Critical Angle Calculator

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.

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.