Refraction and Refractive Index
Refraction is the change in direction of a wave when it changes speed on entering a new medium. Everything in this topic follows from one cause — the change in speed — so if you understand that, the rest is bookkeeping.
1. Why light bends
Light changes speed when it enters a new medium. If it meets the boundary at an angle, one side of the beam slows before the other, so the beam changes direction.
Refraction is caused by a change in SPEED, not by the boundary “pushing” the light. This is the sentence that earns the explanation marks.
Light travels fastest in a vacuum (3 × 10⁸ m/s), slightly slower in air, slower still in water, and slower again in glass. The denser (optically) the medium, the slower the light.
2. Which way does it bend?
Angles are always measured from the NORMAL — the line drawn at 90° to the surface.
Entering a DENSER medium (slowing down): bends TOWARDS the normal. Entering a LESS DENSE medium (speeding up): bends AWAY from the normal.
So going air → glass, the ray bends towards the normal, and the angle of refraction is smaller than the angle of incidence. Coming back out, glass → air, it bends away and the angle gets larger.
This direction is reversed by students constantly — it was one of the most-recorded errors in the topic. A memory hook that works: slow down, bend towards; speed up, bend away.
A ray entering along the normal (at 90° to the surface) does NOT bend. It still changes speed, but there is no change in direction. Questions test this.
Measure from the normal, never from the surface. The angle between the ray and the surface is the complement of the one you want.
3. What changes and what stays the same
This table is the single most examined idea on the page, and it contains the point most often taught incorrectly.
| Quantity | On refraction |
|---|---|
| Frequency | UNCHANGED |
| Speed | CHANGES |
| Wavelength | CHANGES |
| Direction | changes (unless along the normal) |
| Amplitude | may decrease slightly (some energy reflected/absorbed) |
The frequency NEVER changes. It is fixed by the source, and nothing about the new medium can alter how many waves per second arrive. A recorded error was thinking frequency changes when speed changes — it does not.
Because v = fλ and f is fixed: if the speed decreases, the WAVELENGTH MUST DECREASE TOO.
This point deserves emphasis, because it was taught wrongly. In one lesson a student correctly said that the wavelength decreases when light enters a denser medium, and was told that the wavelength stays the same. The student was right.
When light enters glass or water it slows down, so its wavelength gets SHORTER. Only the frequency is unchanged. If you have been told otherwise, check it against v = fλ: with f fixed, v and λ must change together.
4. Refractive index
n = sin i / sin r (Snell’s law)
where i is the angle of incidence and r the angle of refraction, both measured from the normal.
n = speed of light in a vacuum ÷ speed of light in the medium → n = c / v
Typical values: air ≈ 1.0, water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.4.
Refractive index has NO units — it is a ratio of two speeds (or two sines).
n is always greater than 1, because light travels fastest in a vacuum. If your answer is less than 1, you have inverted the fraction.
Worked example. Light travels from air into glass with i = 40° and r = 25°.
- n = sin 40° / sin 25° = 0.643 / 0.423 = 1.52
Worked example — finding an angle. Light enters water (n = 1.33) at i = 50°.
- 1.33 = sin 50° / sin r
- sin r = sin 50° / 1.33 = 0.766 / 1.33 = 0.576
- r = sin⁻¹(0.576) = 35.2°
Going from air INTO a medium, n = sin i / sin r. Coming OUT of the medium into air, the ratio inverts: n = sin r / sin i. Getting this the wrong way round when light exits a denser medium was a specific recorded error. The safe check: the angle in the denser medium is always the smaller one.
Your calculator must be in DEGREE mode, and take care entering the inverse sine.
5. Critical angle and total internal reflection
When light travels from a denser to a less dense medium, increasing the angle of incidence eventually makes the refracted ray bend so far that it runs along the boundary.
The critical angle (c) is the angle of incidence in the denser medium for which the angle of refraction is exactly 90°.
sin c = 1 / n
Example: for glass with n = 1.5, sin c = 1/1.5 = 0.667, so c = 41.8°.
Beyond the critical angle, NO light is refracted — it is all reflected back inside. This is total internal reflection.
Two conditions, both required:
1. The light must be going from a DENSER to a LESS DENSE medium. 2. The angle of incidence must be GREATER than the critical angle.
Both conditions must be stated for full marks — giving only one was a common shortfall.
A larger refractive index gives a SMALLER critical angle — which is why diamond (n = 2.4, c ≈ 24.4°) sparkles so much: light entering it is very easily trapped and bounces repeatedly before escaping.
6. Drawing refraction diagrams
Marks here are for accuracy and labelling.
- Draw the normal as a dashed line at 90° to the surface, at the point where the ray meets it
- Draw the incident ray with an arrow showing direction
- Bend the ray the correct way at the boundary
- Label the angle of incidence and angle of refraction, both from the normal
Always draw arrows on your rays. Tutors flagged this specifically — an unarrowed line can lose the mark.
Make the bend clearly visible. If your incident and refracted rays look almost identical, the examiner cannot tell you bent it the right way. Exaggerate the difference between the angles.
Use a ruler and a sharp pencil, and draw the normal dashed so it isn’t mistaken for a ray.
7. Everyday effects to explain
- A straw looks bent in a glass of water — light from the submerged part refracts away from the normal as it leaves the water, so the straw appears displaced
- A swimming pool looks shallower than it is — light from the bottom bends away from the normal on leaving, so the image appears higher
- A rainbow — refraction plus dispersion in water droplets
- Optical fibres — repeated total internal reflection keeps light inside the fibre
8. Mistakes that cost marks
Bending the ray the wrong way on entering a denser medium.
Measuring angles from the surface rather than the normal.
Saying frequency changes during refraction.
Saying the wavelength stays the same when light enters a denser medium — it decreases.
Saying the speed doesn’t change.
Inverting Snell’s law when light exits a denser medium.
Getting a refractive index less than 1.
Giving units for refractive index.
Confusing the angle of refraction with the angle of reflection.
Giving only one condition for total internal reflection.
Drawing rays without arrows, or with an indistinguishable bend.
Calculator not in degree mode.
Frequently asked questions
What causes refraction? A change in the speed of the wave as it enters a new medium.
Which way does light bend entering glass? Towards the normal, because it slows down.
What happens to frequency during refraction? It stays the same — it is set by the source.
What happens to the wavelength when light enters water? It decreases, because the speed decreases and frequency is fixed (v = fλ).
What is the refractive index? n = sin i / sin r, or c / v. It has no units and is always greater than 1.
What is the critical angle? The angle of incidence in the denser medium that gives an angle of refraction of 90°. sin c = 1/n.
What are the conditions for total internal reflection? Light going from denser to less dense, and an angle of incidence greater than the critical angle.
Why does a straw look bent in water? Light from the submerged part refracts as it leaves the water, so that part appears displaced.
Does light bend if it hits the surface straight on? No — along the normal there is no change in direction, though the speed still changes.
Quick revision checklist
- I know refraction is caused by a change in speed
- I measure all angles from the normal
- I know denser → bends towards the normal
- I know a ray along the normal doesn’t bend
- I know frequency is unchanged
- I know speed and wavelength change together
- I know wavelength decreases in a denser medium
- I can use n = sin i / sin r and n = c/v
- I can invert Snell’s law correctly when light exits a medium
- I know n has no units and exceeds 1
- I can calculate a critical angle with sin c = 1/n
- I can state both conditions for total internal reflection
- I draw normals dashed, rays with arrows, and clear angle differences
- I can explain everyday refraction effects
These notes cover refraction and refractive index in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Where a point was taught inconsistently in those lessons — notably what happens to wavelength in a denser medium — this page states the physics and the reasoning behind it. Always check the current syllabus and formula list for your own exam series.
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