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Home » Find the maximum possible value of $r$ along this path. - 500apps

Find the maximum possible value of $r$ along this path. - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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n_1 \sin heta = n_2 \sin \phi
For a fiber with refractive index \(n\) and assuming the inside of the...
\sin heta = n \sin \phi
Solving for \(\sin \phi\):
\sin \phi = rac{\sin heta}{n}
We seek \(\cos \phi\). Using the identity \(\cos^2 \phi = 1 - \sin^2 \...
\cos^2 \phi = 1 - \left(rac{\sin heta}{n}
ight)^2 = 1 - rac{\sin^2 heta}{n^2}
\cos \phi = \sqrt{1 - rac{\sin^2 heta}{n^2}}
Thus, the expression for \(\cos \phi\) is:

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