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Define and explain Numerical aperture?
Figure shown below shows an incident ray to the fibre,
The light bends at two interfaces, one at the air- core interface and the other is the core cladding interface.At the first interface, we can writen sin O0 = n1 sin O ---------(1)but minimum value of Ø is Øc where Ømax = 90 - Øc, then (1) becomes n sin Omax = n1 sin Ømax = n1 sin (90 - Øc)n sin Omax = n1 cos Øc.............(2)at the second interface, we can writen1 sin Oc = n2 sin 90sin Oc = n2/n1 ........(3)therefore cos Oc = (1- sin2 Oc)1/2 cos Oc = [1- (n1/n2)2]1/2(2) becomes n sin Omax = (n12 - n22)1/2 this is called numerical aperture (NA) of the fibre.NA = (n12 - n22)1/2
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