Consider the representative rays shown in Fig. . A ray entering the glass through surface A and passing along the inner side of the rod will be reflected by the outer side with the smallest angle α , at which the reflected ray is tangent to the inner side. We have to consider the conditions under which the ray will undergo total internal reflection before reaching B.

Fig.

If α > θ c , the critical angle, at which total internal reflection

occurs, all the incident beam will emerge through the surface

B. Hence we require

sin α > .

The geometry gives sin α = .

Therefore ≥ ,

or = = = 2.