Refractive Index Calculator

Get index from light speed in a medium with time per meter.

What it does

Light slows in glass, water, and plastics. Index names the ratio of vacuum speed to medium speed. Water near 1.33 means light runs at three quarters vacuum pace.

The tool above takes speed in m/s and returns index, km/s, and nanoseconds per meter. The default 200000000 matches the worked example, so the page opens showing 1.499. Type a new speed to update all three results.

Index n = 299792458 / v. Time per meter is 1/v in seconds, times 1e9 for nanoseconds. Here 1/200000000 is 5e-9, or 5 ns/m. Vacuum at c gives 1 and 3.34 ns/m.

Use this for Snell setups where n1 sin1 = n2 sin2. Real indices shift with wavelength, so quote color with precision work. Exotic phase speeds above c need other forms outside here.

This page shows the formula, one full hand checked example at 200 million m/s, a reference table, and practice checks that run through the tool.

How to use

1. Type light speed in the medium in m/s.
2. Keep at or below 299792458.
3. Read Index as the main result.
4. Read km/s to compare media.
5. Read ns per meter for timing.
6. Pair with Snell angles for refraction.

Formula

c

299792458 m/s vacuum.

v

Speed in medium m/s.

n

Index, 1 or more here.

Ordinary dielectrics assumed with v at or below c. Metamaterials with phase above c need other models.

Worked example

Reference table

Limits

• v at or below c here.
• Single wavelength assumed. Real n shifts with color.
• Isotropic media only. Crystals split rays.
• No absorption model here.

Common mistakes

• Entering km/s as m/s, off by 1000 times.
• Reading higher n as faster. Higher is slower.
• Using phase above c in this form.
• Mixing group with phase velocity.
• Forgetting color with precision optics.

Try it yourself

Quick checks. Answers sit tucked under each question.

Questions

Sources

• NIST
• BIPM: SI Brochure

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