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First
My college book contains the following passage:

the angle of incidence (relative to the fibre axis ) can't be too large else the ray would be refracting on the core\cladding boundary and transmitted outside the fiber and a very small percentage passes.

Here's how I reasoned and I'd like to be corrected. The geometry I imagined was as follows:

  • light falls with a very large angle $\alpha$ from air,
  • light is refracted with angle $\theta$, $\theta$ < $\alpha$,
  • light falls on cladding with large angle $\beta$ where: $ \alpha > \beta $ and $\beta > \theta c$ of the material of the cladding,
  • light is simply totally internally reflected.

Second

I looked it up and found numerical aperture and acceptance angle articles but I'd like to be cleared out on the first matter first.

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Your reasoning is correct for the most part - except the third bullet: α>β is not always valid.

Consider the following for example: α = 50 deg & refractive index of core = 1.5. By Snell's law, θ = 31 and this leads to a β of 59 (90-31). So α(50) < β (59).

Typically, as α increases, θ will also increase, thereby bringing down β leading to "light leaking out through the cladding". Hope it helps.

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  • $\begingroup$ i checked and youre right , it did help i will rewrite the question with a correction later $\endgroup$ – sarah May 24 '17 at 12:47

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