Question

A step index fibre 6.35 x 10-5 m in diameter
has a core of refractive index 1.52 and a
cladding of refractive index 1.47. Determine
the numerical aperture for the fibre and the
acceptance angle.

Answer 1

Answer on Question #77792, Physics / Optics

A step index fibre $6.35 \times 10^{-5} \, \text{m}$ in diameter has a core of refractive index 1.52 and a cladding of refractive index 1.47. Determine the numerical aperture for the fibre and the acceptance angle.

Solution:

The Numerical Aperture (NA) is a measure of how much light can be collected by an optical system such as an optical fibre or a microscope lens.

The NA of any glass combination may be calculated as follows:

$$NA = \sqrt{n_1^2 - n_2^2}$$

where $n_1$ = the index of refraction of the core glass, and $n_2$ = the index of refraction of the cladding glass.

I$\mu$,

$$NA = \sqrt{1.52^2 - 1.47^2} = 0.387$$

The NA is related to the acceptance angle $\alpha$, which indicates the size of a cone of light that can be accepted by the fibre.

$$NA = n_0 \sin \alpha$$

where $n_0$ is refractive index of medium outside the fiber. For air $n_0 = 1.0003$.

Thus,

$$\alpha = \sin^{-1} \left(\frac{NA}{n_0}\right) = \sin^{-1} \left(\frac{0.387}{1.0003}\right) = 22.74{}^\circ$$

Answer: $NA = 0.387$; $\alpha = 22.7{}^\circ$

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