IGCSE Physics / Light waves
Refractive index: n = sin i / sin r
Edexcel International GCSE Physics (4PH1), chapter 12: Light waves, specification point 3.18, M1E. Free lesson.
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The refractive index compares the sine of the angle of incidence with the sine of the angle of refraction. You can use it to calculate a material's refractive index or find either angle.
What refractive index means
For light travelling from air into a material, the refractive index, n, describes how strongly the material bends the light. It compares the angles on either side of the boundary using their sines. Both angles are measured from the normal, an imaginary line at 90° to the boundary. n = (sin i)/(sin r) i is the angle of incidence in air. r is the angle of refraction inside the material. Both are measured in degrees. Refractive index is a ratio, so it has no unit. For light going from air into a material, n is more than 1. Use the sine of each angle, not the angles…
How to calculate refractive index
Write the equation first, then substitute the two angles. Divide the sine of the incidence angle by the sine of the refraction angle. Keep the sine function around each angle when you enter the calculation.
How to find an angle of refraction
If n and i are known, rearrange the equation to make sin r the subject. The value you find is the sine of the angle, not the angle itself, so use inverse sine to find r. Inverse sine turns a sine value back into an angle. On a calculator, use shift, then sin.
How to find an angle of incidence
If n and r are known, rearrange the equation to make sin i the subject. Multiply n by sin r, then use inverse sine to get i. For light entering water from air, the incidence angle should be larger than the refraction angle.