IGCSE 0625 / Section 3.2 / Extended
Supplement (Extended) content

Counting the slowdown.

How much a material bends light can be captured in a single number. A refractive index of 1.5 means light slows to two-thirds of its vacuum speed inside the glass, and that one number also fixes the critical angle.

The key idea

The refractive index n equals sin(i) divided by sin(r), where i is the angle in air and r the angle in the medium. It also equals the speed of light in vacuum divided by its speed in the medium, and it links to the critical angle by n = 1 / sin(c). A larger n bends light more.

Definition · learn the exact words

The refractive index n is given by n = sin(i) ÷ sin(r); it is also linked to the critical angle by n = 1 ÷ sin(c).

n = sin i ÷ sin r  and  n = 1 ÷ sin c

n also equals the speed of light in a vacuum divided by its speed in the material.

Section 01

Measure the bending.

Change the angle of incidence and read off the angle of refraction to see the refractive index that links them.

Stage 1 · Learn

Check refractive index

Four quick checks. Each correct answer earns XP and lights this skill on your star map.

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The refractive index is given by...

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A material with a higher refractive index bends light...

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The critical angle c and refractive index n are related by...

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Refractive index also equals...

Section 02

One number, three meanings.

The refractive index can be found from angles, from the critical angle, or from speeds.

n = sin i ÷ sin r  ·  n = 1 ÷ sin c
Worked example

Light enters glass with an angle of incidence of 45 degrees and refracts to 28 degrees. Find the refractive index, then the critical angle.

Step 1 · Refractive indexn = sin 45 ÷ sin 28 = 0.707 ÷ 0.469
Step 2 · Evaluaten ≈ 1.5
Step 3 · Critical anglesin c = 1 ÷ 1.5 = 0.667, so c ≈ 42 degrees
Examiner trap

In n = sin i / sin r, i is the angle in air (the less dense medium) and r the angle in the glass. For the critical-angle relation n = 1 / sin c, the critical angle c is measured inside the denser medium. Mixing up which angle is which is the usual error.

Stage 2 · Exam

Exam-style questions

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Light enters glass with an angle of incidence of 45 degrees and refracts to 28 degrees. The refractive index is about...

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A glass has a refractive index of 1.5. Its critical angle is about...

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Compared with a material of refractive index 1.3, a material of refractive index 1.6 will...

Skill unlocked

Refractive index, mastered.

Refractive index mastered. Optical fibres put it to work next.

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Go deeper · practice
Six original Cambridge-style questions
The relations n = sin i / sin r and n = 1 / sin c, the link to the speed of light, and simple calculations. Attempt each, then reveal the worked solution.
Stage 3 · master the unit
Waves challenge
Mixed questions across the whole unit, each one worth XP. Start this only when you feel confident across every topic in the unit, not just refractive index.
Start the unit challenge →