Snell's Law and Refractive Index — Reflection & Refraction | IGCSE Physics

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 9% of your exam marks.

stable

Medium

Stable9%

Ray diagrams, Snell's Law and critical angle calculations appear regularly.

The refractive index

The (n) of a material is the ratio of the speed of light in a vacuum to the speed of light in the material:

n = (speed of light in a vacuum) / (speed of light in the medium)

A few key facts about n:
- Light always travels slower in matter than in a vacuum, so n is always greater than 1
- The higher the refractive index, the slower light moves through the material and the more the ray bends when it enters
- Refractive index is a ratio of two speeds, so it has no units
Typical values for common materials:
- air ≈ 1.00 (effectively the same as vacuum)
- water ≈ 1.33
- perspex / acrylic ≈ 1.49
- crown glass ≈ 1.50
- diamond ≈ 2.42 (one of the largest of any everyday material, which is why cut diamonds sparkle so brightly)

Snell's law

n = sin i / sin r

where:
- n = refractive index of the second medium (taking the first medium as air, where n ≈ 1)
- i = angle of incidence in air (measured from the normal)
- r = angle of refraction in the denser medium (measured from the normal)
Important details:
- sin i / sin r is not the same as i / r; never just cancel the "sin"
- When solving for r, find sin r first, then take sin⁻¹ to get the angle

Exam tip

Calculating with n = sin i / sin r

What comes up: Given a refractive index and one angle, find the other angle — or given both angles, calculate n.

Write (three marks): (1) Quote the correct formula: n = sin i / sin r (or a valid rearrangement). (2) Substitute correctly, evaluating sin of each angle before dividing. (3) Evaluate to give the final answer.

Watch out: The mark scheme explicitly rejects dividing the angles directly (n = i / r). You must take the sine of each angle first, then divide — never cancel the "sin" symbol as though it were a multiplier.

Example A — a ray of light hits a glass block (n = 1.50) at an angle of 30° to the normal. Calculate the angle of refraction inside the glass.

Rearrange Snell's law: sin r = sin i / n
sin r = sin 30° / 1.50 = 0.500 / 1.50 = 0.333
r = sin⁻¹(0.333) = 19.5°

Example B — a light ray enters a water tank from air. The angle of refraction inside the water is 22°. The refractive index of the water is 1.33. Calculate the angle of incidence.

Rearrange Snell's law: sin i = n × sin r
sin i = 1.33 × sin 22° = 1.33 × 0.3746 = 0.4982
i = sin⁻¹(0.4982) = 29.9°