Is this formula given in the exam?

No. SPM Physics papers provide no formula sheet, so this must be recalled.

Does the critical angle depend on the colour of light?

Slightly, because refractive index varies a little with wavelength. In SPM you use the single n value given in the question, so treat the critical angle as fixed for that medium.

Why must light go from dense to less dense for total internal reflection?

Only then can the refracted ray bend to 90° at the critical angle. Beyond that angle no refraction is possible, so all the light reflects back inside.

What is the critical angle if n = 1?

sin c would equal 1, giving c = 90°. This means a medium with the same optical density as its surroundings has no real critical angle, total internal reflection cannot occur.

Critical angle Formula, SPM Physics

Critical angle

n = 1 / sin c

Not given in the exam, recall it.

What it is for

Critical angle 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)	,
`c`	critical angle	°

Rearrangements

sin c = 1 / n
c = sin⁻¹(1 / n)

Worked example

A glass has refractive index n = 1.5. sin c = 1 / n = 1 / 1.5 = 0.667, so c = sin⁻¹(0.667) = 41.8°.

Common trap

Rearrange to sin c = 1/n first. Total internal reflection only happens going from a denser to a less dense medium when the angle exceeds c.

Understanding the critical angle

The critical angle formula n = 1 / sin c links two quantities. n is the refractive index of the denser medium, a pure ratio with no SI unit. c is the critical angle, measured in degrees (°) from the normal.

The two are inversely related: a higher refractive index bends light more strongly, so total internal reflection sets in at a smaller critical angle. That is why diamond (large n) sparkles, its critical angle is very small.

To find the angle, rearrange to sin c = 1 / n, then take the inverse sine, c = sin⁻¹(1 / n). Rearranging the other way gives n = 1 / sin c when the critical angle is measured in an experiment.

Always isolate sin c before pressing the sin⁻¹ key.

A worked example, step by step

Light travels inside water whose refractive index is n = 1.33. Find its critical angle.

Start from the rearranged form:

sin c = 1 / n = 1 / 1.33 = 0.752
c = sin⁻¹(0.752) = 48.8°

So the critical angle for the water–air boundary is c = 48.8° (3 significant figures). Any ray inside the water striking the surface at more than 48.8° to the normal is totally internally reflected instead of escaping.

Notice the answer is larger than the 41.8° you get for glass (n = 1.5). Water bends light less than glass, so its critical angle is bigger, a useful check that your calculation makes physical sense.

Common mistakes and how this is tested

The main trap: rearrange to sin c = 1/n first, and remember total internal reflection only happens going from a denser to a less dense medium when the angle exceeds c.

Other frequent errors:

Forgetting the inverse sine, students write c = 1/n and leave 0.667 as if it were the angle.
Leaving the calculator in radian mode, giving a nonsense value like 0.73.
Measuring the angle from the surface instead of the normal.

Questions ask you to define the critical angle, calculate it from a given n, or explain why light is totally internally reflected in an optical fibre or a prism.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026