GCSE & IGCSE physics practice

Snell's law and refractive index questions and answers

When light passes into a denser material it slows down and bends towards the normal. The refractive index is $n = \dfrac{\sin i}{\sin r}$ , with $i$ the angle in air and $r$ the angle in the material. It's also the ratio of speeds, and links to the critical angle: $n = \dfrac{1}{\sin c}$ . Set your calculator to degrees.

8 questions · Higher tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

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Where snell's law and refractive index comes up

Cambridge IGCSE (0625)	Supplement (Extended): define refractive index and recall and use n = sin i ÷ sin r and n = 1 ÷ sin c; total internal reflection. Core: describe refraction.
GCSE (AQA)	AQA GCSE Physics covers refraction with ray and wave diagrams, but not the refractive index equation.

The method

n = sin i ÷ sin r (i in air, r in the material).
To find r: sin r = sin i ÷ n, then use sin⁻¹.
Critical angle: sin c = 1 ÷ n.
n = speed of light in air ÷ speed in the material.
Total internal reflection happens when the angle inside the denser material is bigger than the critical angle.

Snell's law and refractive index questions

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Warm-up

Question 1Warm-upHigher

Light enters glass at an angle of incidence of 40° and refracts at 25°. Calculate the refractive index to 3 significant figures.

Exam-style

Question 2Exam-styleHigher

Light enters a block with refractive index 1.5 at an angle of incidence of 30°. Calculate the angle of refraction to 1 decimal place.

Question 3Exam-styleHigher

Light leaves water (refractive index 1.33) into air. In the water the angle is 22°. What is the angle in air, to 1 decimal place?

Question 4Exam-styleHigher

Glass has a refractive index of 1.5. Calculate its critical angle to 1 decimal place.

Question 5Exam-styleHigher

Diamond has a critical angle of 24.4°. Calculate its refractive index to 3 significant figures.

Question 6Exam-styleHigher

Light travels at $3.0 \times 10^8$ m/s in air and $2.0 \times 10^8$ m/s in a plastic. What is the plastic's refractive index?

Challenge

Question 7ChallengeHigher

Water has a refractive index of 1.33. Calculate the speed of light in water, given that it travels at $3.0 \times 10^8$ m/s in air. Give your answer to 3 significant figures.

m/s

Question 8ChallengeHigher

A ray inside glass ( $n = 1.5$ , critical angle 41.8°) hits the glass–air surface at 45°. What happens?

Common mistakes

Calculator in radians instead of degrees.
Dividing the angles instead of their sines.
Swapping i and r.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 27 October 2026:

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