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Snell’s Law — Edexcel International GCSE Science Double Award 4SD0 - Physics Revision Notes & Topical Questions

5 min read 9 parts Lesson 12 of 14

📚 Edexcel International GCSE Science Double Award 4SD0 - Physics Hub / Topical Revision
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Section 1 of 9Refractive index

The refractive index n of a material is a measure of how much it slows and bends light. It is defined as the ratio of the speed of light in a vacuum (or air) to the speed in the material:

n = c / v

What the symbols mean: n = refractive index (no unit) · c = speed of light in a vacuum (3.00 × 108 m s−1) · v = speed of light in the material (m s−1)

Since light is always slower in a material than in a vacuum, n is always greater than 1 and has no unit. Typical values: air about 1.00, water 1.33, glass about 1.5, diamond 2.4. A higher refractive index means a slower speed and more bending.

Section 2 of 9Snell's law

For light entering a material from air, the sine of the angle of incidence divided by the sine of the angle of refraction is constant for any angle:

n = sin i / sin r

What the symbols mean: n = refractive index (no unit) · i or θ1 = angle of incidence · r or θ2 = angle of refraction (both measured from the normal)
Snell's law
i = angle of incidence in air, measured from the normal
r = angle of refraction in the material, measured from the normal
n = refractive index of the material

This is known as Snell's law. It means that if n is known, r can be calculated for any i using r = sin−1(sin i / n). Remember to use a calculator in degree mode.

Section 3 of 9Using the equation

You can rearrange the formula as needed: sin i = n sin r and sin r = sin i / n.

Using the equation
When light leaves the material into air, the roles are reversed: the angle in the material is the one with n; the equation becomes n sin(angle inside) = sin(angle in air),
  • as light paths are reversible.
The ray bends away from the normal in this case.

The speed of light in the material can be found from v = c / n.

Using the equation
For glass with n = 1.5, v = 3.0 × 108 / 1.5 = 2.0 × 108 m s−1.
The wavelength in the material is also reduced by a factor of n: λmaterial = λair / n, since the frequency is unchanged.

Section 4 of 9Graphs and measurement

If you measure i and r for several rays, plotting sin i on the vertical axis against sin r on the horizontal axis gives a straight line through the origin whose gradient is the refractive index.

Graphs and measurement
Using the gradient of a best-fit line rather than a single pair of readings makes the value more reliable and reduces the effect of random errors.
A line that does not pass through the origin suggests a systematic error, for example a wrongly placed normal.

Section 5 of 9Why it matters

Refractive index decides how lenses focus light and how prisms spread colours, and explains why diamonds sparkle: the high index of 2.4 gives a small critical angle (see Total Internal Reflection), so light is trapped and reflected many times inside the stone. It also explains apparent depth: a swimming pool appears shallower than its true depth by a factor of roughly n.

Section 6 of 9Worked strategy for refraction questions

A reliable method is to follow the same steps each time.

1
First, identify which medium has the higher refractive index; the ray bends towards the normal in that medium.
2
Second, mark the angle from the normal in each medium.
3
Third, choose the formula: n = sin i / sin r when light goes from air into the material, or sin(angle in air) = n sin(angle inside) in general.
4
Fourth, calculate with the calculator in degree mode and check that the answer is sensible: the angle should be smaller in the denser medium.
5
Finally, quote the answer with the unit (degrees) and a suitable number of significant figures.

The combination of Snell's law with the idea of speed lets you answer more complex questions.

Worked strategy for refraction questions
If a ray is travelling from water (n = 1.33) into glass (n = 1.50), sin i / sin r = 1.50 / 1.33, using the ratio of the indices,
  • but at IGCSE most questions involve air,
  • which is why the simple formula is enough.
When the light moves from the material into air, you can use the critical angle (see Total Internal Reflection) to check whether the light will emerge at all.

Section 7 of 9Worked examples

  1. Light passes from air into glass of refractive index 1.50. The angle of incidence is 45°. Find the angle of refraction.

  2. Light passes from air into water at i = 60° and the angle of refraction is 40.5°. Calculate the refractive index.

  3. Find the speed of light in diamond (n = 2.4).

Section 8 of 9Key terms

TermMeaning
Refractive indexRatio of the speed of light in a vacuum to its speed in the material
Snell’s lawn = sin i / sin r
Optically denseHaving a high refractive index
SineTrigonometric ratio used in the law
GradientSlope of the sin i against sin r graph, equal to n

Section 9 of 9Exam technique

1
Dividing the angles rather than their sines.
2
Having the calculator in radian mode.
3
Taking n < 1 – refractive index is always greater than 1.
4
Using the angle from the surface instead of from the normal.
5
Forgetting that the light bends away from the normal when leaving the denser medium.

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