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.


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.


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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