If you need relative refractive index (nᵣ) and index of refraction and you already have speed of light in vacuum, speed in medium 1 (v₁), speed in medium 2 (v₂) and speed in medium (v), this calculator does the substitution for you. It suits a quick check, a homework answer you want to confirm, or any figure you need to sanity test.
What Is the Index of Refraction Calculator?
This index of refraction calculator is for the kind of problem where you know the physical quantities but not the number you need. It turns speed of light in vacuum, speed in medium 1 (v₁), speed in medium 2 (v₂) and speed in medium (v) into relative refractive index (nᵣ) and index of refraction.
Physics calculations go wrong in predictable ways, usually through mixing units or dropping a digit. Work through the result one step at a time and check that the figures are the size you would expect at each stage.
How the Index of Refraction Physics Works
The relationship is applied step by step, and each step is a standard piece of physics rather than a single opaque formula. That means you can check the intermediate values against what the theory predicts, which is usually faster than checking only the final answer.
Keep every value in the same unit system throughout the calculation. Mixing metres and feet part way through is the single most common reason a correct formula gives a wrong answer.
Units, Assumptions and the Limits of the Model
The calculation assumes ideal conditions: no air resistance, no heat loss, and dimensions that do not change while you work. Those assumptions are reasonable for most classroom and engineering estimates, and unreasonable for anything more precise.
Where a value is a rate, it has to be quoted for the same period as everything else. A per-hour figure cannot be combined with a per-day figure without converting one of them first.
A Worked Example
Working through an example, with speed of light in vacuum set to 10, speed in medium 1 (v₁) set to 5, speed in medium 2 (v₂) set to 2, the calculator returns index of refraction of 0.1, and relative refractive index (nᵣ) of 2.5. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out relative refractive index (nᵣ)?
Enter speed of light in vacuum, speed in medium 1 (v₁), speed in medium 2 (v₂) and speed in medium (v). The calculator then works through the relationship and reports relative refractive index (nᵣ) and index of refraction.
What does the index of refraction actually calculate?
It takes speed of light in vacuum, speed in medium 1 (v₁), speed in medium 2 (v₂) and speed in medium (v) and converts them into relative refractive index (nᵣ) and index of refraction using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter speed of light in vacuum?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.