Halliday, Resnick & Walker — Electromagnetic Waves: Problem 39

39 Figure 33-45 depicts a simplistic optical fiber: a plastic core (\(n_1 = 1.58\)) is surrounded by a plastic sheath (\(n_2 = 1.46\)). A light ray is incident on one end of the fiber at angle \(\theta\). The ray is to undergo total internal reflection at point A, where it encounters the core–sheath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of \(\theta\) that allows total internal reflection at A?