A dielectric waveguide is shown in Figure 12.17 with refractive indices as labeled. Incident light enters the guide at angle φ from the front surface normal as shown. Once inside, the light totally reflects at the upper n1 − n2 interface, where n1 > n2. All subsequent reflections from the upper and lower boundaries will be total as well, and so the light is confined to the
guide. Express, in terms of n1 and n2, the maximum value of φ such that total confinement will occur, with n0 = 1. The quantity sin φ is known as the numerical aperture of the guide
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