Question

An optical fibre communication system works on a wavelength of \( 1.3 \, \mu m \). The number of subscribers it can feed, if a channel requires 20 kHz, are:

• A. \( 2.3 \times 10^{10} \)
• B. \( 1.15 \times 10^{10} \)
• C. \( 1 \times 10^5 \)
• D. None of these

Hint:

Always convert the wavelength into frequency using \( f = \frac{c}{\lambda} \), and then divide by the required bandwidth per user to get total subscribers.

Answer 1

The Correct Option is B

We are given: - Wavelength \( \lambda = 1.3 \, \mu m = 1.3 \times 10^{-6} \, \text{m} \) - Speed of light \( c = 3 \times 10^8 \, \text{m/s} \) - Bandwidth per user/channel = \( 20 \, \text{kHz} = 2 \times 10^4 \, \text{Hz} \) First, calculate the frequency corresponding to the wavelength: \[ f = \frac{c}{\lambda} = \frac{3 \times 10^8}{1.3 \times 10^{-6}} = 2.31 \times 10^{14} \, \text{Hz} \] Now, divide the total available frequency by the required frequency per user: \[ \text{Number of subscribers} = \frac{2.31 \times 10^{14}}{2 \times 10^4} = 1.155 \times 10^{10} \] Rounding appropriately: \[ \boxed{1.15 \times 10^{10}} \]