Index of Refraction Calculator

Index of Refraction and Snell's Law

Light changes direction when it passes between two transparent media because the speed of light depends on the material. The refractive index $n$ compares that speed to vacuum. Snell's law relates the indices and the incident and refracted angles at a boundary.

Formulas

Snell's law:

$$n_1\sin(\theta_1) = n_2\sin(\theta_2)$$

Critical angle for total internal reflection (light traveling from medium 1 to medium 2, with $n_1 > n_2$):

$$\sin(\theta_c) = \frac{n_2}{n_1}$$

Angles are measured from the normal (a line perpendicular to the surface). When $\sin(\theta_2) > 1$, no refracted ray exists and the light is totally internally reflected.

Practical Notes

Common indices include about 1.0 for air, 1.33 for water, and 1.5 for crown glass. Optical fiber and prism problems often require the critical angle. For precise lab work, temperature and wavelength affect the refractive index.

Frequently Asked Questions

What is the refractive index?

It is the ratio of the speed of light in vacuum to the speed of light in the material. Higher n means slower light in that medium.

When does total internal reflection occur?

When light travels from a denser medium to a less dense one and the incident angle exceeds the critical angle.

Are angles measured from the surface or the normal?

Snell's law uses angles measured from the normal, not from the surface.

Can n₂ be less than 1?

Ordinary materials have refractive indices of 1 or greater. Values below 1 are not physical for standard transparent media.

How do I find n₂ from measured angles?

Rearrange Snell's law: $n_2 = n_1\sin(\theta_1)/\sin(\theta_2)$. Use this mode when you know both angles and the first index.

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Index of Refraction Calculator

Index of Refraction and Snell's Law

Formulas

Practical Notes

Frequently Asked Questions

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