Edexcel IGCSE Physics · Spec 3.18-3.20
Refractive Index: Using the Equations
Worked examples using the refractive index equations.
Physics revision video
Refractive Index: Using the Equations
Prefer to watch on YouTube? Open this video on YouTube.
Explained
Two equations, and the calculator habits that go with them
Refractive index is sine i divided by sine r, where i is the angle of incidence and r the angle of refraction, both measured from the normal. The critical angle comes from sine c equals one divided by n.
Neither is difficult. Almost everything that goes wrong in this topic is a calculator problem or a which-angle-is-which problem rather than a physics problem.
Getting n from two angles
Light travels from air into glass at 40 degrees to the normal and refracts to 25 degrees. Then n equals sine 40 divided by sine 25, which is 0.643 divided by 0.423, giving 1.52.
Take the sine of each angle first, then divide. Dividing the angles themselves, 40 by 25, gives 1.6, which looks plausible enough to slip past unnoticed, and is wrong.
Check the answer is greater than one. Light entering a denser material bends towards the normal, so i is bigger than r, so the top of the fraction is bigger than the bottom. An answer below one means the fraction is upside down.
Finding an angle
To find r, rearrange to sine r equals sine i divided by n, work out that value, then use the inverse sine to get the angle back.
The inverse sine step is the one people forget. Stopping at 0.423 gives a number, not an angle, and a number between zero and one written as a number of degrees is an obvious error to an examiner.
The critical angle
Sine c equals one over n. For glass with n equal to 1.5, sine c is 0.667, so c is the inverse sine of 0.667, which is 42 degrees.
A larger refractive index gives a smaller critical angle, so light is trapped more easily inside a denser material. Diamond has a refractive index of about 2.4, giving a critical angle of about 24 degrees, which is why cut diamonds sparkle.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme splits the critical angle calculation into two marks, one for the substitution or rearrangement and one for the evaluation, and it lists the intermediate value as acceptable evidence for the first. So writing sine c equals one divided by 1.2 earns a mark before you have touched the inverse sine key.
It allows any correct rearrangement of sine c equals one over n, and it allows the formula written in words rather than symbols.
A mark scheme from another paper shows how an inverted calculation is treated. It gives the expected answers for each acceptable measured angle, and notes separately what happens when a candidate arrives at a refractive index below one, which is what dividing the wrong way round produces. It also asks for the evaluation to three or more significant figures.
The examiner report on that series records candidates having difficulty using the inverse sine function to obtain the final value for the critical angle, and elsewhere records frequent misuse of the formula producing refractive indices less than one.
Both of those are calculator errors with a physics consequence, and both are caught by the same check: n must be greater than one, and an angle must be an angle.
Before you start any of these
Make sure the calculator is in degrees rather than radians. A calculator in radian mode gives answers that are wrong but not obviously wrong, and it will do so consistently for every question in the paper.
Then identify which angle is which from the diagram. The angle of incidence is between the incoming ray and the normal; the angle of refraction is between the outgoing ray and the normal. Neither is measured from the surface, and that mistake alone accounts for a large share of the lost marks in this topic.
Spec 3.18-3.20
What you need to know
- Use n equals sine i over sine r
- Rearrange it to find an unknown angle
- Use sine c equals one over n to find the critical angle
Active recall
Quick check
Answer each question before opening the answer.
Give the refractive index equation using angles (Snell's law).
n = sin i ÷ sin r.
How is refractive index linked to the critical angle?
n = 1 ÷ sin c, where c is the critical angle.
Physics revision app
Take this topic further in the app
275 guided topics with questions marked as you answer them, section checkpoints and timed practice papers. Fifteen topics are free to try, with no card needed.