How the numerical aperture (NA) of an optical fibre is related tothe refractive index of core and relative refractive index difference(delta) between core and cladding?
Question
How the numerical aperture (NA) of an optical fibre is related tothe refractive index of core and relative refractive index difference(delta) between core and cladding?
Solution
The numerical aperture (NA) of an optical fiber is a measure of its ability to gather light and transmit it to the other end of the fiber. It is defined as the sine of the maximum angle at which the fiber can accept light that will be contained within the fiber.
The numerical aperture is related to the refractive index of the core (n1) and the relative refractive index difference (delta) between the core and the cladding (n2) by the following equation:
NA = sqrt(n1^2 - n2^2)
The relative refractive index difference (delta) is defined as:
delta = (n1 - n2) / n1
Therefore, we can express the numerical aperture in terms of the refractive index of the core and the relative refractive index difference as follows:
NA = n1 * sqrt(2*delta)
This equation shows that the numerical aperture increases with both the refractive index of the core and the relative refractive index difference. This means that a fiber with a higher core refractive index or a larger difference between the core and cladding refractive indices will have a higher numerical aperture, and thus a greater ability to gather and transmit light.
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