverse sine:
r = sin⁻¹(0.532) = 32.1°.
So r = 32.1° (3 significant figures). The refracted angle is smaller than the incident angle, which is correct because light bends towards the normal when entering a denser medium.
Common mistakes and how this is tested
The most common trap is measuring the angles from the surface instead of from the normal. Both i and r are always measured from the normal, so an angle quoted "from the surface" must be subtracted from 90° first.
Other errors: forgetting to take the inverse sine, so leaving the answer as sin r rather than r; putting the calculator in radian mode instead of degrees; and swapping i and r, which inverts n.
Under calculate show n = sin i / sin r, substitute the angles and give n to a sensible number of figures. Under define you may be asked to state Snell’s law or define refractive index.
Under explain, relate a larger n to greater bending.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)