Critical Angle Calculator NZ

This calculator finds the critical angle for total internal reflection, the angle beyond which light striking a boundary cannot escape and is reflected entirely back. When light travels from a denser medium toward a less dense one, such as from glass or water into air, it bends away from the perpendicular as it crosses the boundary. As the angle of incidence increases, the refracted ray bends further until, at a particular angle called the critical angle, it would travel right along the surface. Beyond that angle no light escapes at all: it is completely reflected back into the denser medium, a phenomenon called total internal reflection. This effect is not a curiosity but the working principle behind optical fibres, which trap light and guide it for kilometres, the brilliance of cut diamonds and the function of reflecting prisms in binoculars and cameras. This tool computes the critical angle. You enter the refractive index of the denser medium the light starts in and the index of the less dense medium it meets, and the calculator returns the critical angle, with the indices shown for reference and a note on the condition. The results update as you type. Use it for optics study, for understanding fibre optics and prisms, or for any total internal reflection problem. The critical angle is the inverse sine of the ratio of the smaller index to the larger one, which follows from Snell's law at the point where the refracted ray grazes the surface. Total internal reflection only occurs going from a denser to a less dense medium, so the first index must be larger than the second; if it is not, there is no critical angle, since light can always refract out into a denser medium. A larger difference in indices gives a smaller critical angle, trapping light more easily.

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41.81°
critical angle
Dense index1.5
Less dense index1
Conditionn1 > n2 (OK)

Critical angle = inverse sine of (n2 / n1), and only exists when n1 > n2 (denser to less dense). Beyond it, light is totally internally reflected. Glass ~1.5, water ~1.33, air ~1.0.

How it works

At the critical angle, light refracting from the denser medium would travel exactly along the boundary, at ninety degrees from the perpendicular. Applying Snell's law at that point gives the critical angle as the inverse sine of the ratio of the less dense index to the denser index. Above this angle of incidence, no refraction is possible and the light is totally internally reflected.

Worked example

For light passing from glass, refractive index 1.5, toward air, index 1.0, the critical angle is the inverse sine of 1.0 divided by 1.5, which is the inverse sine of about 0.667, around 41.81 degrees. Light striking the glass-air boundary at more than 41.81 degrees from the perpendicular is totally internally reflected.

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Frequently asked questions

What is the critical angle?

It is the angle of incidence, measured from the perpendicular, beyond which light travelling from a denser to a less dense medium cannot escape and is totally internally reflected. At exactly the critical angle, the refracted ray would skim along the boundary.

What is total internal reflection?

When light strikes a boundary toward a less dense medium at more than the critical angle, none of it refracts out; it is all reflected back into the denser medium. This traps light, which is how optical fibres guide signals and why cut diamonds sparkle.

When is there no critical angle?

Only light going from a denser to a less dense medium, where the first index is larger, has a critical angle. Going the other way, into a denser medium, light can always refract out, so total internal reflection and a critical angle do not exist for that direction.