The V number determines the number of modes that can propagate in a fiber and is defined by the formula:

$$V = \frac{2 \pi a}{\lambda} \sqrt{n_{core}^2 - n_{clad}^2}$$

Where:

• V is the V number.
• a is the core radius of the optical fiber.
• \(\lambda\) is the wavelength of the light being used (in meters).
• \(n_{core}\) is the refractive index of the core material of the fiber.
• \(n_{clad}\) is the refractive index of the cladding material of the fiber.

The V number helps determine whether the fiber will support single-mode or multi-mode propagation. A V number less than 2.405 indicates single-mode operation, while a V number greater than 2.405 suggests multi-mode operation.