A dielectric waveguide is shown in Figure 12.17 with refractive indices as labeled. Incident light enters the guide at angle Ï• from the front surface normal as shown. Once inside, the light totally reflects at the upper n₁ˆ’ n₂interface, 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 n₁and n₂, the maximum value of Ï• such that total confinement will occur, with n₀= 1. The quantity sin Ï• is known as the numerical aperture of the guide.

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