CBSE BOARD XII, asked by googoogaagaa, 1 month ago

Calculate the V-number and number of modes supported by the fiber for an optical fiber of core diameter 40 µm. The refractive indices of the core and cladding are 1.55 and 1.50, respectively. The wavelength of propagating wave is 1400 nm

Answers

Answered by anjalitripathi4125

Answer:

The V-number is approximately 2.244, and the number of modes supported by the fiber is approximately 10.056.

Explanation:

To calculate the V-number (V) and the number of modes supported by the fiber, we can use the formula:

V = (2π/λ) * a * Δ

Where:

V = V-number

π = Pi (approximately 3.14159)

λ = Wavelength of propagating wave

a = Core radius (half of the core diameter)

Δ = Relative refractive index difference

First, let's calculate the core radius (a):

Core diameter = 40 µm

Core radius (a) = 40 µm / 2 = 20 µm

Next, let's calculate the relative refractive index difference (Δ):

Relative refractive index difference (Δ) = (n₁ - n₂) / n₁

n₁ = Refractive index of the core = 1.55

n₂ = Refractive index of the cladding = 1.50

Δ = $\frac{1.55 - 1.50}{1.55} = 0.0323$

Now, let's calculate the V-number (V):

Wavelength (λ) = 1400 nm = 1.4 µm

V = (2π/λ) * a * Δ

$V = (\frac{2 * 3.14159}{1.4} ) * 20 * 0.0323$

V ≈ 2.244

To calculate the number of modes supported by the fiber, we use the approximation formula:

Number of modes (M) ≈ 2 * V²

M ≈ 2 * (2.244)²

M ≈ 10.056

Therefore, the V-number is approximately 2.244, and the number of modes supported by the fiber is approximately 10.056.