Snell's Law Calculator
Snell's law calculator (n₁sinθ₁ = n₂sinθ₂) — enter three of the two refractive indices and two angles, solve for the fourth. Detects total internal reflection. Curriculum-aligned.
Snell's Law Calculator
Enter three values and leave the fourth blank — the calculator solves for it. Angles are in degrees (°); refractive indices are dimensionless.
- Curriculum
- English (global) — Cambridge International + IB
- Built against
- Cambridge IGCSE Physics 0625 + IB Diploma (2023–2025) — Refraction
- Unit system
- SI primary; US/imperial readout below
- First published
- 2 Jun 2026
- Last updated
- 13 Sep 2026
View authoritative scientific sources
- Hecht E. Optics. 5th ed. Boston: Pearson; 2017 — refraction and total internal reflection
- Rashed R. A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses. Isis 1990;81(3):464-491 — the law as written by Ibn Sahl in 984
- refractiveindex.info — refractive-index and dispersion data per material, with the measurement paper cited: https://refractiveindex.info/
⚠️ Educational use only — see full disclaimer
EDUCATIONAL USE DISCLAIMER
This calculator is provided for educational and reference purposes only. It is not a substitute for instruction from a qualified teacher, your prescribed textbook, or your school's official curriculum materials.
When preparing for examinations, always cross-check our calculations and notation against your current syllabus and your teacher's guidance. Syllabus conventions and accepted notation vary between curricula and may change between examination years.
If you believe any calculation, notation, or curriculum reference in this tool is inaccurate, please let us know via the feedback button. We review feedback promptly and update tools when verified corrections are needed.
RECATOOLS accepts no liability for academic, examination, professional, or research outcomes arising from use of this tool.
How to Use the Snell's Law Calculator
Pick your curriculum
Use the curriculum pills above to match your syllabus (Cambridge/IB, 高考 or SBMPTN). Terminology and the whole page follow your selection.
Enter three values
Type three of the medium-1 index, angle of incidence, medium-2 index and angle of refraction — leave the one you want to find blank.
Read the result
The calculator solves for the blank quantity. Angles are in degrees; if total internal reflection occurs, the calculator tells you.
Check against your syllabus
The Tool Information block shows exactly which syllabus this is built against. Spot something off? Use the feedback button.
Snell's Law, in Your Curriculum's Words
Snell's Law (n₁ sin θ₁ = n₂ sin θ₂)
Example: Light travels from air (n₁ = 1.00) into glass (n₂ = 1.50) at an angle of incidence of 30°. Find the angle of refraction.
Given: n₁ = 1.00, θ₁ = 30°, n₂ = 1.50. Using n₁ sin θ₁ = n₂ sin θ₂:
sin θ₂ = (1.00 × sin 30°) / 1.50 = 0.333 → θ₂ ≈ 19.5°
Snell's law (the law of refraction) describes how the direction of light changes as it crosses the boundary between two media: n₁ sin θ₁ = n₂ sin θ₂. Here n is the refractive index (a dimensionless number for how much a medium slows light), and θ is the angle measured from the normal. As light enters a denser medium (larger n) it bends towards the normal; into a less dense medium it bends away from the normal.
If light passes into a less dense medium at a large enough angle, no refracted ray emerges — all the light is reflected back. This is total internal reflection, and the calculator tells you when it happens. Refractive indices and angles have no imperial equivalent, so results are shown as-is. All calculation happens in your browser — nothing is uploaded, and the tool works offline once loaded.
Snell's law explains why a straw looks bent in a glass of water, and how lenses and optical fibres steer light.
Light bends because its speed changes
Snell's law: n₁ sin θ₁ = n₂ sin θ₂.
The refractive index n is dimensionless — a ratio of light speeds.
Vacuum index = 1; water ≈ 1.33; glass ≈ 1.5.
Angles are measured from the normal, not the surface.
Into a denser medium, light bends towards the normal.
Total internal reflection occurs above the critical angle.
Optical fibres work by total internal reflection.
Named after Willebrord Snellius (1621).
n = c / v — speed of light divided by its speed in the medium.
This calculator runs in your browser — your working stays private.
Frequently Asked Questions
- n₁ sin θ₁ = n₂ sin θ₂ — the product of the refractive index and the sine of the angle is equal on both sides of the boundary. The calculator solves for whichever quantity you leave blank, whether a refractive index or an angle, and handles the arcsine cases automatically.
- The refractive index n is a dimensionless number for how much a medium slows light, defined as n = c / v, where c is the speed of light in a vacuum and v is its speed in the medium. A vacuum is 1, air is nearly 1, water is about 1.33 and glass about 1.5.
- All angles in Snell's law are measured from the normal — the line perpendicular to the surface at the point of incidence — not from the surface itself. This is the standard convention in every curriculum, so make sure your angles are measured the same way.
- When light passes from a denser into a less dense medium at an angle of incidence above the critical angle, no refracted ray emerges and all the light is reflected. The calculator detects this and tells you, instead of returning an impossible result.
- Yes. Enter three of the four quantities (the two refractive indices and the two angles) and leave the fourth blank — the calculator rearranges n₁ sin θ₁ = n₂ sin θ₂ and solves for the missing one.
- The physics — Snell's law — is identical worldwide. What changes is the terminology; "refraction" is 折射 in Chinese, while SBMPTN students see the Indonesian term. The calculated value is the same.
- The Tool Information block lists the exact syllabus for your selected curriculum (e.g. SBMPTN/SNBT Fisika). It is a study aid, not a substitute for your official syllabus or teacher.
- No. Every calculation runs in your browser; nothing you type is uploaded. It works offline once the page has loaded.
- The index depends on wavelength, so always say which one. At the sodium D line (589 nm) and 20 °C, water is about 1.333, BK7 crown glass about 1.517 and diamond about 2.42; air is about 1.0003 and is taken as 1. For exam questions use the values the question gives (usually 1.33 and 1.5); for optical design read the value at your wavelength from a dispersion table such as refractiveindex.info.
Method & sources
How it computes
Snell's law of refraction, n₁ sin θ₁ = n₂ sin θ₂, rearranged for whichever one of the four quantities you leave blank: angles are measured from the normal and entered in degrees, refractive indices are dimensionless. Where the rearrangement would require the arcsine of a value above 1 the calculator reports total internal reflection instead of a number, and results are rounded to the significant figures of the least precise input.
What this tool implements
- Angle and sign convention as set out in Hecht's Optics, 5th edition: every angle is measured from the normal to the surface at the point of incidence, never from the surface itself, and light entering a medium of higher index bends towards the normal.
- Total internal reflection is detected rather than approximated or silently clamped: when n₁ sin θ₁ / n₂ exceeds 1 there is no refracted ray, and refusing to print an angle is the physically correct answer, not an error state. The critical angle follows as arcsin(n₂/n₁) — for water to air, 48.6°.
- No material index table is built in; both indices are user inputs, because the index depends on wavelength. The page gives sodium D line (589 nm) values at 20 °C as reference points — water about 1.333, BK7 crown glass about 1.517, diamond about 2.42, air about 1.0003 and taken as 1 — and directs anyone doing optical design to a dispersion database rather than to a single number.
- The three curriculum profiles (Cambridge IGCSE Physics 0625 with IB Diploma, 高考物理 光的折射, and SBMPTN/SNBT Fisika) change terminology, worked examples and page language only. The arithmetic is identical across all three, which the page states explicitly so a student does not suspect the answer is syllabus-dependent.
Sources
- Hecht E. Optics. 5th ed. Boston: Pearson; 2017 — refraction, the angle-from-normal convention, the critical angle and total internal reflection.
- Rashed R. A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses. Isis 1990;81(3):464-491 — the law as written by Ibn Sahl in 984, six centuries before Snellius.
- Mikhail Polyanskiy, refractiveindex.info — refractive index and dispersion data by material and wavelength, each entry carrying the measurement paper it is taken from. https://refractiveindex.info/
What can make this go out of date
- None at runtime. Snell's law is a physical relation and does not change on a schedule, and the calculator hardcodes no material indices — the two indices are supplied by the user on every calculation.
- The one thing that can go out of date is the curriculum alignment: the Cambridge IGCSE 0625 and IB (2023–2025) syllabus references, 高考物理 (2017 revision) and the SBMPTN/SNBT framework are administrative and are revised on their own cycles.
Pick up where you left off
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