V- number or cut off frequency or normalized frequency in optical fibers is equal to
V = Пd(Numerical Aperture)/λ
Where d is the diameter of the core and λ is the wavelength of light passing through the core of the fiber.
As NA = √n12 – n22 or
NA = Sin θ or
NA = n1√2 Δ
Therefore, V number relation can be changed after putting the above relations in basic relation of V according to the need.
Significance of V number:
If V is less than 2.405 then the fiber is mono mode but if V is greater than 2.405 then fiber is multimode.
V number is also related with the number of modes is the fiber as:
N = V2/ 2 for step index fiber and
Number of modes for graded index fiber is N = V2/ 4.