109. A light ray traveling directly along the central axis reaches the end in time tLvnLcdirect==11. For the ray taking the critical zig-zag path, only its velocity component along the core axis direction contributes to reaching the other end of the fiber. That component is v1cos θ ', so the time of travel for this ray is ()1zig zag211cos1sin/Ltvcnθ′−using results from the previous solution. Plugging in sin=−nn1222and simplifying,
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