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PX284 - T3c - spherical surface using trigonometric properties

PX284 - T3c - spherical surface.png|500

i=α+γt=γ−β n1sin⁡(α+γ)=n2sin⁡(γ−β) n1(α+γ)≃n2(γ−β) \begin{gather} \tan \alpha \simeq \alpha \simeq \frac{y}{u+x} \simeq \frac{y}{u} \\ \tan \gamma \simeq \gamma \simeq \frac{y}{R-x} \simeq \frac{y}{R}\\ \tan \beta \simeq \beta \simeq \frac{y}{v-x} \simeq \frac{y}{v} \1\n\2\n