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https://texercises.com/exercise/geometrische-optik-reflexion-und-brechung-12/
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The following quantities appear in the problem: Winkel \(\theta\) / Brechzahl \(n\) /
The following formulas must be used to solve the exercise: \(n_1 \sin\alpha_1 = n_2 \sin\alpha_2 \quad \)
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Exercise:
Der Einfallswinkel betrage .sidegree der Brechungswinkel in Wasser .sidegree. a Wie gross ist der Brechungsindex des Einfallsmediums? b Berechnen Sie den Grenzwinkel der Totalreflexion.

Solution:
% . April Lie. * &texta n_sinalpha_ n_sinalpha_ Rightarrow n_ n_fracsinalpha_sinalpha_ .fracsin.sidegreesin.sidegree uuline. &textb n_sinalpha_G n_sinsidegree Rightarrow alpha_G fracn_n_ fracsinalpha_sinalpha_ Rightarrow &qquad alpha_G arcsinleft fracsinalpha_sinalpha_ right arcsinleft fracsin.sidegreesin.sidegree right uuline.sidegree * newpage
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Exercise:
Der Einfallswinkel betrage .sidegree der Brechungswinkel in Wasser .sidegree. a Wie gross ist der Brechungsindex des Einfallsmediums? b Berechnen Sie den Grenzwinkel der Totalreflexion.

Solution:
% . April Lie. * &texta n_sinalpha_ n_sinalpha_ Rightarrow n_ n_fracsinalpha_sinalpha_ .fracsin.sidegreesin.sidegree uuline. &textb n_sinalpha_G n_sinsidegree Rightarrow alpha_G fracn_n_ fracsinalpha_sinalpha_ Rightarrow &qquad alpha_G arcsinleft fracsinalpha_sinalpha_ right arcsinleft fracsin.sidegreesin.sidegree right uuline.sidegree * newpage
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