The minimum bend radius of a fiber optic cable is determined by the critical angle of internal reflection, which can be calculated using the formula $$\theta_c = sin^{-1}(\frac{n_{cladding}}{n_{core}})$$. This angle is crucial for understanding how light behaves when it encounters a curved surface. The relationship between the critical angle and the radius of curvature involves geometric principles, specifically the concept of chords in a circle. A ray's path changes as it becomes a chord, affecting the angle of incidence and, consequently, the minimum bend radius.
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sophiecentaur said:What is it that determines whether a ray will be internally reflected or not? How could that idea be applied to a curved surface? Try some sketch diagrams of rays and curves.
It would be essentially the same for a curved surface. A curved surface is simply a combination of several flat surfaces.doggydan42 said:For internal reflection, I tried to find the critical angle, which would be:
$$\theta_c = sin^{-1}(\frac{n_{cladding}}{n_{core}})$$
However, I was confused about how this would be applied to the curved surface. Is there a specific equation for that?
Thank you.
That makes sense but how do I relate the critical angle to the radius of the surface?lekh2003 said:It would be essentially the same for a curved surface. A curved surface is simply a combination of several flat surfaces.
doggydan42 said:That makes sense but how do I relate the critical angle to the radius of the surface?