Reflection and Refraction of Light26322.59Applying Snell’s law at the first surface in the figure at the right gives the angle of incidence as (11212sinsinsinsinairnnnθ)θθ−−==((1) Since the sum of the interior angles of a triangle equals 180°, observe that )()29090φθ+° −+° −233180θ=°, which reduces to θφθ=−(. Thus, equation (1) becomes )()1113sinsinsinsinn3cossin3ncosθφθ−−=−=1φθφθ−At the smallest allowed value for θ, 3θis equal to the critical angle at the second surface, or 31sinsinaircnnnθθ===. Then, 2233211sin1nnnθθcos1−=−=−=, and ()2inn112
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