A Demonstration of the Critical Angle Without Using Total Internal Reflection

Abstract

The success of a light ray's transmission to a medium of lower index of refraction depends upon its incident angle at the boundary. If this angle, when measured from the normal, is greater than a certain critical angle, the ray will reflect totally, remaining in the high-index medium. Snell's law, which says that n1 sin θ1 = n2 sin θ2, easily gives the critical angle as θ1 = sin−1(n2/n1) by setting the angle of refraction to θ2 = 90°. Demonstrations of the critical angle phenomenon usually work with this operational definition. For example, as in Fig. 1, one directs a beam of light radially through the curved surface of a semicircular piece of glass and rotates the semicircle until no ray is seen exiting the flat surface. We describe here a demonstration of the critical angle that does not employ rays leaving the higher-index medium but entering it.