Numerical aperture of a step index fiber :

• Numerical aperture (N.A) of the fiber is the light collecting efficiency of the fiber and is the measure of the amount of light rays that can be accepted by the fiber. 
• It is equal to the sine of acceptance.

2      2  1/2

N.A=sinΦmax=(n1 -n2 )

where n1 and n2 are the refractive indices of core and cladding respectively.