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Home » This One Diamond Level Changed How I Mine—Are You Ready to Learn? - Carbonext

This One Diamond Level Changed How I Mine—Are You Ready to Learn? - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A science communicator is creating a video about the geometry of light paths in optical fibers. They describe a scenario where a light ray enters a fiber at an angle \( heta\) relative to the normal. If the refractive index of the fiber is \(n\), find the angle \(\phi\) of the light ray relative to the fiber's axis after refraction, using Snell's Law, and express \(\cos \phi\) in terms of \( heta\) and \(n\).

📌 Snell's Law relates the angle of incidence \( heta\) and the angle of refraction \(\phi\) as:

📌 n_1 \sin heta = n_2 \sin \phi

📌 For a fiber with refractive index \(n\) and assuming the inside of the fiber is air (refractive index 1), we have:

📌 \sin heta = n \sin \phi

📌 Solving for \(\sin \phi\):

📌 \sin \phi = rac{\sin heta}{n}

📌 We seek \(\cos \phi\). Using the identity \(\cos^2 \phi = 1 - \sin^2 \phi\):

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