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Snell’s law calculator
Waves
Relates the angles of a ray in two materials to their refractive indices.
n1 sin(θ1) = n2 sin(θ2)
This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.
Quantity to find
Working
- Write the equationn1 sin(θ1) = n2 sin(θ2)
- Rearrange to make θ2 the subjectθ2 = sin−1(n1 sin(θ1) / n2)
- Substitute the valuesθ2 = sin−1(1 × sin(40°) ÷ 1.5)
- Calculateθ2 = 25.374°
- Give the answer to 3 significant figuresθ2 = 25.4°
Worked example
Find θ2, the angle of refraction. Given: refractive index of the first material n1 = 1.00; angle of incidence θ1 = 40.0°; refractive index of the second material n2 = 1.50.
- Write the equationn1 sin(θ1) = n2 sin(θ2)
- Rearrange to make θ2 the subjectθ2 = sin−1(n1 sin(θ1) / n2)
- Substitute the valuesθ2 = sin−1(1 × sin(40°) ÷ 1.5)
- Calculateθ2 = 25.374°
- Give the answer to 3 significant figuresθ2 = 25.4°
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| n1 | Refractive index of the first material | no unit |
| θ1 | Angle of incidence | ° |
| n2 | Refractive index of the second material | no unit |
| θ2 | Angle of refraction | ° |
Snell’s law: rearranged
- To find refractive index of the first material: n1 = n2 sin(θ2) / sin(θ1)
- To find refractive index of the second material: n2 = n1 sin(θ1) / sin(θ2)
- To find angle of incidence: θ1 = sin−1(n2 sin(θ2) / n1)
- To find angle of refraction: θ2 = sin−1(n1 sin(θ1) / n2)
Exam tip
Angles are measured from the normal, not from the surface. If the sine would be greater than 1, there is total internal reflection and no refracted ray.
Common questions
What is the formula for snell’s law?
The equation is n1 sin(θ1) = n2 sin(θ2), where n1 is the refractive index of the first material; θ1 is the angle of incidence (°); n2 is the refractive index of the second material; θ2 is the angle of refraction (°).
What units should I use for snell’s law?
In SI units: refractive index of the first material in no unit (a ratio), angle of incidence in °, refractive index of the second material in no unit (a ratio), angle of refraction in °. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange n1 sin(θ1) = n2 sin(θ2)?
Rearranging gives these forms: to find refractive index of the first material: n1 = n2 sin(θ2) / sin(θ1). to find refractive index of the second material: n2 = n1 sin(θ1) / sin(θ2). to find angle of incidence: θ1 = sin⁻¹(n2 sin(θ2) / n1). to find angle of refraction: θ2 = sin⁻¹(n1 sin(θ1) / n2).
Practise snell’s law questions
Press the button for a question with random numbers. Work it out on paper first, then type your answer.
Related
Read the full explanation on the Refraction (Snell’s law) formula page. More waves equations: Wave speed, Frequency and time period, Magnification, Refractive index, Critical angle, Double-slit fringe spacing, Diffraction grating, Intensity. See the full list on the a-level physics equation calculator page.